2024-03-28T10:36:46Z
http://sdvcmr-prod-oai01:8080/oai/
oai:qucosa:de:qucosa:17308
2021-03-29T09:29:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Objektorientierte Implementation eines PPCG-Verfahrens
Thomas
Ermer
Lothar
Grabowsky
004
004
C++
Finite-Elemente-Methode
Objektorientierte Programmierung
Parallelisierung
Koppelrandkommunikation
Ein üblicher Ansatz bei der Parallelisierung von
FEM-Verfahren ist die Gebietszerlegung. Typisch hierbei
ist, dass die beteiligten Prozessoren weitgehend
lokal arbeiten können und nur an wenigen Punkten
eine so genannte Koppelrandkommunikation erforderlich
ist.
Während sich ein solcher Algorithmus recht einfach
formal angeben lässt, bedingen die von prozeduralen
Sprachen bereitgestellten Mittel eine Anpassung der
Programmstruktur an konkrete Kommunikationsbibliotheken
und Hardware-Systeme.
Abhilfe bringen hier objektorientierte Methoden.
Anhand eines parallelen konjugierten Gradientenverfahrens
wird die Verwendung von C++ als Implementationssprache
demonstriert.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-12
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501096
Preprintreihe des Chemnitzer SFB 393, 98-13
ger
Preprintreihe des Chemnitzer SFB 393, 98-13
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17308/zip/
urn:nbn:de:swb:ch1-200501096
oai:qucosa:de:qucosa:17419
2021-03-29T09:31:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Efficient time step parallelization of full multigrid techniques
J.
Weickert
T.
Steidten
510
510
MSC 65N55
This paper deals with parallelization methods for time-dependent
problems where the time steps are shared out among the
processors. A Full Multigrid technique serves as solution
algorithm, hence information of the preceding time step and of
the coarser grid is necessary to compute the solution at each new
grid level. Applying the usual extrapolation formula to process
this information, the parallelization will not be very efficient.
We developed another extrapolation technique which causes a much
higher parallelization effect. Test examples show that no
essential loss of exactness appears, such that the method
presented here shall be well-applicable.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800466
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17419/zip/
urn:nbn:de:bsz:ch1-199800466
oai:qucosa:de:qucosa:17420
2021-03-29T09:31:23Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Lokale Realisierung von Vektoroperationen auf Parallelrechnern
U.
Groh
510
510
parallel computers
vector operation
local implementation
distributed memory
MSC 65Y05
For the basic algebraic vector operations several variants of a local
implementation on distributed memory parallel computers are presented and discussed
systematically. In particular necessary and sufficient conditions are shown for the local realizability
of the multiplication matrix by vector.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800478
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17420/zip/
urn:nbn:de:bsz:ch1-199800478
oai:qucosa:de:qucosa:17418
2021-03-29T09:31:21Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A parallel version of the preconditioned conjugate gradient method for boundary element equations
M.
Pester
S.
Rjasanow
510
510
conjugate gradient algorithm
fast Fourier transform
preconditioning
numerical experiments
Galerkin boundary element method
Laplace equation
parallelization
MSC 65N38
MSC 65F10
MSC 65Y05
MSC 65F35
MSC 35J05
The parallel version of precondition techniques is developed for
matrices arising from the Galerkin boundary element method for
two-dimensional domains with Dirichlet boundary conditions.
Results were obtained for implementations on a transputer network
as well as on an nCUBE-2 parallel computer showing that iterative
solution methods are very well suited for a MIMD computer. A
comparison of numerical results for iterative and direct solution
methods is presented and underlines the superiority of iterative
methods for large systems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800455
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17418/zip/
urn:nbn:de:bsz:ch1-199800455
oai:qucosa:de:qucosa:17421
2021-03-29T09:31:24Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Bibliotheken zur Entwicklung paralleler Algorithmen
G.
Haase
T.
Hommel
A.
Meyer
M.
Pester
004
004
MSC 65Y05
The purpose of this paper is to supply a summary of library
subroutines and functions for parallel MIMD computers. The
subroutines have been developed at the University of Chemnitz
during a period of the last five years. In detail, they are
concerned with vector operations, inter-processor communication
and simple graphic output to workstations. One of the most
valuable features is the machine-independence of the
communication subroutines proposed in this paper for a hypercube
topology of the parallel processors (excepting a kernel of only
two primitive system-dependend operations). They were
implemented and tested for different hardware and operating
systems including transputer, nCube, KSR, PVM. The vector
subroutines are optimized by the use of C language and enrolled
loops (BLAS1-like). The paper includes hints for using the
libraries with both Fortran and C programs.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800486
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17421/zip/
urn:nbn:de:bsz:ch1-199800486
oai:qucosa:de:qucosa:17423
2021-03-29T09:31:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Tauextrapolation - theoretische Grundlagen, numerische Experimente und Anwendungen auf die Navier-Stokes-Gleichungen
K.
Bernert
510
510
linear problems
nonlinear problems
improved convergence
one-dimensional test
MSC 76M20
MSC 65N55
MSC 76D05
The paper deals with tau-extrapolation - a modification of the
multigrid method, which leads to solutions with an improved con-
vergence order. The number of numerical operations depends
linearly on the problem size and is not much higher than for a
multigrid method without this modification. The paper starts
with a short mathematical foundation of the tau-extrapolation.
Then follows a careful tuning of some multigrid components
necessary for a successful application of tau-extrapolation. The
next part of the paper presents numerical illustrations to the
theoretical investigations for one- dimensional test problems.
Finally some experience with the use of tau-extrapolation for the
Navier-Stokes equations is given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800506
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17423/zip/
urn:nbn:de:bsz:ch1-199800506
oai:qucosa:de:qucosa:17422
2021-03-29T09:31:24Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On an automatically parallel generation technique for tetrahedral meshes
G.
Globisch
510
510
Mesh generation
Parallel preprocessing
Finite elements
Domain decomposition
MSC 65Y05
In order to prepare modern finite element analysis a program for
the efficient parallel generation of tetrahedral meshes in a wide
class of three dimensional domains having a generalized cylindric
shape is presented. The applied mesh generation strategy is based
on the decomposition of some 2D-reference domain into single con-
nected subdomains by means of its triangulations the tetrahedral
layers are built up in parallel. Adaptive grid controlling as
well as nodal renumbering algorithms are involved. In the paper
several examples are incorporated to demonstrate both program's
capabilities and the handling with.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800499
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17422/zip/
urn:nbn:de:bsz:ch1-199800499
oai:qucosa:de:qucosa:17424
2021-03-29T09:31:26Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Implicit extrapolation methods for multilevel finite element computations
M.
Jung
U.
Rüde
510
510
Extrapolation
Finite Elements
Multigrid
Elasticity
MSC 65F10
MSC 65F50
MSC 65N22
MSC 65N50
MSC 65N55
Extrapolation methods for the solution of partial differential equations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as \034 -extrapolation. For finite element systems this algorithm can be shown to be equivalent to higher order finite elements. The analysis is local and does not use global expansions, so that the implicit extrapolation technique may be used on unstructured meshes and in cases where the solution fails to be globally smooth. Furthermore, the natural multilevel structure can be used to construct efficient multigrid and multilevel preconditioning techniques. The effectivity of the method is demonstrated for heat conduction problems and problems from elasticity theory.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800516
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17424/zip/
urn:nbn:de:bsz:ch1-199800516
oai:qucosa:de:qucosa:17428
2021-03-29T09:31:29Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A parallel preconditioned iterative realization of the panel method in 3D
M.
Pester
S.
Rjasanow
510
510
preconditioning
parallel computation
panel boundary element,method
iterative methods
MIMD computer.
MSC 65N38
MSC 65F10
MSC 35J25
MSC 65F35
MSC 65Y05
The parallel version of precondition iterative techniques is
developed for matrices arising from the panel boundary element
method for three-dimensional simple connected domains with
Dirichlet boundary conditions. Results were obtained on an
nCUBE-2 parallel computer showing that iterative solution methods
are very well suited also in three-dimensional case for
implementation on a MIMD computer and that they are much more
efficient than usual direct solution techniques.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800562
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17428/zip/
urn:nbn:de:bsz:ch1-199800562
oai:qucosa:de:qucosa:17425
2021-03-29T09:31:27Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Verarbeitung von Sparse-Matrizen in Kompaktspeicherform KLZ/KZU
A.
Meyer
M.
Pester
510
510
sparse matrices
numerical methods
software
MSC 65F50
MSC 65Y05
The paper describes a storage scheme for sparse symmetric or
nonsymmetric matrices which has been developed and used for many
years at the Technical University of Chemnitz. An overview of
existing library subroutines using such matrices is included.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800520
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17425/zip/
urn:nbn:de:bsz:ch1-199800520
oai:qucosa:de:qucosa:17429
2021-03-29T09:31:30Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Preconditioning the Pseudo-Laplacian for finite element simulation of incompressible flow
A.
Meyer
510
510
Finite numerical methods
PDE
BVP
pseudo-laplacian
MSC 65N30
In this paper, we investigate the question of the spectrally equivalence of the so-
called Pseudo-Laplacian to the usual discrete Laplacian in order to use hierarchical
preconditioners for this more complicate matrix. The spectral equivalence is shown to
be equivalent to a Brezzi-type inequality, which is fulfilled for the finite element spaces
considered here.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800574
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17429/zip/
urn:nbn:de:bsz:ch1-199800574
oai:qucosa:de:qucosa:17426
2021-03-29T09:31:28Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Realization and comparison of various mesh refinement strategies near edges
T.
Apel
F.
Milde
510
510
singularities near edges
Fichera corner
finite element methods
convergence
a priori mesh grading algorithms
adaptive mesh,refinement
Poisson's equation
MSC 65N50
MSC 65N30
MSC 35J05
This paper is concerned with mesh refinement techniques for
treating elliptic boundary value problems in domains with re-
entrant edges and corners, and focuses on numerical experiments.
After a section about the model problem and discretization
strategies, their realization in the experimental code FEMPS3D is
described. For two representative examples the numerically
determined error norms are recorded, and various mesh refinement
strategies are compared.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800531
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17426/zip/
urn:nbn:de:bsz:ch1-199800531
oai:qucosa:de:qucosa:17427
2021-03-29T09:31:29Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshes
T.
Apel
S.
Nicaise
510
510
anisotropic weighted Sobolev spaces
local interpolation error,estimates
MSC 35A40
MSC 35J05
MSC 65N30
MSC 35B65
This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800553
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17427/zip/
urn:nbn:de:bsz:ch1-199800553
oai:qucosa:de:qucosa:17430
2021-03-29T09:31:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Bibliotheken zur Entwicklung paralleler Algorithmen - Basisroutinen für Kommunikation und Grafik
Matthias
Pester
510
510
Parallelverarbeitung / Programmierung
Visualisierung
Wissenschaftlich-technische Software
message passing
numerical algorithms
The purpose of this paper is to supply a summary of
library subroutines and functions for parallel MIMD
computers. The subroutines have been developed and
continously extended at the University of Chemnitz
since the end of the eighties. In detail, they are
concerned with vector operations, inter-processor
communication and simple graphic output to
workstations. One of the most valuable features is
the machine-independence of the communication
subroutines proposed in this paper for a hypercube
topology of the parallel processors (excepting a
kernel of only two primitive system-dependend
operations). They were implemented and tested for
different hardware and operating systems including
PARIX for transputers and PowerPC, nCube, PVM, MPI.
The vector subroutines are optimized by the use
of C language and unrolled loops (BLAS1-like).
Hardware-optimized BLAS1 routines may be
integrated. The paper includes hints for
programmers how to use the libraries with both
Fortran and C programs.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-04
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600429
Preprintreihe des Chemnitzer SFB 393, 02-01; Überarbeitung eines früheren Preprints SPC 95_20
ger
Preprintreihe des Chemnitzer SFB 393, 02-01; Überarbeitung eines früheren Preprints SPC 95_20
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17430/zip/
urn:nbn:de:swb:ch1-200600429
oai:qucosa:de:qucosa:17432
2021-03-29T09:31:32Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Stabilization of large linear systems
C.
He
V.
Mehrmann
510
510
Riccati equation
stabilization
linear
multi-input
control system
MSC 65F05
We discuss numerical methods for the
stabilization of large linear multi-input
control systems of the form x=Ax + Bu via a
feedback of the form u=Fx. The method
discussed in this paper is a stabilization
algorithm that is based on subspace splitting.
This splitting is done via the matrix
sign-function method. Then a projection into
the unstable subspace is performed followed by
a stabilization technique via the solution of
an appropriate algebraic Riccati equation.
There are several possibilities to deal with the
freedom in the choice of the feedback as well
as in the cost functional used in the Riccati
equation. We discuss several optimality criteria
and show that in special cases the feedback
matrix F of minimal spectral norm is obtained
via the Riccati equation with the zero constant term.
A theoretical analysis about the distance to
instability of the closed loop system is given
and furthermore numerical examples are presented
that support the practical experience with
this method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800595
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17432/zip/
urn:nbn:de:bsz:ch1-199800595
oai:qucosa:de:qucosa:17431
2021-03-29T09:31:32Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A step towards a unified treatment of continuous and discrete time control problems
V.
Mehrmann
510
510
generalized Cayley transformation
generalized algebraic Riccati
equations
discrete algebraic Riccati equations
MSC 93B17
MSC 93C60
MSC 93C55
MSC 49N10
In this paper introduce new approach for
unified theory for continuous and discrete time
(optimal) control problems based on the
generalized Cayley transformation. We also relate
the associated discrete and continuous generalized
algebraic Riccati equations. We demonstrate the
potential of this new approach proving new
result for discrete algebraic Riccati equations.
But we also discuss where this new approach as
well as all other approaches still is
non-satisfactory. We explain a discrepancy
observed between the discrete and continuous
cse and show that this discrepancy is partly due
to the consideration of the wrong analogues. We
also present an idea for a metatheorem that
relates general theorems for discrete and
continuous control problems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800581
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17431/zip/
urn:nbn:de:bsz:ch1-199800581
oai:qucosa:de:qucosa:17433
2021-03-29T09:31:33Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Grafik-Ausgabe vom Parallelrechner für 2D-Gebiete
M.
Pester
510
510
MSC 65Y05
MSC 68Q22
The paper mainly describes the user interface of some graphical
visualization tools for parallel finite element applications in
2D (layer problems, deformation problems, fluid dynamics). There
are presented some examples of various methods to display the
numerical results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800602
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17433/zip/
urn:nbn:de:bsz:ch1-199800602
oai:qucosa:de:qucosa:17437
2021-03-29T09:31:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh refinement in stabilized Galerkin methods
Thomas
Apel
Gert
Lube
510
510
elliptic boundary value problems
Galerkin finite element methods
anisotropic mesh refinement
MSC 65N30
MSC 65N50
MSC 35J25
The numerical solution of the convection-diffusion-reaction problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least squares type accomodates diffusion-dominated as well as convection- and/or reaction- dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is accomplished using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800640
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17437/zip/
urn:nbn:de:bsz:ch1-199800640
oai:qucosa:de:qucosa:17434
2021-03-29T09:31:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Matrix Sign Function Method and the Computation of Invariant Subspaces
R.
Byers
C.
He
V.
Mehrmann
510
510
matrix sign function
invariant subspaces
stability
Newton
iteration
numerical examples
MSC 65F30
MSC 65F15
A perturbation analysis shows that if a numerically stable
procedure is used to compute the matrix sign function, then it is competitive
with conventional methods for computing invariant subspaces.
Stability analysis of the Newton iteration improves an earlier result of Byers
and confirms that ill-conditioned iterates may cause numerical
instability. Numerical examples demonstrate the theoretical results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800619
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17434/zip/
urn:nbn:de:bsz:ch1-199800619
oai:qucosa:de:qucosa:17438
2021-03-29T09:31:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Implementierung eines parallelen vorkonditionierten Schur-Komplement CG-Verfahrens in das Programmpaket FEAP
Mathias
Meisel
Arnd
Meyer
510
510
Schur-Complement
Conjugate Gradient
parallel realisation
domain decomposition
MSC 65Y05
MSC 65N30
A parallel realisation of the Conjugate Gradient Method with Schur-Complement preconditioning, based on a domain decomposition approach, is described in detail. Special kinds of solvers for the resulting interiour and coupling systems are presented. A large range of numerical results is used to demonstrate the properties and behaviour of this solvers in practical situations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800651
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17438/zip/
urn:nbn:de:bsz:ch1-199800651
oai:qucosa:de:qucosa:17435
2021-03-29T09:31:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local inequalities for anisotropic finite elements and their application to convection-diffusion problems
Thomas
Apel
Gert
Lube
510
510
MSC 65N30
The paper gives an overview over local inequalities for anisotropic simplicial Lagrangian finite elements. The main original contributions are the estimates for higher derivatives of the interpolation error, the formulation of the assumptions on admissible anisotropic finite elements in terms of geometrical conditions in the three-dimensional case, and an anisotropic variant of the inverse inequality. An application of anisotropic meshes in the context of a stabilized Galerkin method for a convection-diffusion problem is given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800625
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17435/zip/
urn:nbn:de:bsz:ch1-199800625
oai:qucosa:de:qucosa:17439
2021-03-29T09:31:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Grafik-Ausgabe vom Parallelrechner für 3D-Gebiete
M.
Meyer
510
510
MSC 65Y05
MSC 68Q22
The paper describes a method for Visualization of computational results in parallel finite element applications for 3D problems. The visualization itself is done on a workstation using a post- processing tool based on GRAPE, which interacts with the parallel program to obtain data.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800669
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17439/zip/
urn:nbn:de:bsz:ch1-199800669
oai:qucosa:de:qucosa:17436
2021-03-29T09:31:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Analysis und Numerik linearer differentiell-algebraischer Gleichungen
Peter
Kunkel
Volker
Mehrmann
510
510
consistent systems
numerical procedures
MSC 65L05
In Analysis and Numerik differential-algebraischer Gleichungen P. Kunkel and V. Mehrmann give a survey of relevant conditions for consistent systems, for existence and uniqueness of solutions, and touch numerical procedures for obtaining the solutions.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800633
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17436/zip/
urn:nbn:de:bsz:ch1-199800633
oai:qucosa:de:qucosa:17441
2021-03-29T09:31:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Ein technologisches Konzept zur Erzeugung adaptiver hierarchischer Netze für FEM-Schemata
U.
Groh
510
510
FEM
adaptive
mesh refinement
irregular
hierarchical
MSC 65Y05
MSC 65N30
Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800686
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17441/zip/
urn:nbn:de:bsz:ch1-199800686
oai:qucosa:de:qucosa:17442
2021-03-29T09:31:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Ein Residuenfehlerschätzer für anisotrope Tetraedernetze und Dreiecksnetze in der Finite-Elemente-Methode
G.
Kunert
510
510
finite elements
error estimator
anisotropic solution
stretched elements
tetrahedral mesh
triangular mesh
MSC 65N30
MSC 65N15
Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the finite element method (FEM), anisotropically refined meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For isotropic meshes such estimators are known but they fail when applied to anisotropic meshes. Rectangular (or cuboidal) anisotropic meshes were already investigated. In this paper an error estimator is presented for tetrahedral or triangular meshes which offer a much greater geometrical flexibility.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800691
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17442/zip/
urn:nbn:de:bsz:ch1-199800691
oai:qucosa:de:qucosa:17440
2021-03-29T09:31:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallel solution of finite element equation systems: efficient inter-processor communication
T.
Apel
G.
Haase
A.
Meyer
M.
Pester
510
510
MSC 65Y05
MSC 65N30
This paper deals with the application of domain decomposition methods for the parallel solution of boundary value problems for partial differential equations over a domain $Omegabset R^d$, $d=2,3$. The attention is focused on the conception of efficient communication routines for the data exchange which is necessary for example in the preconditioned cg-algorithm for solving the resulting system of algebraic equations. The paper describes the data structure, different algorithms, and computational tests.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800670
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17440/zip/
urn:nbn:de:bsz:ch1-199800670
oai:qucosa:de:qucosa:17446
2021-03-29T09:31:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Kommunikationstechnologien beim parallelen vorkonditionierten Schur-Komplement CG-Verfahren
M.
Meisel
A.
Meyer
510
510
Conjugate-Gradient
communication
parallelized
MSC 65Y05
Two alternative technologies of communication inside a parallelized Conjugate-Gradient algorithm are presented and compared to the well known hypercubecommunication. The amount of communication is diskussed in detail. A large range of numerical results corroborate the theoretical investigations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800734
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17446/zip/
urn:nbn:de:bsz:ch1-199800734
oai:qucosa:de:qucosa:17443
2021-03-29T09:31:41Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Canonical forms for linear descriptor systems with variable coefficients
W.
Rath
510
510
descriptor systems
closed loop system
MSC 65Y05
We study linear descriptor systems with rectangular variable coefficient matrices.
Using local and global equivalence transformations we introduce normal and
condensed forms and get sets of characteristic quantities. These quantities allow us to
decide whether a linear descriptor system with variable coefficients is regularizable
by derivative and/or proportional state feedback or not. Regularizable by feedback
means for us that their exist a feedback which makes the closed loop system uniquely
solvable for every consistent initial vector.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800708
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17443/zip/
urn:nbn:de:bsz:ch1-199800708
oai:qucosa:de:qucosa:17444
2021-03-29T09:31:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Placing plenty of poles is pretty preposterous
C.
He
A. J.
Laub
V.
Mehrmann
510
510
control models
pretty preposterous
eigenvalues
ill-conditioned
MSC 65Y05
We discuss the pole placement problem for single-input or multi-input control models of the form _x=Ax+Bu. This is the problem of determining a linear state feedback of the formu=F xsuch that in the closed-loop system _x= (A+BF)x, the matrixA+BFhas a prescribed set of eigenvalues. We analyze the conditioning of this problem and show that it is an intrinsically ill-conditioned problem, and especially so when the system dimension is large. Thus even the best numerical methods for this problem may yield very bad results. On the other hand, we also discuss the question of whether one really needs to solve the pole placement problem. In most circum- stances what is really required is stabilization or that the poles are in a specified region of the complex plane. This related problem may have much better conditioning. We demonstrate this via the example of stabilization.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800712
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17444/zip/
urn:nbn:de:bsz:ch1-199800712
oai:qucosa:de:qucosa:17447
2021-03-29T09:31:44Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Bibliotheken zur Entwicklung paralleler Algorithmen
G.
Haase
T.
Hommel
A.
Meyer
M.
Pester
510
510
parallel algorithms
message passing
numerical software
computer graphics
MSC 65Y05
MSC 65Y25
The purpose of this paper is to supply a summary of library subroutines and functions for parallel MIMD computers. The subroutines have been developed at the University of Chemnitz during a period of the last five years. In detail, they are concerned with vector operations, inter-processor communication and simple graphic output to workstations. One of the most valuable features is the machine-independence of the communication subroutines proposed in this paper for a hypercube topology of the parallel processors (excepting a kernel of only two primitive system-dependend operations). They were implemented and tested for different hardware and operating systems including transputer, nCube, KSR, PVM. The vector subroutines are optimized by the use of C language and enrolled loops (BLAS1-like). The paper includes hints for using the libraries with both Fortran and C programs.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800749
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17447/zip/
urn:nbn:de:bsz:ch1-199800749
oai:qucosa:de:qucosa:17445
2021-03-29T09:31:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Dampening controllers via a Riccati equation approach
J. J.
Hench
C.
He
V.
Kučera
V.
Mehrmann
510
510
linear quadratic controller
dampening feedback
damped dynamics
periodic systems
periodic Riccati equation
MSC 65L05
An algorithm is presented which computes a state feedback for a standard linear system which not only stabilizes, but also dampens the closed-loop system dynamics. In other words, a feedback gain vector is computed such that the eigenvalues of the closed-loop state matrix are within the region of the left half-plane where the magnitude of the real part of each eigenvalue is greater than the imaginary part. This may be accomplished by solving one periodic algebraic Riccati equation and one degenerate Riccati equation. The solution to these equations are computed using numerically robust algorithms. Finally, the periodic Riccati equation is unusual in that it produces one symmetric and one skew symmetric solution, and as a result two different state feedbacks. Both feedbacks dampen the system dynamics, but produce different closed-loop eigenvalues, giving the controller designer greater freedom in choosing a desired feedback.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800720
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17445/zip/
urn:nbn:de:bsz:ch1-199800720
oai:qucosa:de:qucosa:17448
2021-03-29T09:31:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case
P.
Benner
A. J.
Laub
V.
Mehrmann
510
510
benchmark
Riccati equations
MSC 65L05
A collection of benchmark examples is presented for the numerical solution of continuous-time algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800758
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17448/zip/
urn:nbn:de:bsz:ch1-199800758
oai:qucosa:de:qucosa:17450
2021-03-29T09:31:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Newtons method with exact line search for solving the algebraic Riccati equation
P.
Benner
R.
Byers
510
510
Newton method
algebraic Riccati equation
exact line search step
size control
MSC 65F30
MSC 15A24
This paper studies Newton's method for solving the algebraic Riccati equation combined with an exact line search. Based on these considerations we present a Newton{like method for solving algebraic Riccati equations. This method can improve the sometimes erratic convergence behavior of Newton's method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800775
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17450/zip/
urn:nbn:de:bsz:ch1-199800775
oai:qucosa:de:qucosa:17449
2021-03-29T09:31:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A collection of benchmark examples for the numerical solution of algebraic Riccati equations II: Discrete-time case
P.
Benner
A. J.
Laub
V.
Mehrmann
510
510
Riccati equations
benchmark
MSC 65L05
This is the second part of a collection of benchmark examples for the numerical solution of algebraic Riccati equations. After presenting examples for the continuous-time case in Part I, our concern in this paper is discrete-time algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800765
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17449/zip/
urn:nbn:de:bsz:ch1-199800765
oai:qucosa:de:qucosa:17451
2021-03-29T09:31:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallelization of multi-grid methods based on domain decomposition ideas
M.
Jung
510
510
Multi-grid methods
Parallel algorithms
Finite element discretizations
MSC 65N55
MSC 65Y05
MSC 65N30
In the paper, the parallelization of multi-grid methods for solving second-order elliptic boundary value problems in two-dimensional domains is discussed. The parallelization strategy is based on a non-overlapping domain decomposition data structure such that the algorithm is well-suited for an implementation on a parallel machine with MIMD architecture. For getting an algorithm with a good paral- lel performance it is necessary to have as few communication as possible between the processors. In our implementation, communication is only needed within the smoothing procedures and the coarse-grid solver. The interpolation and restriction procedures can be performed without any communication. New variants of smoothers of Gauss-Seidel type having the same communication cost as Jacobi smoothers are presented. For solving the coarse-grid systems iterative methods are proposed that are applied to the corresponding Schur complement system. Three numerical examples, namely a Poisson equation, a magnetic field problem, and a plane linear elasticity problem, demonstrate the efficiency of the parallel multi- grid algorithm.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800781
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17451/zip/
urn:nbn:de:bsz:ch1-199800781
oai:qucosa:de:qucosa:17452
2021-03-29T09:31:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Eigenvibrations of a plate with elastically attached load
Sergey I.
Solov'ëv
510
510
Eigenschwingung
Nichtlineares Eigenwertproblem
Spektraltheorie
natural oscillations
plate
This paper is concerned with the investigation of the nonlinear eigenvalue problem describing the natural oscillations of a plate with a load that elastically attached to it. We study properties of eigenvalues and eigenfunctions of this eigenvalue problem and prove the existence theorem for eigensolutions. Theoretical results are illustrated by numerical experiments.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600638
Preprintreihe des Chemnitzer SFB 393, 03-06
eng
Preprintreihe des Chemnitzer SFB 393, 03-06
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17452/zip/
urn:nbn:de:swb:ch1-200600638
oai:qucosa:de:qucosa:17455
2021-03-29T09:31:50Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Domain Decomposition and Multilevel Techniques for Preconditioning Operators
S. V.
Nepomnyaschikh
510
510
domain decomposition
multilevel
preconditioning
MSC 65N55
Introduction In recent years, domain decomposition methods have been used extensively to efficiently solve boundary value problems for partial differential equations in complex{form domains. On the other hand, multilevel techniques on hierarchical data structures also have developed into an effective tool for the construction and analysis of fast solvers. But direct realization of multilevel techniques on a parallel computer system for the global problem in the original domain involves difficult communication problems. I this paper, we present and analyze a combination of these two approaches: domain decomposition and multilevel decomposition on hierarchical structures to design optimal preconditioning operators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800815
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17455/zip/
urn:nbn:de:bsz:ch1-199800815
oai:qucosa:de:qucosa:17453
2021-03-29T09:31:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem
P.
Benner
H.
Faßbender
510
510
symplectic Lanczos method
implicit restarting
Hamiltonian matrix
eigenvalues
low rank approximate solution
algebraic Riccati equation
MSC 65F15
MSC 65F50
A restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem is presented. The Lanczos vectors are constructed to form a symplectic basis. Breakdowns and near-breakdowns are overcome by inexpensive implicit restarts. The method is used to compute eigenvalues, eigenvectors and invariant subspaces of large and sparse Hamiltonian matrices and low rank approximations to the solution of continuous-time algebraic Riccati equations with large and sparse coefficient matrices.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800797
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17453/zip/
urn:nbn:de:bsz:ch1-199800797
oai:qucosa:de:qucosa:17456
2021-03-29T09:31:51Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallel Preconditioners for Plate Problem
H.
Matthes
510
510
Schur-complement
conjugate gradient
plate bending problems
Domain decomposition,preconditioners
parallel
MSC 65Y05
This paper concerns the solution of plate bending problems in domains composed of rectangles. Domain decomposition (DD) is the basic tool used for both the parallelization of the conjugate gradient method and the construction of efficient parallel preconditioners. A so-called Dirich- let DD preconditioner for systems of linear equations arising from the fi- nite element approximation by non-conforming Adini elements is derived. It is based on the non-overlapping DD, a multilevel preconditioner for the Schur-complement and a fast, almost direct solution method for the Dirichlet problem in rectangular domains based on fast Fourier transform. Making use of Xu's theory of the auxiliary space method we construct an optimal preconditioner for plate problems discretized by conforming Bogner-Fox-Schmidt rectangles.
Results of numerical experiments carried out on a multiprocessor sys- tem are given. For the test problems considered the number of iterations is bounded independent of the mesh sizes and independent of the number of subdomains. The resulting parallel preconditioned conjugate gradient method requiresO(h^-2 ln h^-1 ln epsilon^-11) arithmetical operations per processor in order to solve the finite element equations with the relative accuracy epsilon.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800826
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17456/zip/
urn:nbn:de:bsz:ch1-199800826
oai:qucosa:de:qucosa:17454
2021-03-29T09:31:49Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Exact discretizations of two-point boundary value problems
G.
Windisch
510
510
exact discretizations
nonlinear
boundary value problem
tridiagonal
MSC 65L10
In the paper we construct exact three-point discretizations of linear and nonlinear two-point boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal M-matrices in the linear case and M-functions in the nonlinear case.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800804
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17454/zip/
urn:nbn:de:bsz:ch1-199800804
oai:qucosa:de:qucosa:17457
2021-03-29T09:31:52Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
SPC-PM Po 3D --- Users Manual
Th.
Apel
510
510
004
004
MSC 65Y05
The experimental program ¨SPC-PM Po 3D¨ is part of the ongoing research of the Chemnitz research group Scientific Parallel Computing (SPC) into finite element methods for problems over three dimensional domains. The package in its version 2.0 is documented in two manuals. The User's Manual provides an overview over the program, its capabilities, its installation, and handling. Moreover, test examples are explained. The aim of the Programmer's Manual is to provide a description of the algorithms and their realization. It is written for those who are interested in a deeper insight into the code, for example for improving and extending. In Version 2.0 the program can solve the Poisson equation and the Lam\'e system of linear elasticity with in general mixed boundary conditions of Dirichlet and Neumann type. The domain $\Omega\subset\R^3$ can be an arbitrarily bounded polyhedron. The input is a coarse mesh, a description of the data and some control parameters. The program distributes the elements of the coarse mesh to the processors, refines the elements, generates the system of equations using linear or quadratic shape functions, solves this system and offers graphical tools to display the solution. Further, the behavior of the algorithms can be monitored: arithmetic and communication time is measured, the discretization error is measured, different preconditioners can be compared. We plan to extend the program in the next future by including a multigrid solver, an error estimator and adaptive mesh refinement, as well as the treatment of coupled thermo-elastic problems. The program has been developed for MIMD computers; it has been tested on Parsytec machines (GCPowerPlus-128 with Motorola Power PC601 processors and GCel-192 on transputer basis) and on workstation clusters using PVM. The special case of only one processor is included, that means the package can be compiled for single processor machines without any change in the source files.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800836
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17457/zip/
urn:nbn:de:bsz:ch1-199800836
oai:qucosa:de:qucosa:17458
2021-03-29T09:31:52Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
SPC-PM Po 3D --- Programmers Manual
Th.
Apel
F.
Milde
M.
Theß
510
510
004
004
parallel computing
finite element methods
MSC 65Y05
The experimental program ¨SPC-PM Po 3D¨ is part of the ongoing research of the Chemnitz research group Scientific Parallel Computing (SPC) into finite element methods for problems over three dimensional domains. The package in its version 2.0 is documented in two manuals. The User's Manual provides an overview over the program, its capabilities, its installation, and handling. Moreover, test examples are explained. The aim of the Programmer's Manual is to provide a description of the algorithms and their realization. It is written for those who are interested in a deeper insight into the code, for example for improving and extending. In Version 2.0 the program can solve the Poisson equation and the Lam'e system of linear elasticity with in general mixed boundary conditions of Dirichlet and Neumann type. The domain $\Omega\subset\R^3$ can be an arbitrarily bounded polyhedron. The input is a coarse mesh, a description of the data and some control parameters. The program distributes the elements of the coarse mesh to the processors, refines the elements, generates the system of equations using linear or quadratic shape functions, solves this system and offers graphical tools to display the solution. Further, the behavior of the algorithms can be monitored: arithmetic and communication time is measured, the discretization error is measured, different preconditioners can be compared. We plan to extend the program in the next future by including a multigrid solver, an error estimator and adaptive mesh refinement, as well as the treatment of coupled thermo-elastic problems. The program has been developed for MIMD computers; it has been tested on Parsytec machines (GCPowerPlus-128 with Motorola Power PC601 processors and GCel-192 on transputer basis) and on workstation clusters using PVM. The special case of only one processor is included, that means the package can be compiled for single processor machines without any change in the source files.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800848
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17458/zip/
urn:nbn:de:bsz:ch1-199800848
oai:qucosa:de:qucosa:17459
2021-03-29T09:31:53Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the preconditioning in the domain decomposition technique for the p-version finite element method. Part I
S. A.
Ivanov
V. G.
Korneev
510
510
MSC 65N55
MSC 65N30
Abstract P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary re- sults for 1D case, condition number estimates and some inequalities for 2D reference element.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800856
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17459/zip/
urn:nbn:de:bsz:ch1-199800856
oai:qucosa:de:qucosa:17460
2021-03-29T09:31:54Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the preconditioning in the domain decomposition technique for the p-version finite element method. Part II
S. A.
Ivanov
V. G.
Korneev
510
510
Schur complement preconditioner
MSC 65N55
MSC 65N30
P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary results for 1D case, condition number estimates and some inequalities for 2D reference element. Part II is devoted to the derivation of the Schur complement preconditioner and conditionality number estimates for the p-version finite element matrixes. Also DD preconditioning is considered.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800862
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17460/zip/
urn:nbn:de:bsz:ch1-199800862
oai:qucosa:de:qucosa:17464
2021-03-29T09:31:57Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Zur Berechnung von Spannungs- und Deformationsfeldern an Interface-Ecken im nichtlinearen Deformationsbereich auf Parallelrechnern
M.
Scherzer
A.
Meyer
510
510
parallel
stiffness
deformation field calculation
MSC 65Y05
Using material models on the basis of the flow theory of plasticity the asymptotic behaviour of solid mechanics solutions in crack tips, interface corners etc. strongly depends on the local realized load trajectory. For incrementally proportional load paths the equations determining the asymptotic fields are very simple ones. The paper considers two-dimensional statements in the neighbourhood of an interface corner consisting of two material ranges. At a distance from the corner the finite element nodes of a regular net are established in a polar co-ordinate system together with the displacement degrees of freedom. The main idea of the presented singular and non-singular stress and deformation field calculation at interface corners characterizes an replacement of the corner neighbourhood effect to the surrounding body by introducing stiffness actions which in usual manner can be assembled together with the other element stiffness matrices to the global stiffness matrix of the body. According to this there exists an in teresting invariant stiffness independence in corner and crack neighbourhoods. The applied technique allows extensions to non-proportional local load increments simplifying the mathematical calculations for the presentation of stress and strain fields in this general case. All computations are made on modern parallel computers. Concrete examples show the advantages of the presented approach.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800902
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17464/zip/
urn:nbn:de:bsz:ch1-199800902
oai:qucosa:de:qucosa:17461
2021-03-29T09:31:55Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Thermoelastic Oscillations of Anisotropic Bodies
L.
Jentsch
D.
Natroshvili
510
510
thermoelasticity
oscillations
anisotropic bodies
potential method
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
The generalized radiation conditions at infinity of Sommerfeld-Kupradze type are established in the theory of thermoelasticity of anisotropic bodies. Applying the potential method and the theory of pseudodifferential equations on manifolds the uniqueness and existence theorems of solutions to the basic three-dimensional exterior boundary value problems are proved and representation formulas of solutions by potential type integrals are obtained.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800871
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17461/zip/
urn:nbn:de:bsz:ch1-199800871
oai:qucosa:de:qucosa:17465
2021-03-29T09:31:58Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils
P.
Benner
V.
Mehrmann
H.
Xu
510
510
eigenvalue problem
Hamiltonian pencil matrix
symplectic pencil matrix
skew-Hamiltonian matrix
MSC 65F15
A new method is presented for the numerical computation of the generalized eigen- values of real Hamiltonian or symplectic pencils and matrices. The method is strongly backward stable, i.e., it is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order sqrt(epsilon), where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800915
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17465/zip/
urn:nbn:de:bsz:ch1-199800915
oai:qucosa:de:qucosa:17462
2021-03-29T09:31:56Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Thermoelastic Oscillations of Anisotropic Bodies (Sommerfeld 96 - Workshop)
L.
Jentsch
D.
Natroshvili
510
510
thermoelasticity
oscillations
anisotropic bodies
potential methods
MSC 73D30
MSC 73B40
Three-dimensional basic problems of statics, pseudo-oscillations, general dynamics and steady state oscillations of the thermoelasticity of isotropic bodies have been completely investigated by many authors. In particular, exterior steady state oscillation problems have been studied on the basis of Sommerfeld-Kupradze radiation conditions in the thermoelasticity, and the uniqueness theorems were proved with the help of the well-known Rellich's lemma, since the components of the displacement vector and the temperature in the isotropic case can be represented as a sum of metaharmonic functions . Unfortunately, the methods of investigation of thermoelastic steady state oscillation problems developed for the isotropic case are not applicable in the case of general anisotropy. This is stipulated by a very complicated form of the corresponding characteristic equation which plays a significant role in the study of far field behaviour of solutions to the oscillation equa- tions. We note that the basic and crack type boundary value problems (BVPs) for the pseudo-oscillation equations of the thermoelasticity theory in the anisotropic case are considered in [3,14]. To the best of the authors' knowledge the problems of thermoelastic steady oscillations for anisotropic bodies have not been treated in the scientific literature. In the present paper we will consider a wide class of basic and mixed type BVPs for the equations of thermoelastic steady state oscillations. We will formulate thermoelastic radiation conditions for an anisotropic medium (the generalized Sommerfeld-Kupradze type radiation conditions) and prove the uniqueness theorems in corresponding spaces. To derive these conditions we have essentially applied results of Vainberg. Further, using the potential method and the theory of pseudodifferential equations on manifolds we will prove existence theorems in various functional spaces and establish the smoothness properties of solutions.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800886
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17462/zip/
urn:nbn:de:bsz:ch1-199800886
oai:qucosa:de:qucosa:17466
2021-03-29T09:31:59Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
HAMEV and SQRED: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices Using Van Loanss Square Reduced Method
P.
Benner
R.
Byers
E.
Barth
510
510
eigenvalues
square-reduced Hamiltonian matrix
skew-Hamiltonian matrix
algebraic Riccati equation
MSC 65F15
MSC 93B40
This paper describes LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. The transformation of the Hamilto- nian matrix to a square-reduced Hamiltonian uses only orthogonal symplectic similarity transformations. The eigenvalues can then be determined by applying the Hessenberg QR iteration to a matrix of half the order of the Hamiltonian matrix and taking the square roots of the computed values. Using scaling strategies similar to those suggested for algebraic Riccati equations can in some cases improve the accuracy of the computed eigenvalues. We demonstrate the performance of the subroutines for several examples and show how they can be used to solve some control-theoretic problems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800926
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17466/zip/
urn:nbn:de:bsz:ch1-199800926
oai:qucosa:de:qucosa:17463
2021-03-29T09:31:56Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Numerical solution of generalized Lyapunov equations
T.
Penzl
510
510
mathematical software
generalized Lyapunov equation
generalized Stein equation
condition estimation
MSC 65F05
MSC 65F15
MSC 93B40
MSC 93B51
Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first one is a generalization of the Bartels--Stewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based subroutines are implemented in a quite flexible way. They can handle the transposed equations and provide scaling to avoid overflow in the solution. Moreover, the Bartels--Stewart subroutine offers the optional estimation of the separation and the reciprocal condition number. A brief description of both algorithms is given. The performance of the software is demonstrated by numerical experiments.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800893
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17463/zip/
urn:nbn:de:bsz:ch1-199800893
oai:qucosa:de:qucosa:17467
2021-03-29T09:32:00Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Portierbare numerische Simulation auf parallelen Architekturen
W.
Rehm
004
004
Benchmarking
Parallel Computing
FEM
Shared Memory
Implementations
Message Passing
Efficiency,
MSC 68M99
MSC 68Q22
The workshop ¨Portierbare numerische Simulationen auf parallelen Architekturen¨
(¨Portable numerical simulations on parallel architectures¨) was organized by the Fac-
ulty of Informatics/Professorship Computer Architecture at 18 April 1996 and held in
the framework of the Sonderforschungsbereich (Joint Research Initiative) ¨Numerische
Simulationen auf massiv parallelen Rechnern¨ (SFB 393) (¨Numerical simulations on
massiv parallel computers¨) ( http://www.tu-chemnitz.de/~pester/sfb/sfb393.html )
The SFB 393 is funded by the German National Science Foundation (DFG).
The purpose of the workshop was to bring together scientists using parallel computing
to provide integrated discussions on portability issues, requirements and future devel-
opments in implementing parallel software efficiently as well as portable on Clusters of
Symmetric Multiprocessorsystems.
I hope that the present paper gives the reader some helpful hints for further discussions
in this field.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800931
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17467/zip/
urn:nbn:de:bsz:ch1-199800931
oai:qucosa:de:qucosa:17469
2021-03-29T09:32:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local Ill-Posedness and Source Conditions of Operator Equations in Hilbert Spaces
B.
Hofmann
O.
Scherzer
510
510
nonlinear operator equations
ill-posedness
Frechet derivative
source conditions
stability estimates
ill-posedness measurres
a posteriori estimates
MSC 65J15
MSC 65J20
MSC 47H15
MSC 47H17
The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods for the solution of nonlinear partial differential equations, but these techniques are in general not applicable to inverse an ill-posed problems. Additionally we show for the well-known Landweber method and the iteratively regularized Gauss-Newton method that they satisfy a posteriori estimates under source conditions; this can be used to prove convergence rates results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800957
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17469/zip/
urn:nbn:de:bsz:ch1-199800957
oai:qucosa:de:qucosa:17468
2021-03-29T09:32:00Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Navier-Stokes equations as a differential-algebraic system
J.
Weickert
510
510
MSC 76D05
Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800942
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17468/zip/
urn:nbn:de:bsz:ch1-199800942
oai:qucosa:de:qucosa:17470
2021-03-29T09:32:02Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Three-dimensional mathematical Problems of thermoelasticity of anisotropic Bodies
Lothar
Jentsch
David
Natroshvili
510
510
boundary value problems
thermoelasticity
anisotropic bodies
interface problems
mixed and crack type problems
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 35J55
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
MSC 73C35
MSC 73K20
CHAPTER I. Basic Equations. Fundamental Matrices. Thermo-Radiation Conditions
1. Basic differential equations of thermoelasticity theory
2. Fundamental matrices
3. Thermo-radiating conditions. Somigliana type integral representations
CHAPTER II. Formulation of Boundary Value and Interface Problems
4. Functional spaces
5. Formulation of basic and mixed BVPs
6. Formulation of crack type problems
7. Formulation of basic and mixed interface problems
CHAPTER III. Uniqueness Theorems
8. Uniqueness theorems in pseudo-oscillation problems
9. Uniqueness theorems in steady state oscillation problems
CHAPTER IV. Potentials and Boundary Integral Operators
10. Thermoelastic steady state oscillation potentials
11. Pseudo-oscillation potentials
CHAPTER V. Regular Boundary Value and Interface Problems
12. Basic BVPs of pseudo-oscillations
13. Basic exterior BVPs of steady state oscillations
14. Basic interface problems of pseudo-oscillations
15. Basic interface problems of steady state oscillations
CHAPTER VI. Mixed and Crack Type Problems
16. Basic mixed BVPs
17. Crack type problems
18. Mixed interface problems of steady state oscillations
19. Mixed interface problems of pseudo-oscillations
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800967
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17470/zip/
urn:nbn:de:bsz:ch1-199800967
oai:qucosa:de:qucosa:17474
2021-03-29T09:32:05Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the Lagrange-Newton-SQP Method for the Optimal Control of Semilinear Parabolic Equations
Fredi
Tröltzsch
510
510
optimal control
parabolic equation
semilinear equation
sequential quadratic programming
Lagrange-Newton method
convergence analysis
MSC 49J20
MSC 49M15
MSC 65K10
MSC 49K20
A class of Lagrange-Newton-SQP methods is investigated for optimal control problems
governed by semilinear parabolic initial- boundary value problems. Distributed and boundary
controls are given, restricted by pointwise upper and lower bounds. The convergence of the method
is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality condition
for the reference solution, local quadratic convergence is proved. The proof is based on the
theory of Newton methods for generalized equations in Banach spaces.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800995
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17474/zip/
urn:nbn:de:bsz:ch1-199800995
oai:qucosa:de:qucosa:17471
2021-03-29T09:32:03Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Interface Crack Problem for Anisotropic Bodies
David
Natroshvili
Shota
Zazashvili
510
510
anisotropic body
interface crack problem
MSC 31A10
MSC 35J55
MSC 73B40
MSC 73C35
MSC 73M25
The two-dimensional interface crack problem is investigated for anisotropic bodies in the Comninou formulation. It is established that, as in the isotropic case, properly incorporating contact zones at the crack tips avoids contradictions connected with the oscillating asymptotic behaviour of physical and mechanical characteristics leading to the overlapping of material. Applying the special integral representation formulae for the displacement field the problem in question is reduced to the scalar singular integral equation with the index equal to -1. The analysis of this equation is given. The comparison with the results of previous authors shows that the integral equations corresponding to the interface crack problems in the anisotropic and isotropic cases are actually the same from the point of view of the theoretical and numerical analysis.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800979
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17471/zip/
urn:nbn:de:bsz:ch1-199800979
oai:qucosa:de:qucosa:17475
2021-03-29T09:32:06Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations
Kazimierz
Malanowski
Fredi
Tröltzsch
510
510
optimal control
semilinear parabolic equations
Lipschitz stability
supremum norm
MSC 49K20
MSC 49K40
A class of parametric optimal control problems for semilinear parabolic
equations is considered. Using recent regularity results for solutions of such equations,
sufficient conditions are derived under which the solutions to optimal control problems
are locally Lipschitz continuous functions of the parameter in the L1-norm. It is shown
that these conditions are also necessary, provided that the dependence of data on the
parameter is sufficiently strong.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801001
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17475/zip/
urn:nbn:de:bsz:ch1-199801001
oai:qucosa:de:qucosa:17472
2021-03-29T09:32:04Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Stability Rates for Linear Ill-Posed Problems with Convolution and Multiplication Operators
B.
Hofmann
G.
Fleischer
510
510
Linear ill-posed problems
compact and noncompact linear operators in Hilbert spaces
discrete least-squares method
stability rates
singular values
convolution and multiplication operators
Galerkin matrices
condition numbers
increasing rearrangements
MSC 65J20
MSC 47B38
MSC 65R30
In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199800987
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17472/zip/
urn:nbn:de:bsz:ch1-199800987
oai:qucosa:de:qucosa:17476
2021-03-29T09:32:07Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Second Order Sufficient Optimality Conditions for Nonlinear Parabolic Control Problems with State Constraints
Jean-Pierre
Raymond
Fredi
Tröltzsch
510
510
Boundary control
distributed control
semilinear parabolic equations
sufficient optimality conditions
pointwise state constraints
MSC 49K20
MSC 35J25
In this paper, optimal control problems for semilinear parabolic equations with
distributed and boundary controls are considered. Pointwise constraints on the control and on
the state are given. Main emphasis is laid on the discussion of second order sufficient optimality
conditions. Sufficiency for local optimality is verified under different assumptions imposed
on the dimension of the domain and on the smoothness of the given data.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801014
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17476/zip/
urn:nbn:de:bsz:ch1-199801014
oai:qucosa:de:qucosa:17478
2021-03-29T09:32:08Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A cyclic low rank Smith method for large, sparse Lyapunov equations with applications in model reduction and optimal control
T.
Penzl
510
510
ADI iteration
Smith method
iterative methods
Lyapunov equation
matrix equation
model reduction
balanced truncation
optimal control
Riccati equation
Newton method
MSC 65F30
MSC 65F10
MSC 15A24
MSC 93C05
We present a new method for the computation of low rank approximations
to the solution of large, sparse, stable Lyapunov equations. It is based
on a generalization of the classical Smith method and profits by the
usual low rank property of the right hand side matrix.
The requirements of the method are moderate with respect to both
computational cost and memory.
Hence, it provides a possibility to tackle large scale control
problems.
Besides the efficient solution of the matrix equation itself,
a thorough integration of the method into several control
algorithms can improve their performance
to a high degree.
This is demonstrated for algorithms
for model reduction and optimal control.
Furthermore, we propose a heuristic for determining a set of
suboptimal ADI shift parameters. This heuristic, which is based on a
pair of Arnoldi processes, does not require any a priori
knowledge on the spectrum of
the coefficient matrix of the Lyapunov equation.
Numerical experiments show the efficiency of the iterative scheme
combined with the heuristic for the ADI parameters.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801035
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17478/zip/
urn:nbn:de:bsz:ch1-199801035
oai:qucosa:de:qucosa:17477
2021-03-29T09:32:07Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:530
openaire
Two interfacing particles in a random potential: The random model revisited
T.
Vojta
R. A.
Römer
M.
Schreiber
530
530
coupling matrix
random matrix model
random potential
Imry
MSC 60K40
We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an effective random matrix model. To this end we first study numerically how the non-interacting basis is coupled by the interaction. Our results indicate that the typical coupling matrix element decreases significantly faster with increasing single-particle localization length than is assumed in the random matrix model. We further show that even for models where the dependency of the coupling matrix element on the single-particle localization length is correctly described by the corresponding random matrix model its predictions for the localization length can be qualitatively incorrect. These results indicate that the mapping of an interacting random system onto an effective random matrix model is potentially dangerous. We also discuss how Imry's block-scaling picture for two interacting particles is influenced by the above arguments.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801028
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17477/zip/
urn:nbn:de:bsz:ch1-199801028
oai:qucosa:de:qucosa:17479
2021-03-29T09:32:09Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:530
openaire
Blocking vs. Non-blocking Communication under MPI on a Master-Worker Problem
André
Fachat
Karl Heinz
Hoffmann
530
530
004
004
MPI
MPICH
blocking communication
non-blocking communication
MSC 68-04
In this report we describe the conversion of a simple Master-Worker parallel
program from global blocking communications to non-blocking communications.
The program is MPI-based and has been run on different computer architectures.
By moving the communication to the background the processors can use
the former waiting time for computation. However we find that the
computing time increases by the time the communication time decreases in
the used MPICH implementation on a cluster of workstations.
Also using non-global communication instead of the global communication
slows the algorithm down on computers with optimized global communication
routines like the Cray T3D.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801043
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17479/zip/
urn:nbn:de:bsz:ch1-199801043
oai:qucosa:de:qucosa:17482
2021-03-29T09:32:11Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A note on anisotropic interpolation error estimates for isoparametric quadrilateral finite elements
Th.
Apel
510
510
MSC 65N30
Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian finite elements with straight edges. These elements are allowed to have diameters with different asymptotic behaviour in different space directions.
The case of affine elements (parallelepipeds) with arbitrarily high degree of the shape functions is considered first. Then, a careful examination of the multi-linear map leads to estimates for certain classes of more general, isoparametric elements.
As an application, the Galerkin finite element method for a reaction diffusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801071
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17482/zip/
urn:nbn:de:bsz:ch1-199801071
oai:qucosa:de:qucosa:17483
2021-03-29T09:32:12Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh refinement for singularly perturbed reaction diffusion problems
Th.
Apel
G.
Lube
510
510
elliptic boundary value problems
Galerkin finite element methods
anisotropic mesh refinement
MSC 65N30
MSC 65N50
MSC 35J25
The paper is concerned with the finite element resolution of layers appearing
in singularly perturbed problems. A special anisotropic grid of Shishkin type
is constructed for reaction diffusion problems. Estimates of the finite element
error in the energy norm are derived for two methods, namely the standard
Galerkin method and a stabilized Galerkin method. The estimates are uniformly
valid with respect to the (small) diffusion parameter. One ingredient is a
pointwise description of derivatives of the continuous solution. A numerical
example supports the result.
Another key ingredient for the error analysis is a refined estimate for
(higher) derivatives of the interpolation error. The assumptions on admissible
anisotropic finite elements are formulated in terms of geometrical conditions
for triangles and tetrahedra. The application of these estimates is not
restricted to the special problem considered in this paper.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801080
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17483/zip/
urn:nbn:de:bsz:ch1-199801080
oai:qucosa:de:qucosa:17484
2021-03-29T09:32:13Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Scalability, efficiency, and robustness of parallel multilevel solvers for nonlinear equations
B.
Heise
M.
Jung
510
510
004
004
MSC 65Y05
In this paper we compare the performance, scalability, and robustness of different parallel algorithms for the numerical solution of nonlinear boundary value problems arising in the magnetic field computation and in solid mechanics. These problems are discretized by using the finite element method with triangular meshes and piecewise linear functions. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely multigrid methods and conjugate gradient methods with preconditioners based on domain decomposition, multigrid, or BPX techniques, respectively. The basis of the implementation of all solvers is a non-overlapping domain decomposition data structure such that they are well-suited for parallel machines with MIMD architecture.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801090
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17484/zip/
urn:nbn:de:bsz:ch1-199801090
oai:qucosa:de:qucosa:17480
2021-03-29T09:32:10Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Der objektorientierte hierarchische Netzgenerator Netgen69-C++
Marko
Meyer
004
004
Object Oriented Programming
CPLUSPLUS
Mesh Generation
FEM
Parallel Programming
MSC 68-00
Im Rahmen der Arbeit in der damaligen DFG-Forschungsgruppe ¨Scientific Parallel
Computing¨ wurde ein hierarchischer paralleler Netzgenerator fuer das Finite-Elemente-
Programmpaket SPC-PM CFD unter dem Namen NETGEN69 entwickelt.
Als Programmiersprache wurde seinerzeit - wie auch in den FEM-Programmen
selbst - FORTRAN benutzt. Im Rahmen des Teilprojektes B2 im Sonderforschungsbereich 393
bestand nunmehr die Aufgabe, den Netzgenerator in ein objektorientiertes Layout zu fassen
und in C++zu implementieren.
Die Beschreibung von Ein- und Ausgabedaten kann in [3] nachgelesen werden. Die Form
der Eingabedaten hat sich aus Kompatibilitaetsgruenden nicht geaendert und wird auch in
Zukunft so beibehalten werden. Auch das der Assemblierung und FEM-Rechnung zuge-
wandte Interface wurde vorerst nicht geaendert. Ein Wrapper, der fuer die Generierung der
erwarteten Ausgabedaten aus den netzgeneratoreigenen Datenbestaenden sorgt, ist derzeit
in Planung. Diese Lösung ist freilich nur voruebergehender Natur; sie ermoeglicht es uns, den
Netzgenerator innerhalb der FEM-Bibliotheken zu testen.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801052
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17480/zip/
urn:nbn:de:bsz:ch1-199801052
oai:qucosa:de:qucosa:17485
2021-03-29T09:32:14Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Partitionierung von Finite-Elemente-Netzen
U.
Reichel
510
510
MSC 65N30
MSC 65N50
The realization of the finite element method on parallel computers
is usually based on a domain decomposition approach. This paper is
concerned with the problem of finding an optimal decomposition and an
appropriate mapping of the subdomains to the processors. The quality
of this partitioning is measured in several metrics but it is also
expressed in the computing time for solving specific systems of
finite element equations.
The software environment is first described. In particular, the data
structure and the accumulation algorithm are introduced. Then
several partitioning algorithms are compared. Spectral bisection was
used with different modifications including Kernighan-Lin refinement,
post-processing techniques and terminal propagation. The final
recommendations should give good decompositions for all finite
element codes which are based on principles similar to ours.
The paper is a shortened English version of Preprint SFB393/96-18
(Uwe Reichel: Partitionierung von Finite-Elemente-Netzen), SFB 393,
TU Chemnitz-Zwickau, December 1996. To be selfcontained, some material
of Preprint SPC95_5 (see below) is included. The paper appeared as
Preprint SFB393/96-18a, SFB 393, TU Chemnitz-Zwickau, January 1997.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801107
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17485/zip/
urn:nbn:de:bsz:ch1-199801107
oai:qucosa:de:qucosa:17481
2021-03-29T09:32:11Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:530
openaire
Smoothed universal correlations in the two-dimensional Anderson model
V.
Uski
B.
Mehlig
R. A.
Romer
M.
Schreiber
530
530
correlations
Anderson model
twodimensional
MSC 15A52
We report on calculations of smoothed spectral correlations in the twodimensional
Anderson model for weak disorder. As pointed out in (M. Wilkinson,
J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing
dependence of the correlation functions provides a sensitive means of establishing
consistency with random matrix theory. We use a semiclassical approach
to describe these fluctuations and offer a detailed comparison between
numerical and analytical calculations for an exhaustive set of two-point correlation
functions. We consider parametric correlation functions with an external
Aharonov-Bohm flux as a parameter and discuss two cases, namely
broken time-reversal invariance and partial breaking of time-reversal invariance.
Three types of correlation functions are considered: density-of-states,
velocity and matrix element correlation functions. For the values of smoothing
parameter close to the mean level spacing the semiclassical expressions
and the numerical results agree quite well in the whole range of the magnetic
flux.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801066
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17481/zip/
urn:nbn:de:bsz:ch1-199801066
oai:qucosa:de:qucosa:17486
2021-03-29T09:32:15Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:530
openaire
No enhancement of the localization length for two interacting particles in a random potential
R. A.
Römer
M.
Schreiber
530
530
potential chain
Hubbard,
MSC 60K40
We study two interacting particles in a random potential chain by means of the transfer matrix
method. The dependence of the two-particle localization length lampta_2 on disorder and interaction
strength is investigated. Our results demonstrate that the recently proposed enhancement of lampta_2 as
compared to the results for single particles is entirely due to the finite size of the systems considered.
This is shown for a Hubbard-like onsite interaction and also a long-range interaction.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801117
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17486/zip/
urn:nbn:de:bsz:ch1-199801117
oai:qucosa:de:qucosa:17487
2021-03-29T09:32:15Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Two-point boundary value problems with piecewise constant coefficients: weak solution and exact discretization
G.
Windisch
510
510
MSC 65L10
For two-point boundary value problems in weak formulation with piecewise constant coefficients and piecewise continuous right-hand side functions we derive a representation of its weak solution by local Green's functions. Then we use it to generate exact three-point discretizations by Galerkin's method on essentially arbitrary grids. The coarsest possible grid is the set of points at which the piecewise constant coefficients and the right- hand side functions are discontinuous. This grid can be refined to resolve any solution properties like boundary and interior layers much more correctly. The proper basis functions for the Galerkin method are entirely defined by the local Green's functions. The exact discretizations are of completely exponentially fitted type and stable. The system matrices of the resulting tridiagonal systems of linear equations are in any case irreducible M-matrices with a uniformly bounded norm of its inverse.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801123
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17487/zip/
urn:nbn:de:bsz:ch1-199801123
oai:qucosa:de:qucosa:17491
2021-03-29T09:32:18Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Interaction between Thermoelastic and Scalar Oscillation Fields (general anisotropic case)
L.
Jentsch
D
Natroshvili
510
510
Fluid-solid interaction
anisotropic bodies
boundary integral method
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
Three-dimensional mathematical problems of the interaction between thermoelastic
and scalar oscillation fields are considered in a general anisotropic case. An elastic
structure is assumed to be a bounded homogeneous anisortopic body occupying domain
$\Omega^+\sub\R^3$ , where the thermoelastic field is defined, while in the
physically anisotropic unbounded exterior domain $\Omega^-=\R^3\\ \overline{\Omega^+}$
there is defined the scalar field. These two fields
satisfy the differential equations of steady state oscillations in the corresponding
domains along with the transmission conditions of special type on the interface
$\delta\Omega^{+-}$. Uniqueness and existence theorems, for the non-resonance case, are proved
by the reduction of the original interface problems to equivalent systems of boundary
pseudodifferential equations ($\Psi DEs$) . The invertibility of the corresponding
matrix pseudodifferential operators ($\Psi DO$) in appropriate functional spaces is
shown on the basis of generalized Sommerfeld-Kupradze type thermoradiation conditions
for anisotropic bodies. In the resonance case, the co-kernels of the $\Psi DOs$ are
analysed and the efficent conditions of solvability of the transmission problems
are established.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801162
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17491/zip/
urn:nbn:de:bsz:ch1-199801162
oai:qucosa:de:qucosa:17488
2021-03-29T09:32:16Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Variable preconditioning procedures for elliptic problems
M.
Jung
S. V.
Nepomnyaschikh
510
510
MSC 65N30
For solving systems of grid equations approximating elliptic boundary value problems a method of constructing variable preconditioning procedures is presented. The main purpose is to discuss how an efficient preconditioning iterative procedure can be constructed in the case of elliptic problems with disproportional coefficients, e.g. equations with a large coefficient in the reaction term (or a small diffusion coefficient). The optimality of the suggested technique is based on fictitious space and multilevel decom- position methods. Using an additive form of the preconditioners, we intro- duce factors into the preconditioners to optimize the corresponding conver- gence rate. The optimization with respect to these factors is used at each step of the iterative process. The application of this technique to two-level $p$-hierarchical precondi- tioners and domain decomposition methods is considered too.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801137
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17488/zip/
urn:nbn:de:bsz:ch1-199801137
oai:qucosa:de:qucosa:17492
2021-03-29T09:32:19Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Minimum Norm Regularization of Descriptor Systems by Output Feedback
D.
Chu
V.
Mehrmann
510
510
regularization
mixed outputp
differential and algebraic equations
orthogonal matrix transformation
MSC 93B05
MSC 93B40
MSC 93B52
MSC 65F35
We study the regularization problem for linear, constant coefficient descriptor
systems $E x^. = AX + Bu, y_1 = Cx, y_2=\Gamma x^.$ by proportional and derivative
mixed output feedback. Necessary and sufficient conditions are given, which guarantee
that there exist output feedbacks such that the closed-loop system is regular, has
index at most one and $E +BG\Gamma$ has
a desired rank, i.e. there is a desired number of differential and algebraic equations.
To resolve the freedom in the choice of the feedback matrices we then discuss how
to obtain the desired regularizing feedback of minimum norm and show that this approach
leads to useful results in the sense of robustness only if the rank of E is
decreased. Numerical procedures are derived to construct the desired feedbacks gains.
These numerical procedures are based on orthogonal matrix transformations which
can be implemented in a numerically stable way.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801177
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17492/zip/
urn:nbn:de:bsz:ch1-199801177
oai:qucosa:de:qucosa:17489
2021-03-29T09:32:17Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On-line visualization in parallel computations
M.
Pester
510
510
parallel algorithms
postprocessing
computer graphics
visualization
MSC 65Y05
MSC 68Q22
MSC 65Y25
The investigation of new parallel algorithms for MIMD computers
requires some postprocessing facilities for quickly evaluating
the behavior of those algorithms We present two kinds of
visualization tool implementations for 2D and 3D finite element
applications to be used on a parallel computer and a host
workstation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801143
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17489/zip/
urn:nbn:de:bsz:ch1-199801143
oai:qucosa:de:qucosa:17493
2021-03-29T09:32:20Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On Ill-Posedness and Local Ill-Posedness of Operator
Equations in Hilbert Spaces
On Ill-Posedness and Local Ill-Posedness of OperatorEquations in Hilbert Spaces
B.
Hofmann
510
510
Nonlinear inverse problems
oerator equations
ill-posedness
stability estimates
local ill-posedness
Frechet derivative
linearized problem
compact operators
integral equations
parameter identification
MSC 65J20
MSC 47H15
MSC 65J10
MSC 65J15
MSC 65R30
MSC 45G10
In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems
in a Hilbert space setting. We define local ill-posedness of a nonlinear operator
equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear
problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an
appropriate ill-posedness concept for the linarized equation we define intrinsic
ill-posedness for linear operator equations $Ax = y$ and compare this approach with
the ill-posedness definitions due to Hadamard and Nashed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801185
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17493/zip/
urn:nbn:de:bsz:ch1-199801185
oai:qucosa:de:qucosa:17490
2021-03-29T09:32:18Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Mixed Interface Problems of Thermoelastic Pseudo-Oscillations
L.
Jentsch
D.
Natroshvili
I.
Sigua
510
510
mixed interface problems
thermoelastic pseudo-oscillations
pseudodifferential equations
MSC 31B10
MSC 31B25
MSC 35C15
MSC 35E05
MSC 45F15
MSC 73B30
MSC 73B40
MSC 73C15
MSC 73D30
Three-dimensional basic and mixed interface problems of the mathematical
theory of thermoelastic pseudo-oscillations are considered for piecewise homogeneous
anisotropic bodies. Applying the method of boundary potentials and the theory of
pseudodifferential equations existence and uniqueness theorems of solutions are proved
in the space of regular functions C^(k+ alpha) and in the Bessel-potential (H^(s)_(p))
and Besov (B^(s)_(p,q)) spaces. In addition to the classical regularity results
for solutions to the basic interface problems, it is shown that in the mixed interface
problems the displacement vector and the temperature are Hölder continuous with
exponent 0<alpha<1/2.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801150
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17490/zip/
urn:nbn:de:bsz:ch1-199801150
oai:qucosa:de:qucosa:17495
2021-03-29T09:32:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the Autoconvolution Equation and Total Variation Constraints
G.
Fleischer
R.
Gorenflo
B.
Hofmann
510
510
autoconvolution
ill-posed problem
discretization
constrained least squares approach
bounded total variation
MSC 65J20
MSC 45G10
MSC 65R30
This paper is concerned with the numerical analysis of the autoconvolution equation
$x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least
squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where
the regularization is based on a prescribed bound for the total variation of admissible
solutions. This approach includes the case of non-smooth solutions possessing jumps.
Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone
functions are added. The paper is completed by a numerical case study concerning
the determination of non-monotone smooth and non-smooth functions x from the autoconvolution
equation with noisy data y.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801196
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17495/zip/
urn:nbn:de:bsz:ch1-199801196
oai:qucosa:de:qucosa:17496
2021-03-29T09:32:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local theory of a collocation method for Cauchy singular integral equations on an interval
P.
Junghanns
U.
Weber
510
510
Cauchy singular integral equations
collocation methods
stability
MSC 45E05
MSC 45L10
We consider a collocation method for Cauchy singular integral equations on the interval
based on weighted Chebyshev polynomials , where the coefficients of the operator are
piecewise continuous. Stability conditions are derived using Banach algebra methods,
and numerical results are given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801203
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17496/zip/
urn:nbn:de:bsz:ch1-199801203
oai:qucosa:de:qucosa:17497
2021-03-29T09:32:23Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On a SQP-multigrid technique for nonlinear parabolic boundary control problems
H.
Goldberg
F.
Tröltzsch
510
510
optimal control
semilinear parabolic equation
multigrig method
SQP method
MSC 49M40
MSC 49M05
An optimal control problem governed by the heat equation with nonlinear boundary
conditions is considered. The objective functional consists of a quadratic terminal
part and a quadratic regularization term. It is known, that an SQP method converges
quadratically to the optimal solution of the problem. To handle the quadratic optimal
control subproblems with high precision, very large scale mathematical programming
problems have to be treated. The constrained problem is reduced to an unconstrained
one by a method due to Bertsekas. A multigrid approach developed by Hackbusch is
applied to solve the unconstrained problems. Some numerical examples illustrate the
behaviour of the method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801210
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17497/zip/
urn:nbn:de:bsz:ch1-199801210
oai:qucosa:de:qucosa:17500
2021-03-29T09:32:26Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Ill-Posedness Aspects of Some Nonlinear Inverse Problems and their Linearizations
G.
Fleischer
B.
Hofmann
510
510
degree of ill-posedness
multiplication op erators
nonlinear inverse problems
parameter identification
MSC 65J20
MSC 47B38
In this paper we deal with aspects of
characterizing the ill-posedn ess of nonlinear
inverse problems based on the discussion of
specific examples. In particular, a parameter
identification problem to a second order
differential equation and its ill-posed
linear components are under consideration.
A new approach to the classification
ofill-posedness degrees for multiplication
operators completes the paper.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801242
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17500/zip/
urn:nbn:de:bsz:ch1-199801242
oai:qucosa:de:qucosa:17498
2021-03-29T09:32:24Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Lipschitz stability of solutions to linear-quadratic parabolic control problems with respect to perturbations
F.
Tröltzsch
510
510
Boundary control
distributed control
linear parabolic equation
control constraints
Lipschitz continuity
supremum norm
MSC 49K20
MSC 49K40
We consider a class of control problems governed by a linear parabolic initial-boundary
value problem with linear-quadratic objective and pointwise constraints on the control.
The control system contains different types of perturbations. They appear in the
linear part of the objective functional, in the right hand side of the equation,
in its boundary condition, and in the initial value. Making use of parabolic regularity
in the whole scale of $L^p$ the known Lipschitz stability in the $L^2$-norm
is improved to the supremum-norm.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801229
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17498/zip/
urn:nbn:de:bsz:ch1-199801229
oai:qucosa:de:qucosa:17501
2021-03-29T09:32:26Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Simulation of Weakly Correlated Functions and its Application to Random Surfaces and Random Polynomials
Benno
Fellenberg
Jürgen vom
Scheidt
Matthias
Richter
510
510
stochastic simulation
random processes
random fields
weakly correlated functions
random polynomials
MSC 65C05
MSC 60G35
The paper is dedicated to the modeling and the
simulation of random processes and fields.
Using the concept and the theory of weakly
correlated functions a consistent representation
of sufficiently smooth random processes
will be derived. Special applications will be
given with respect to the simulation of road
surfaces in vehicle dynamics and to the
confirmation of theoretical results with
respect to the zeros of random polynomials.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801258
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17501/zip/
urn:nbn:de:bsz:ch1-199801258
oai:qucosa:de:qucosa:17499
2021-03-29T09:32:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Estimates for the condition numbers of large semi-definite Toeplitz matrices
A.
Böttcher
S. M.
Grudsky
510
510
Toeplitz operator
Toeplitz matrices
singular values
eigenvalues
Wiener-Hopf
MSC 47B35
This paper is devoted to asymptotic estimates for the condition numbers
$\kappa(T_n(a))=||T_n(a)|| ||T_n^(-1)(a)||$
of large $n\cross n$ Toeplitz matrices $T_N(a)$ in the case where
$\alpha \element L^\infinity$ and $Re \alpha \ge 0$ . We describe several classes
of symbols $\alpha$ for which $\kappa(T_n(a))$ increases like $(log n)^\alpha, n^\alpha$ ,
or even $e^(\alpha n)$ . The consequences of the results for singular values, eigenvalues,
and the finite section method are discussed. We also consider Wiener-Hopf integral
operators and multidimensional Toeplitz operators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801238
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17499/zip/
urn:nbn:de:bsz:ch1-199801238
oai:qucosa:de:qucosa:17502
2021-03-29T09:32:27Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Asymptotic Expansions for Second-Order Moments of Integral Functionals of Weakly Correlated Random Functions
Jrgen vom
Scheidt
Hans-Jrg
Starkloff
Ralf
Wunderlich
510
510
asymptotic expansions
stationary random processes
weakly correlated functions
MSC 60G12
MSC 41A60
In the paper asymptotic expansions for
second-order moments of integral functionals
of a class of random functions are considered.
The random functions are assumed to be
$\epsilon$-correlated, i.e. the values are not
correlated excluding a $\epsilon$-neighbourhood
of each point. The asymptotic expansions are
derived for $\epsilon \to 0$. With the help of
a special weak assumption there are found
easier expansions as in the case of general
weakly correlated functions.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801269
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17502/zip/
urn:nbn:de:bsz:ch1-199801269
oai:qucosa:de:qucosa:17503
2021-03-29T09:32:28Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the analytic representation of the correlation function of linear random vibration systems
J.
Gruner
J. vom
Scheidt
R.
Wunderlich
510
510
random vibrations
correlation function
asymptotic expansion
weakly correlated random function
MSC 70L05
MSC 60G10
This paper is devoted to the computation of statistical characteristics of
the response of discrete vibration systems with a random external excitation.
The excitation can act at multiple points and is modeled by a time-shifted
random process and its derivatives up to the second order. Statistical characteristics
of the response are given by expansions as to the correlation length
of a weakly correlated random process which is used in the excitation model.
As the main result analytic expressions of some integrals involved in the expansion terms are derived.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801272
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17503/zip/
urn:nbn:de:bsz:ch1-199801272
oai:qucosa:de:qucosa:17504
2021-03-29T09:32:29Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Local theory of projection methods for Cauchy singular integral equations on an interval
P.
Junghanns
U.Weber
510
510
Cauchy singular integral equation
projection methods
stability
MSC 45E05
MSC 45L10
We consider a finite section (Galerkin) and a collocation method for Cauchy singular
integral equations on the interval based on weighted Chebyshev polymoninals, where
the coefficients of the operator are piecewise continuous.
Stability conditions are derived using Banach algebra techniques, where
also the system case is mentioned. With the help of
appropriate Sobolev spaces a result on convergence rates is proved.
Computational aspects are discussed in order to develop
an effective algorithm. Numerical results, also
for a class of nonlinear singular integral equations,
are presented.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801281
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17504/zip/
urn:nbn:de:bsz:ch1-199801281
oai:qucosa:de:qucosa:17509
2021-03-29T09:32:33Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
FEM auf irregulären hierarchischen Dreiecksnetzen
U.
Groh
510
510
PDE
FEM
triangular mesh
hierarchical refinement
elliptic model
BPX
Yserentant
precondition
domain decomposition
MSC 65N30
From the viewpoint of the adaptive solution of partial differential equations a finit
e element method on hierarchical triangular meshes is developed permitting hanging nodes
arising from nonuniform hierarchical refinement.
Construction, extension and restriction of the nonuniform hierarchical basis and the
accompanying mesh are described by graphs. The corresponding FE basis is generated by
hierarchical transformation. The characteristic feature of the generalizable concept is the
combination of the conforming hierarchical basis for easily defining and changing the FE
space with an accompanying nonconforming FE basis for the easy assembly of a FE
equations system. For an elliptic model the conforming FEM problem is solved by an iterative
method applied to this nonconforming FEM equations system and modified by
projection into the subspace of conforming basis functions. The iterative method used is the
Yserentant- or BPX-preconditioned conjugate gradient algorithm.
On a MIMD computer system the parallelization by domain decomposition is easy and
efficient to organize both for the generation and solution of the equations system and for
the change of basis and mesh.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801330
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17509/zip/
urn:nbn:de:bsz:ch1-199801330
oai:qucosa:de:qucosa:17505
2021-03-29T09:32:30Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Multiplication operators and its ill-posedness properties
G.Fleischer
510
510
ill-posed
multiplication operator
MSC 47B38
MSC 65J20
This paper deals with the characterization of multiplication operators,
especially with its behavior in the ill-posed case.
We want to classify the different types and degrees of ill-posedness. We give
some connections between this classification and regularization methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801292
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17505/zip/
urn:nbn:de:bsz:ch1-199801292
oai:qucosa:de:qucosa:17506
2021-03-29T09:32:30Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A new method for computing the stable invariant subspace of a real Hamiltonian matrix or Breaking Van Loans curse?
P.
Benner
V.
Mehrmann
H.
Xu.
510
510
MSC 65F15
A new backward stable, structure preserving method of complexity
O(n^3) is presented for computing the stable invariant subspace of
a real Hamiltonian matrix and the stabilizing solution of the
continuous-time algebraic Riccati equation. The new method is based
on the relationship between the invariant subspaces of the
Hamiltonian matrix H and the extended matrix /0 H\ and makes use
\H 0/
of the symplectic URV-like decomposition that was recently
introduced by the authors.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801309
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17506/zip/
urn:nbn:de:bsz:ch1-199801309
oai:qucosa:de:qucosa:17510
2021-03-29T09:32:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Interpolation of non-smooth functions on anisotropic finite element meshes
Th.
Apel
510
510
anisotropic weighted Sobolev spaces
local interpolation error,estimates.
MSC 35A40
MSC 35J05
MSC 65N30
MSC 35B65
In this paper, several modifications of the quasi-interpolation operator
of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed.
The modified operators are defined for non-smooth functions and are suited
for the application on anisotropic meshes. The anisotropy of the elements
is reflected in the local stability and approximation error estimates.
As an application, an example is considered where anisotropic finite element
meshes are appropriate, namely the Poisson problem in domains with edges.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801341
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17510/zip/
urn:nbn:de:bsz:ch1-199801341
oai:qucosa:de:qucosa:17507
2021-03-29T09:32:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Rank-revealing top-down ULV factorizations
B.
Benhammouda
510
510
MSC 65F15
Rank-revealing ULV and URV factorizations are useful tools to determine the rank and to compute bases for null-spaces of a matrix. However, in the practical ULV (resp. URV ) factorization each left (resp. right) null vector is recomputed from its corresponding right (resp. left) null vector via triangular solves. Triangular solves are required at initial factorization, refinement and updating. As a result, algorithms based on these factorizations may be expensive, especially on parallel computers where triangular solves are expensive. In this paper we propose an alternative approach. Our new rank-revealing ULV factorization, which we call ¨top-down¨ ULV factorization ( TDULV -factorization) is based on right null vectors of lower triangular matrices and therefore no triangular solves are required. Right null vectors are easy to estimate accurately using condition estimators such as incremental condition estimator (ICE). The TDULV factorization is shown to be equivalent to the URV factorization with the advantage of circumventing triangular solves.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801313
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17507/zip/
urn:nbn:de:bsz:ch1-199801313
oai:qucosa:de:qucosa:17511
2021-03-29T09:32:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges
Th.
Apel
S.
Nicaise
510
510
MSC 65N30
This paper is concerned with a specific finite element strategy for solving elliptic boundary value problems in domains with corners and edges. First, the anisotropic singular behaviour of the solution is described. Then the finite element method with anisotropic, graded meshes and piecewise linear shape functions is investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates for functions from anisotropically weighted spaces are derived. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801355
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17511/zip/
urn:nbn:de:bsz:ch1-199801355
oai:qucosa:de:qucosa:17508
2021-03-29T09:32:32Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Convergence of Asynchronous Jacobi-Newton-Iterations
U.
Schrader
510
510
convergence
asynchronous Jacobi-Newton-iterations
nonlinear
equations
MSC 65H10
Asynchronous iterations often converge under different conditions than their syn- chronous counterparts. In this paper we will study the global convergence of Jacobi- Newton-like methods for nonlinear equationsF x = 0. It is a known fact, that the synchronous algorithm converges monotonically, ifF is a convex M-function and the starting valuesx0 andy0 meet the conditionF x04 04F y0 . In the paper it will be shown, which modifications are necessary to guarantee a similar convergence behavior for an asynchronous computation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801324
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17508/zip/
urn:nbn:de:bsz:ch1-199801324
oai:qucosa:de:qucosa:17512
2021-03-29T09:32:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Nutzung von MPI für parallele FEM-Systeme
L.
Grabowsky
Th.
Ermer
J.
Werner
004
004
MPI
FEM
MSC 65Y05
MSC 65N30
Der Standard des Message Passing Interfaces (MPI) stellt dem Entwickler paralleler Anwendungen ein mächtiges Werkzeug zur Verfügung, seine Softwa- re effizient und weitgehend unabhängig von Details des parallelen Systems zu entwerfen.
Im Rahmen einer Projektarbeit erfolgte die Umstellung der Kommunikationsbibliothek eines bestehenden FEM-Programmes auf den MPI-Mechanismus. Die Ergebnisse werden in der hier gegebenen Beschreibung der Cubecom-Implementierung zusammengefasst.
In einem zweiten Teil dieser Arbeit wird untersucht, auf welchem Wege mit der in MPI verfügbaren Funktionalität auch die Koppelrandkommunikation mit einem einheitlichen und effizienten Verfahren durchgeführt werden kann.
Sowohl fuer die Basisimplementierung als auch die MPI-basierte Koppelrandkommunikation wird die Effizienz untersucht und ein Ausblick auf weitere Anwendungsmoeglichkeiten gegeben.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801365
ger
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17512/zip/
urn:nbn:de:bsz:ch1-199801365
oai:qucosa:de:qucosa:17513
2021-03-29T09:32:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:530
openaire
Monte-Carlo Simulations of the Dynamical Behavior of the Coulomb Glass
T.
Wappler
Th.
Vojta
M.
Schreiber
530
530
Monte-Carlo simulations
MSC 65C05
MSC 65Y05
We study the dynamical behavior of disordered many-particle systems
with long-range Coulomb interactions by means of damage-spreading
simulations. In this type of Monte-Carlo simulations one investigates the
time evolution of the damage, i.e. the difference of the o ccupation
numbers of two systems, subjected to the same thermal noise. We analyze
the dependence of the damage on temperature and disorder strength. For
zero disorder the spreading transition coincides with the equilibrium phase
transition, whereas for finite disorder, we find an evidence for a dynamical
phase transition well below the transition temperature of the pure system.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801378
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17513/zip/
urn:nbn:de:bsz:ch1-199801378
oai:qucosa:de:qucosa:17518
2021-03-29T09:32:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Parallel Multilevel Preconditioners for Problems of Thin Smooth Shells
M.
Thess
510
510
004
004
thin shell problems
linear partial differential equations
parallel computing
multilevel methods
additive splittings
finite element methods
cooling towers
MSC 65Y05
In the last years multilevel preconditioners like BPX became more and more
popular for solving second-order elliptic finite element discretizations by iterative
methods. P. Oswald has adapted these methods for discretizations of the fourth
order biharmonic problem by rectangular conforming Bogner-Fox-Schmidt elements
and nonconforming Adini elements and has derived optimal estimates for the
condition numbers of the preconditioned linear systems. In this paper we generalize
the results from Oswald to the construction of BPX and Multilevel Diagonal
Scaling (MDS-BPX) preconditioners for the elasticity problem of thin smooth shells of
arbitrary forms where we use Koiter's equations of equilibrium for an homogeneous
and isotropic thin shell, clamped on a part of its boundary and loaded by a
resultant on its middle surface. We use the two discretizations mentioned above and the
preconditioned conjugate gradient method as iterative method. The parallelization
concept is based on a non-overlapping domain decomposition data structure. We
describe the implementations of the multilevel preconditioners. Finally, we show
numerical results for some classes of shells like plates, cylinders, and hyperboloids.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801416
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17518/zip/
urn:nbn:de:bsz:ch1-199801416
oai:qucosa:de:qucosa:17514
2021-03-29T09:32:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Behandlung gekrümmter Oberflächen in einem 3D-FEM-Programm für Parallelrechner
M.
Pester
510
510
004
004
finite element meshes
curved surfaces
mesh refinement
parallel computing
MSC 65Y05
MSC 65N30
The paper presents a method for generating curved
surfaces of 3D finite element meshes by mesh
refinement starting with a very coarse grid.
This is useful for parallel implementations where
the finest meshes should be computed and not read from
large files. The paper deals with simple geometries
as sphere, cylinder, cone. But the method may be
extended to more complicated geometries.
(with 45 figures)
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801386
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17514/zip/
urn:nbn:de:bsz:ch1-199801386
oai:qucosa:de:qucosa:17519
2021-03-29T09:32:41Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:530
openaire
The two-dimensional Anderson model of localization with random hopping
A.
Eilmes
R. A.
Römer
M.
Schreiber
530
530
Hamiltonian
Anderson
eigenstates
multifractal
MSC 60K40
We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in the center of the band which show critical behavior up to the system size N=200x200 considered. This result is confirmed by an independent analysis of the localization lengths in quasi-1D strips with the help of the transfermatrix method. Adding a very small additional onsite potential disorder, the critical states become localized.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801429
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17519/zip/
urn:nbn:de:bsz:ch1-199801429
oai:qucosa:de:qucosa:17516
2021-03-29T09:32:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The hierarchical preconditioning having unstructured grids
G.
Globisch
S. V.
Nepomnyaschikh
510
510
partial differential equations
parallel computing
multilevel methods
hierarchical preconditioning
finite element methods
automatical grid generation
MSC 65N55
MSC 65N22
MSC 65N22
MSC 78A30
In this paper we present two hierarchically preconditioned methods for the fast solution of mesh equations that approximate 2D-elliptic boundary value problems on unstructured quasi uniform triangulations. Based on the fictitious space approach the original problem can be embedded into an auxiliary one, where both the hierarchical grid information and the preconditioner by decomposing functions on it are well defined. We implemented the corresponding Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration having optimal computational costs. Several numerical examples demonstrate the efficiency of the artificially constructed hierarchical methods which can be of importance in the industrial engineering, where often only the nodal coordinates and the element connectivity of the underlying (fine) discretization are available.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801398
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17516/zip/
urn:nbn:de:bsz:ch1-199801398
oai:qucosa:de:qucosa:17520
2021-03-29T09:32:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
ddc:530
openaire
Some Remarks on the Constant in the Strengthened C.B.S. Inequality: Application to $h$- and $p$-Hierarchical Finite Element Discretizations of Elasticity Problems
M.
Jung
J. F.
Maitre
530
530
510
510
finite elements
elasticity problems
hierarchical methods
multilevel methods
MSC 65N30
MSC 65F10
MSC 65N55
MSC 73C02
For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h -hierarchical and p -hierarchical finite element discretizations with triangular meshes differ by the factor 0.75.
For plane linear elasticity problems and triangulations with right isosceles tri- angles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements.
Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801431
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17520/zip/
urn:nbn:de:bsz:ch1-199801431
oai:qucosa:de:qucosa:17517
2021-03-29T09:32:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:530
openaire
The Mott-Anderson transition in the disordered one-dimensional Hubbard model
R. V.
Pai
A.
Punnoose
R. A.
Römer
530
530
matrix renormalization
Hubbard,
MSC 60K40
We use the density matrix renormalization group to study the quantum
transitions that occur in the half-filled one-dimensional fermionic Hubbard
model with onsite potential disorder. We find a transition from the gapped
Mott phase with algebraic spin correlations to a gapless spin-disordered phase
beyond a critical strength of the disorder 1 c ss U= 2. Both the transitions in
the charge and spin sectors are shown to be coincident. We also establish the
finite-size corrections to the charge gap and the spin-spin correlation length
in the presence of disorder and using a finite-size-scaling analysis we obtain
the zero temperature phase diagram of the various quantum phase transitions
that occur in the disorder-interaction plane.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801405
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17517/zip/
urn:nbn:de:bsz:ch1-199801405
oai:qucosa:de:qucosa:17521
2021-03-29T09:32:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Error Estimation for Anisotropic Tetrahedral and Triangular Finite Element Meshes
G.
Kunert
510
510
finite elements
error estimator
anisotropic solution,
MSC 65N30
MSC 65N15
MSC 35B25
Some boundary value problems yield anisotropic solutions, e.g. solutions
with boundary layers. If such problems are to be solved with the finite
element method (FEM), anisotropically refined meshes can be
advantageous.
In order to construct these meshes or to control the error
one aims at reliable error estimators.
For \emph{isotropic} meshes many estimators are known, but they either fail
when used on \emph{anisotropic} meshes, or they were not applied yet.
For rectangular (or cuboidal) anisotropic meshes a modified
error estimator had already been found.
We are investigating error estimators on anisotropic tetrahedral or
triangular meshes because such grids offer greater geometrical flexibility.
For the Poisson equation a residual error estimator, a local Dirichlet problem
error estimator, and an $L_2$ error estimator are derived, respectively.
Additionally a residual error estimator is presented for a singularly
perturbed reaction diffusion equation.
It is important that the anisotropic mesh corresponds to the anisotropic
solution. Provided that a certain condition is satisfied, we have proven
that all estimators bound the error reliably.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801440
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17521/zip/
urn:nbn:de:bsz:ch1-199801440
oai:qucosa:de:qucosa:17522
2021-03-29T09:32:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
MPI-basierte Koppelrandkommunikation und Einfluß der Partitionierung im 3D-Fall
L.
Grabowsky
004
004
Koppelrandkommunikation
FEM
MSC 68M10
MSC 68Q22
In der vorliegenden Arbeit wird die Anwendung eines bereits im 2D-Fall benutzten Mechanismus zur MPI-basierten Koppelrandkommunikation auf das 3D-FEM-System SPC PMPo-3D beschrieben. Insbesondere soll der Einfluss der Partitionierung auf die Laufzeit im Vergleich mit den Resultaten für das Originalsystem, fuer das entsprechende Untersuchungen bereits in durchgefuehrt wurden, betrachtet werden. Weiterhin wird ein Ausblick auf weitere Optimierungsmöglichkeiten des Verfahrens gegeben.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801453
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17522/zip/
urn:nbn:de:bsz:ch1-199801453
oai:qucosa:de:qucosa:17523
2021-03-29T09:32:44Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:530
openaire
Weak delocalization due to long-range interaction for two electrons in a random potential chain
R. A.
Römer
M.
Schreiber
530
530
random potential chain
Hubbard
weak delocalization
MSC 60K40
We study two interacting particles in a random potential chain by a transfer matrix method which allows a correct handling of the symmetry of the two- particle wave function, but introduces an artificial ¨bag¨ interaction. The dependence of the two-particle localization length lambta 2on disorder, interaction strength and range is investigated. Our results demonstrate that the recently proposed enhancement of lambta 2 as compared to the results for single particles is vanishingly small for a Hubbard interaction. For longer-range interactions, we observe a small enhancement but with a different disorder dependence than proposed previously.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1998-10-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199801462
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17523/zip/
urn:nbn:de:bsz:ch1-199801462
oai:qucosa:de:qucosa:17536
2021-03-29T09:32:55Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Hamiltonian eigenvalue symmetry for quadratic operator eigenvalue problems
Cornelia
Pester
510
510
Nichtlineares Eigenwertproblem
Operatorbüschel
Spektraltheorie
Hamiltonian eigenvalue symmetry
operator pencil
When the eigenvalues of a given eigenvalue problem are symmetric with respect to the real and the imaginary axes, we speak about a Hamiltonian eigenvalue symmetry or a Hamiltonian structure of the spectrum. This property can be exploited for an efficient computation of the eigenvalues. For some elliptic boundary value problems it is known that the derived eigenvalue problems have this Hamiltonian symmetry. Without having a specific application in mind, we trace the question, under which assumptions the spectrum of a given quadratic eigenvalue problem possesses the Hamiltonian structure.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601470
Preprintreihe des Chemnitzer SFB 393, 04-09
eng
Preprintreihe des Chemnitzer SFB 393, 04-09
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17536/zip/
urn:nbn:de:swb:ch1-200601470
oai:qucosa:de:qucosa:17535
2021-03-29T09:32:54Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Beschreibung des Sicherheitssystems im MONARCH
Holger
Trinks
Bert
Auerbach
004
004
Sicherheit
PGP
Hash-Algorithmus
Elektronische Unterschrift
MONARCH
Das Dokument beschreibt in kurzer Form das Sicherheitskonzept
im Archivsystem MONARCH.Die archivierten Dokumente werden
durch verschiedene Hash-Algorithmen und digitale
Signaturen vor nachträglichen Veränderungen geschützt. Dadurch
kann dem Benutzer von MONARCH die Unversehrtheit der archivierten
Publikationen garantiert werden.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1999-02-10
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199900042
ger
info:eu-repo/semantics/openAccess
14
https://monarch.qucosa.de/api/qucosa%3A17535/zip/
urn:nbn:de:bsz:ch1-199900042
oai:qucosa:de:qucosa:17555
2021-03-29T09:33:10Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:670
openaire
Eine neuartige vollmechanisierte Schweißanlage für die Sanierung von Heizflächen in Kraftwerks- und Müllverbrennungsanlagen
K.-J.
Matthes
Prof. Dr.-Ing. habil.
Thomas
Kohler
Dipl.-Ing.
Sören
Heitz
Dipl.-Ing.
670
670
Schweißen
Heizkessel
Auftragschweißen
Automatisierung
Wärmetauscher
Zur Sanierung von Heizflächen in Kraftwerks- und Müllverbrennungsanlagen ist das
Auftragschweißen eine bewährte Methode. Dazu wurde von der
DH Schweißtechnologie & Service Hohenthurm GmbH & Co. KG in Zusammenarbeit mit der
Technischen Universität Chemnitz eine neue vollmechanisierte Schweißanlage
entwickelt. Durch das Anlagenkonzept ergeben sich neue technologische
Möglichkeiten sowie Qualitätsverbesserungen der aufgetragenen Schichten und eine
Reduzierung der Fertigungszeit.
Weld overlay is a proven method for refurbishing boiler tubes in power plants and
sewage sludge burning plants.
DH Schweisstechnologie & Service Hohenthurm GmbH & Co. KG in cooperation with
the University of Technology Chemnitz developed a new automatic welding with
different welding alloys, different thicknesses and coating structures under any
adjusted to the operating condition of the boiler.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
1999-06-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-199900340
ger
info:eu-repo/semantics/openAccess
7
https://monarch.qucosa.de/api/qucosa%3A17555/zip/
urn:nbn:de:bsz:ch1-199900340
oai:qucosa:de:qucosa:17557
2021-03-29T09:33:12Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign Function
Sergio
Barrachina
Peter
Benner
Enrique S.
Quintana-Ortí
510
510
Kontrolltheorie
Matrixproblem
Parallelrechner
Bernoulli equation
control and system theory
matrix sign function
We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601684
Preprintreihe des Chemnitzer SFB 393, 05-15
eng
Preprintreihe des Chemnitzer SFB 393, 05-15
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A17557/zip/
urn:nbn:de:swb:ch1-200601684
oai:qucosa:de:qucosa:17580
2021-03-29T09:33:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh construction and error estimation in the finite element method
Gerd
Kunert
510
510
adaptive algorithm,
finite element,
anisotropic mesh,
anisotropic function,
error estimation,
Hessian
In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh.
However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators.
Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error.
The focus of this paper is on error estimation on anisotropic meshes.
It is known that such error estimation is reliable and efficient only
if the anisotropic mesh is aligned with the anisotropic solution.
The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution.
The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form.
Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2000-01-13
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200000033
eng
info:eu-repo/semantics/openAccess
18
https://monarch.qucosa.de/api/qucosa%3A17580/zip/
urn:nbn:de:bsz:ch1-200000033
oai:qucosa:de:qucosa:17642
2021-03-29T09:34:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Anisotropic mesh construction and error estimation in the finite element method
Gerd
Kunert
510
510
adaptive algorithm
finite element
anisotropic mesh
anisotropic function
error estimation
Hessian
In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh. However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators. Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error.
The focus of this paper is on error estimation on anisotropic meshes. It is known that such error estimation is reliable and efficient only if the anisotropic mesh is aligned with the anisotropic solution.
The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution. The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form. Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2000-07-27
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200000664
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17642/zip/
urn:nbn:de:bsz:ch1-200000664
oai:qucosa:de:qucosa:17660
2021-03-29T09:34:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Robust a posteriori error estimation for a singularly perturbed reaction-diffusion equation on anisotropic tetrahedral meshes
Gerd
Kunert
510
510
004
004
error estimator
anisotropic solution
stretched elements
reaction diffusion equation
singularly perturbed problem
We consider a singularly perturbed reaction-diffusion problem and
derive and rigorously analyse an a posteriori residual error
estimator that can be applied to anisotropic finite element meshes.
The quotient of the upper and lower error bounds is the so-called
matching function which depends on the anisotropy (of the
mesh and the solution) but not on the small perturbation parameter.
This matching function measures how well the anisotropic finite
element mesh corresponds to the anisotropic problem.
Provided this correspondence is sufficiently good, the matching
function is O(1).
Hence one obtains tight error bounds, i.e. the error estimator
is reliable and efficient as well as robust with respect to the
small perturbation parameter.
A numerical example supports the anisotropic error analysis.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2000-11-09
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200000867
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17660/zip/
urn:nbn:de:bsz:ch1-200000867
oai:qucosa:de:qucosa:17668
2021-03-29T09:34:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes
Gerd
Kunert
510
510
error estimator
anisotropic solution
stretched elements
reaction diffusion
singularly perturbed problem equation
Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation.
To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly in the small perturbation parameter.
The error estimation is efficient, i.e. a lower error bound holds. The error estimator is also reliable, i.e. an upper error bound holds, provided that the anisotropic mesh discretizes the problem sufficiently well.
A numerical example supports the analysis of our anisotropic error estimator.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-01-03
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100011
eng
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A17668/zip/
urn:nbn:de:bsz:ch1-200100011
oai:qucosa:de:qucosa:17672
2021-03-29T09:34:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A note on the energy norm for a singularly perturbed model problem
Gerd
Kunert
510
510
singularly perturbed problem
reaction diffusion equation
adaptive algorithm
error estimator
A singularly perturbed reaction-diffusion model problem is considered, and the choice of an appropriate norm is discussed. Particular emphasis is given to the energy norm. Certain prejudices against this norm are investigated and disproved. Moreover, an adaptive finite element algorithm is presented which exhibits an optimal error decrease in the energy norm in some simple numerical experiments. This underlines the suitability of the energy norm.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-01-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100062
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17672/zip/
urn:nbn:de:bsz:ch1-200100062
oai:qucosa:de:qucosa:17728
2021-03-29T09:35:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
ddc:510
openaire
Zienkiewicz-Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes
Gerd
Kunert
Serge
Nicaise
510
510
004
004
anisotropic mesh
error estimator
Zienkiewicz-Zhu estimator
recovered gradient
We consider a posteriori error estimators that can be applied to anisotropic tetrahedral finite element meshes, i.e. meshes where the aspect ratio of the elements can be arbitrarily large.
Two kinds of Zienkiewicz-Zhu (ZZ) type error estimators are derived which are both based on some recovered gradient. Two different, rigorous analytical approaches yield the equivalence of both ZZ error estimators to a known residual error estimator. Thus reliability and efficiency of the ZZ error estimation is obtained. Particular attention is paid to the requirements on the anisotropic mesh.
The analysis is complemented and confirmed by several numerical examples.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-07-10
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100599
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17728/zip/
urn:nbn:de:bsz:ch1-200100599
oai:qucosa:de:qucosa:17740
2021-03-29T09:35:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A posteriori H^1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes
Gerd
Kunert
510
510
error estimator
H^1 seminorm
anisotropic mesh
reaction diffusion equation
singularly perturbed problem
The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H^1 seminorm that can be applied to anisotropic finite element meshes.
A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably.
Furthermore three modifications of these estimators are introduced and discussed.
Numerical experiments for all estimators complement and confirm the theoretical results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2001-08-24
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200100730
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17740/zip/
urn:nbn:de:bsz:ch1-200100730
oai:qucosa:de:qucosa:17783
2021-03-29T09:36:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Grundgleichungen und adaptive Finite-Elemente-Simulation bei "Großen Deformationen"
Basic Equations and adaptive Finite Element Simulation on 'Large Deformations'
Arnd
Meyer
510
510
Deformation <Mathematik>
Fehlerabschätzung
Finite-Elemente-Methode
Simulation
large deformations
Eine einfache Darstellung der Grundgleichungen für
'Große Deformationen' und Herleitung eines geeigneten
Fehlerschätzers für die adaptive FEM.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-27
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701960
ger
Chemnitz Scientific Computing Preprints ; 07-02
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A17783/zip/
urn:nbn:de:bsz:ch1-200701960
oai:qucosa:de:qucosa:17803
2021-03-29T09:36:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A posteriori error estimation for convection dominated problems on anisotropic meshes
Gerd
Kunert
510
510
error estimator
anisotropic solution
stretched elements
convection diffusion equation
singularly perturbed problem
A singularly perturbed convection-diffusion problem in two and three space dimensions is discretized using the streamline upwind Petrov Galerkin (SUPG) variant of the finite element method. The dominant convection frequently gives rise to solutions with layers; hence anisotropic finite elements can be applied advantageously.
The main focus is on a posteriori energy norm error estimation that is robust in the perturbation parameter and with respect to the mesh anisotropy. A residual error estimator and a local problem error estimator are proposed and investigated.
The analysis reveals that the upper error bound depends on the alignment of the anisotropies of the mesh and of the solution. Hence reliable error estimation is possible for suitable anisotropic meshes. The lower error bound depends on the problem data via a local mesh Peclet number. Thus efficient error estimation is achieved for small mesh Peclet numbers.
Altogether, error estimation approaches for isotropic meshes are successfully extended to anisotropic elements. Several numerical experiments support the analysis.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2002-03-22
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200200255
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17803/zip/
urn:nbn:de:bsz:ch1-200200255
oai:qucosa:de:qucosa:17816
2021-03-29T09:36:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:620
ddc:621.3
openaire
Schweißen per Mausklick
Thomas
Kohler
Mario
Kusch
620
620
Ablaufsteuerung
PC-Steuerung
Softwaresteuerung
Hybridschweißen
Plasma-MIG-Schweißen
Für den Plasma-MIG-Schweißprozess wurde exemplarisch eine Ablaufsteuerung auf PC-Basis entwickelt, welche flexibel innerhalb kürzester Zeit umgestellt, weiterentwickelt und damit geänderten Anforderungen schnellstmöglich angepasst werden kann. Aufgrund einheitlicher Schnittstellen ist ein Anschluss anderer Verfahren/Hybridverfahren jederzeit unkompliziert möglich.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2002-05-03
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200200370
ger
info:eu-repo/semantics/openAccess
9
https://monarch.qucosa.de/api/qucosa%3A17816/zip/
urn:nbn:de:bsz:ch1-200200370
oai:qucosa:de:qucosa:17861
2021-03-29T09:37:22Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:620
ddc:621.3
openaire
A Method For Modifying Segmented Human Voxel Models
Dr.Bernd
Heide
620
620
Voxel model
Surface deformation
Voxel fitting
Fine adjustment of voxel volume
A method for modifying segmented human voxel models is depicted. The method is a practical approach to set
up voxel models for dose calculations in medical physics. It could also be applied in other fields requiring human
voxel models. The basic strategy of the method is: 1. Generate triangulated surfaces from voxel representations
of the objects (organs, bones, or tissues) of a segmented human voxel model. 2. Perform surface deformations
and/or rearrangements. 3. Reconstruct voxel representations from the triangulated surfaces and put them back
into the segmented human voxel model. The voxel volume of the modified organs can be adjusted up to the
volume of half a voxel. The practicability of the method is demonstrated by means of the spleen of a leukaemia
patient.
Es wird eine praktische Methode zum Verändern von segmentierten
menschlichen Voxel-Modellen dargelegt. Die Methode kann in der
Medizinphysik im Zusammenhang mit Strahlendosisberechnungen
angewendet werden. Sie kann jedoch auch in
anderen Gebieten benutzt werden, bei denen menschliche Voxel-Modelle zur
Anwendung kommen. Die grundlegende Strategie
der Methode besteht aus den folgenden Schritten: 1. Erzeugung
triangulierter
Oberflächen aus Objekten (Organen, Knochen, Geweben) eines segmentierten
menschlichen Voxel-Modells. 2. Durchführung interaktiver
Oberflächendeformationen und/oder
Verschiebungen. 3. Re-Überführung der triangulierten Oberflächen in
Voxel-Darstellungen der Organe und Rückschreibung in das
segmentierte menschliche Voxel-Modell. Das Voxel-Volumen der
modifizierten
Organe kann mindestens bis auf ein halbes Voxel
genau eingestellt werden. Die Anwendbarkeit der Methode wird anhand der
Milz
einer Leukämie-Patientin demonstriert.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2002-07-01
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200200823
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A17861/zip/
urn:nbn:de:bsz:ch1-200200823
oai:qucosa:de:qucosa:17935
2021-03-29T09:38:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
An Asymptotic Approach to Progressive Censoring
Asymptotics for Progressive Censoring
Glenn
Hofmann
Erhard
Cramer
N.
Balakrishnan
Gerd
Kunert
510
510
Order statistics
best linear estimation
extreme value distribution
generalized
variance
optimal censoring scheme
progressive censoring
Weibull distribution
normal distribution
Progressive Type-II censoring was introduced by Cohen (1963) and has since been
the topic of much research. The question stands whether it is sensible to use this
sampling plan by design, instead of regular Type-II right censoring. We introduce
an asymptotic progressive censoring model, and find optimal censoring schemes for
location-scale families. Our optimality criterion is the determinant of the 2x2 covariance
matrix of the asymptotic best linear unbiased estimators. We present an explicit
expression for this criterion, and conditions for its boundedness. By means of numerical
optimization, we determine optimal censoring schemes for the extreme value,
the Weibull and the normal distributions. In many situations, it is shown that these
progressive schemes significantly improve upon regular Type-II right censoring.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2002-12-10
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200201539
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17935/zip/
urn:nbn:de:bsz:ch1-200201539
oai:qucosa:de:qucosa:17956
2021-03-29T09:38:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A posteriori error estimation for the Stokes problem: Anisotropic and isotropic discretizations
A posteriori Fehlerschätzer für das Stokes Problem: Anisotrope und isotrope Diskretisierungen
Emmanuel
Creusé
Dr.
Gerd
Kunert
Dr.
Serge
Nicaise
Prof.
510
510
Stokes problem
anisotropic solution
error estimator
stretched elements
The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic error estimators fail.
Our analysis covers two- and three-dimensional domains, conforming and nonconforming discretizations as well as different elements.
This large variety of settings requires different approaches and results in different estimators. Furthermore many examples of finite element pairs that are covered by the analysis are presented.
Lower and upper error bounds form the main result with minimal assumptions on the elements. The lower error bound is uniform with respect to the mesh anisotropy with the exception of nonconforming 3D discretizations made of pentahedra or hexahedra. The upper error bound depends on a proper alignment of the anisotropy of the mesh which is a common feature of anisotropic error estimation.
In the special case of isotropic meshes, the results simplify, and upper and lower error bounds hold unconditionally. Some of the corresponding results seem to be novel (in particular for 3D domains), and cover element pairs of practical importance.
The numerical experiments confirm the theoretical predictions and show the usefulness of the anisotropic error estimators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2003-01-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200300057
eng
info:eu-repo/semantics/openAccess
4
https://monarch.qucosa.de/api/qucosa%3A17956/zip/
urn:nbn:de:bsz:ch1-200300057
oai:qucosa:de:qucosa:18288
2021-03-29T09:43:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:620
ddc:621.3
openaire
Modellierung, Reglerentwurf und Praxistest eines hochdynamischen MEMS-Präzisionsbeschleunigungssensors
Model Building, Control Design and Practical Tests of a high-dynamical MEMS Acceleration Sensor
Heiko
Wolfram
Dipl.-Ing.
620
620
Beschleunigungssensor
Identifikation
H-Infinity Control
MEMS
Mixed-Sensitivity Approach
This paper presents the development of building up a controlled MEMS acceleration sensor. The first samples have archived a resolution of better than 500 ug and a bandwidth of more than 200 Hz. A theoretical model is built from the physical principles of the complete sensor system, consisting of the MEMS sensor, the charge amplifier and the PWM driver for the sensor element. A reduced order model of the system is used to design a robust control with the Mixed-Sensitivity H-infinity Approach. Limitations for the control design are given since the system contains time delays and an unstable pole imposed by the electrostatic spring softening effect. The theoretical model might be inaccurate or lacks of completeness, because the parameters for the theoretical model building vary from sample to sample or might be not known. A new two-stage identification scheme is deployed to obtain directly the system parameters from the samples. The focus of this paper is the complete system development and identification process including practical tests in a DSP TI-TMS320C3000 environment with 12/14-bit A/D-D/A converters.
Der Artikel beschreibt die Entwicklungsschritte eines geregelten MEMS-Beschleunigungssensors. Die ersten Prototypen erreichten dabei eine Auflösung von weniger als 500 ug und eine Bandbreite von mehr als 200 Hz. Ein theoretisches Modell für den Reglerentwurf wird aus den physikalischen Zusammenhängen des Gesamtsystems, bestehend aus dem mechanischen Sensorelement, dem Ladungsverstärker und der PWM-Treiberstufe, gebildet. Für den Reglerentwurf wird der H-Infinity Mixed-Sensitivity Approach verwendet. Wegen Systemtotzeiten und dem Effekt der elektrostatischen Federerweichung sind Grenzen für die Wahl der Bandbreite zu beachten. Da Parameter für das theoretische Modell stark variieren oder schwer zu bestimmen sind, wird eine 2-Stufen-Identifikationsmethode vorgeschlagen, um ein Modell für den Reglerentwurf zu erhalten. Praktische Tests wurden mit einem DSP TI-TMS320C3000 mit 12/14-Bit A/D-D/A Wandlerstufen durchgeführt.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-04-05
2021-03-29
preprint
urn:nbn:de:swb:ch1-200500304
ger
info:eu-repo/semantics/openAccess
5
https://monarch.qucosa.de/api/qucosa%3A18288/zip/
urn:nbn:de:swb:ch1-200500304
oai:qucosa:de:qucosa:18347
2021-03-29T09:44:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Optimal Multilevel Extension Operators
Sergey V.
Nepomnyaschikh
510
510
Extension
Finite-Elemente-Methode
Operator
finite-element functions
multilevel decomposition
In the present paper we suggest the norm-preserving
explicit operator for the extension of
finite-element functions from boundaries of domains
into the inside. The construction of this operator
is based on the multilevel decomposition of
functions on the boundaries and on the equivalent
norm for this decomposition. The cost of the action
of this operator is proportional to the number of
nodes.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-05
2021-03-29
preprint
urn:nbn:de:swb:ch1-200500971
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18347/zip/
urn:nbn:de:swb:ch1-200500971
oai:qucosa:de:qucosa:18349
2021-03-29T09:44:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Hierarchically preconditioned parallel CG-solvers with and without coarse-matrix-solvers inside FEAP
Mathias
Meisel
Arnd
Meyer
510
510
Finite-Elemente-Methode
Implementation
Lineares System
Paralleler Algorithmus
hierarchical preconditioner
After some remarks on the parallel implementation of the Finite Element package FEAP, our realisation of the parallel CG-algorithm is sketched. From a technical point of view, a hierarchical preconditioner with and without additional global crosspoint preconditioning is presented. The numerical properties of this preconditioners are discussed and compared to a Schur-complement-preconditioning, using a wide range of data from computations on technical and academic examples from elasticity.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-07
2021-03-29
preprint
urn:nbn:de:swb:ch1-200500995
Preprintreihe des Chemnitzer SFB 393
eng
Preprintreihe des Chemnitzer SFB 393
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18349/zip/
urn:nbn:de:swb:ch1-200500995
oai:qucosa:de:qucosa:18350
2021-03-29T09:44:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Solving stable generalized Lyapunov equations with the matrix sign function
Peter
Benner
Enrique S.
Quintana-Ortí
510
510
Lineares System
Ljapunov-Gleichung
Ljapunov-Stabilitätstheorie
Systemtheorie
matrix sign function
We investigate the numerical solution of the stable generalized Lyapunov equation via the sign function method. This approach has already been proposed to solve standard Lyapunov equations in several publications. The extension to the generalized case is straightforward. We consider some modifications and discuss how to solve generalized Lyapunov equations with semidefinite constant term for the Cholesky factor. The basic computational tools of the method are basic linear algebra operations that can be implemented efficiently on modern computer architectures and in particular on parallel computers. Hence, a considerable speed-up as compared to the Bartels-Stewart and Hammarling's methods is to be expected. We compare the algorithms by performing a variety of numerical tests.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-07
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501005
Preprintreihe des Chemnitzer SFB 393
eng
Preprintreihe des Chemnitzer SFB 393
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18350/zip/
urn:nbn:de:swb:ch1-200501005
oai:qucosa:de:qucosa:18355
2021-03-29T09:44:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Anderson Model of Localization: A Challenge for Modern Eigenvalue Methods
Ulrich
Elsner
Volker
Mehrmann
Rudolf A.
Römer
Michael
Schreiber
510
510
Eigenwertproblem
Lanczos-Algorithmus
Anderson model of localization
Arnoldi algorithm
polynomial convergence accelerators
We present a comparative study of the application of modern eigenvalue algorithms to an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for the large, sparse, real, symmetric, and indefinite matrices of the Anderson model of localization. We compare the Lanczos algorithm in the 1987 implementation of Cullum and Willoughby with the implicitly restarted Arnoldi method coupled with polynomial and several shift-and-invert convergence accelerators as well as with a sparse hybrid tridiagonalization method. We demonstrate that for our problem the Lanczos implementation is faster and more memory efficient than the other approaches. This seemingly innocuous problem presents a major challenge for all modern eigenvalue algorithms.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-09
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501053
Preprintreihe des Chemnitzer SFB 393
eng
Preprintreihe des Chemnitzer SFB 393
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18355/zip/
urn:nbn:de:swb:ch1-200501053
oai:qucosa:de:qucosa:18351
2021-03-29T09:44:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A Multi-Grid Method for Generalized Lyapunov Equations
Thilo
Penzl
510
510
Algebraische Riccati-Gleichung
Lineares System
Ljapunov-Gleichung
Multi-level-Verfahren
Multi-grid method
We present a multi-grid method for a class of
structured generalized Lyapunov matrix equations.
Such equations need to be solved in each step of
the Newton method for algebraic Riccati equations,
which arise from linear-quadratic optimal control
problems governed by partial differential equations.
We prove the rate of convergence of the two-grid
method to be bounded independent of the dimension
of the problem under certain assumptions.
The multi-grid method is based on matrix-matrix
multiplications and thus it offers a great
potential for a parallelization. The efficiency
of the method is demonstrated by numerical
experiments.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-07
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501010
Preprintreihe des Chemnitzer SFB 393
eng
Preprintreihe des Chemnitzer SFB 393
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18351/zip/
urn:nbn:de:swb:ch1-200501010
oai:qucosa:de:qucosa:18356
2021-03-29T09:44:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Canonical forms for Hamiltonian and symplectic matrices and pencils
Volker
Mehrmann
Hongguo
Xu
510
510
Algebraische Riccati-Gleichung
Eigenwertproblem
Hamiltonian pencil (matrix)
Jordan canonical form
Kronecker canonical form
linear quadratic control
symplectic pencil (matrix)
We study canonical forms for Hamiltonian and
symplectic matrices or pencils under equivalence
transformations which keep the class invariant.
In contrast to other canonical forms our forms
are as close as possible to a triangular structure
in the same class. We give necessary and
sufficient conditions for the existence of
Hamiltonian and symplectic triangular Jordan,
Kronecker and Schur forms. The presented results
generalize results of Lin and Ho [17] and simplify
the proofs presented there.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-09
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501069
Preprintreihe des Chemnitzer SFB 393
eng
Preprintreihe des Chemnitzer SFB 393
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18356/zip/
urn:nbn:de:swb:ch1-200501069
oai:qucosa:de:qucosa:18352
2021-03-29T09:44:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The hierarchical preconditioning having unstructured threedimensional grids
Gerhard
Globisch
510
510
Finite-Elemente-Methode
Multi-level-Verfahren
Partielle Differentialgleichung
automatic mesh generation
hierarchical preconditioning
parallel computing
Continuing the previous work in the preprint 97-11 done for the 2D-approach in this paper we describe the Yserentant preconditioned conjugate gradient method as well as the BPX-preconditioned cg-iteration fastly solving 3D-elliptic boundary value problems on unstructured quasi uniform grids. These artificially constructed hierarchical methods have optimal computational costs. In the case of the sequential computing several numerical examples demonstrate their efficiency not depending on the finite element types used for the discretiziation of the original potential problem. Moreover, implementing the methods in parallel first results are given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-09
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501021
Preprintreihe des Chemnitzer SFB 393; Preprint SFB393/97-11
eng
Preprintreihe des Chemnitzer SFB 393; Preprint SFB393/97-11
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18352/zip/
urn:nbn:de:swb:ch1-200501021
oai:qucosa:de:qucosa:18357
2021-03-29T09:44:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Mappingstrategien für Kommunikatoren
Thomas
Ermer
004
004
Finite-Elemente-Methode
Kommunikation
MPI
Parallelrechner
Kommunikatoren
Kommunikatoren
Split-Algorithmus
Es werden Fragen der effektiven Kommunikation in parallelen FEM-Systemen behandelt. Durch geschickte Partitionierung des betrachteten Gebietes und Verteilung auf die vorhandenen Prozessoren kann man versuchen, die Kommunikationslast zu minimieren, z. B. mit dem Programmsystem chaco. Ein möglichst paralleler Datenaustausch wird durch Anordnung der Kommunikationsschritte in so genannten Linkleveln versucht. In der vorliegenden Arbeit wird ausgehend von der MPI-basierten Koppelrandkommunikation ein Split-Algorithmus vorgestellt, der versucht, die Koppelranddaten großer Kommunikatoren auf die kleinerer Sub-Kommunikatoren abzubilden und damit die Anzahl der zu übertragenden Datenpakete zu minimieren.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-12
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501073
Preprintreihe des Chemnitzer SFB 393, 98-10
ger
Preprintreihe des Chemnitzer SFB 393, 98-10
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18357/zip/
urn:nbn:de:swb:ch1-200501073
oai:qucosa:de:qucosa:18353
2021-03-29T09:44:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Schur-Like Forms for Matrix Lie Groups, Lie Algebras and Jordan Algebras
Gregory
Ammar
Christian
Mehl
Volker
Mehrmann
510
510
Jordan-Algebra
Lie-Algebra
Lie-Gruppe
Schur form
associated Lie algebra
We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transformations. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also discuss matrices in intersections of these classes and their Schur-like forms. Such multistructered matrices arise in applications from quantum physics and quantum chemistry.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-09
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501032
Preprintreihe des Chemnitzer SFB 393
eng
Preprintreihe des Chemnitzer SFB 393
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18353/zip/
urn:nbn:de:swb:ch1-200501032
oai:qucosa:de:qucosa:18358
2021-03-29T09:44:44Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Ein Standard-File für 3D-Gebietsbeschreibungen
Dag
Lohse
004
004
Dateiformat
Geometrische Topologie
Strukturierte Daten
Einleseroutine
Gebietsbeschreibung
Randrepräsentation
Es handelt sich hierbei um die Dokumentation eines Dateiformats zur Beschreibung dreidimensionaler FEM-Gebiete in Randrepräsentation. Eine interne Datenbasis dient als Verbindung zwischen externem Dateiformat und verschiedenen verarbeitenden Programmen.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-12
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501080
Preprintreihe des Chemnitzer SFB 393, 98-11
ger
Preprintreihe des Chemnitzer SFB 393, 98-11
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18358/zip/
urn:nbn:de:swb:ch1-200501080
oai:qucosa:de:qucosa:18354
2021-03-29T09:44:41Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Graph partitioning - a survey
Ulrich
Elsner
510
510
Graphentheorie
Partitionierung
mesh partitioning
multilevel graph partitioning
spectral bisection
Many problems appearing in scientific computing
and other areas can be formulated as a graph
partitioning problems. Examples include data
distribution for parallel computers, decomposition
of sparse matrices and VLSI-design.
In this survey we present the graph partitioning
problem, describe some applications and introduce
many of the algorithms used to solve the problem.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-09
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501047
Preprintreihe des Chemnitzer SFB 393
eng
Preprintreihe des Chemnitzer SFB 393
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18354/zip/
urn:nbn:de:swb:ch1-200501047
oai:qucosa:de:qucosa:18359
2021-03-29T09:44:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
DGRSVX and DMSRIC: Fortran 77 subroutines for solving continuous-time matrix algebraic Riccati equations with condition and accuracy estimates
P. Hr.
Petkov
M. M.
Konstantinov
V.
Mehrmann
510
510
Algebraische Riccati-Gleichung
FORTRAN-Programm
LAPACK
Schur method
matrix sign function method
We present new Fortran 77 subroutines which implement the Schur method and the
matrix sign function method for the solution of the continuoustime matrix algebraic
Riccati equation on the basis of LAPACK subroutines. In order to avoid some of
the wellknown difficulties with these methods due to a loss of accuracy, we combine
the implementations with block scalings as well as condition estimates and forward
error estimates. Results of numerical experiments comparing the performance of both
methods for more than one hundred well and illconditioned Riccati equations of order
up to 150 are given. It is demonstrated that there exist several classes of examples for
which the matrix sign function approach performs more reliably and more accurately
than the Schur method. In all cases the forward error estimates allow to obtain a reliable
bound on the accuracy of the computed solution.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-12
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501109
Preprintreihe des Chemnitzer SFB 393, 98-16
eng
Preprintreihe des Chemnitzer SFB 393, 98-16
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18359/zip/
urn:nbn:de:swb:ch1-200501109
oai:qucosa:de:qucosa:18360
2021-03-29T09:44:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Ein Standard-File für 3D-Gebietsbeschreibungen. - Datenbasis und Programmschnittstelle data_read
Dag
Lohse
004
004
Geometrische Modellierung
Strukturierte Daten
Datenbasis
Einleseroutine
Gebietsbeschreibung
Auf der Grundlage der in Preprint 98-11 dieser Reihe
gegebenen Dokumentation des Dateiformats wird hier
eine Programmschnittstelle beschrieben, die das
Einlesen solcher Gebietsdatenfiles ermöglicht.
Die Struktur der internen Datenbasis wird
beschrieben.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-13
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501126
Preprintreihe des Chemnitzer SFB 393, 98-17; Definition des Fileformats: Preprint 98-11
ger
Preprintreihe des Chemnitzer SFB 393, 98-17; Definition des Fileformats: Preprint 98-11
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18360/zip/
urn:nbn:de:swb:ch1-200501126
oai:qucosa:de:qucosa:18361
2021-03-29T09:44:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Lagrangian invariant subspaces of Hamiltonian matrices
Volker
Mehrmann
Hongguo
Xu
510
510
Algebraische Riccati-Gleichung
Eigenwertproblem
Symplektische Matrix
Hamiltonian matrix
Lagrangian invariant subspace
The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and sufficient conditions are given in terms of the Jordan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Hermitian solutions of continuous time algebraic Riccati equations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-14
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501133
Preprintreihe des Chemnitzer SFB 393, 98-25
eng
Preprintreihe des Chemnitzer SFB 393, 98-25
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18361/zip/
urn:nbn:de:swb:ch1-200501133
oai:qucosa:de:qucosa:18362
2021-03-29T09:44:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Partial Fourier approximation of the Lamé equations in axisymmetric domains
Boniface
Nkemzi
Bernd
Heinrich
510
510
A-priori-Abschätzung
Finite-Elemente-Methode
Lamé-Gleichung
Lineare Elastizitätstheorie
Randwertproblem
axisymmetric domain
partial Fourier method
In this paper, we study the partial Fourier method for
treating the Lamé equations in three-dimensional
axisymmetric domains subjected to nonaxisymmetric loads.
We consider the mixed boundary value problem of the
linear theory of elasticity with the displacement u,
the body force f \in (L_2)^3 and homogeneous Dirichlet
and Neumann boundary conditions. The partial Fourier
decomposition reduces, without any error, the
threedimensional boundary value problem to an infinite
sequence of twodimensional boundary value problems,
whose solutions u_n (n = 0,1,2,...) are the Fourier
coefficients of u. This process of dimension reduction
is described, and appropriate function spaces are given
to characterize the reduced problems in two dimensions.
The trace properties of these spaces on the rotational
axis and some properties of the Fourier coefficients u_n
are proved, which are important for further numerical
treatment, e.g. by the finite-element method.
Moreover, generalized completeness relations are described
for the variational equation, the stresses and the strains.
The properties of the resulting system of twodimensional
problems are characterized. Particularly, a priori
estimates of the Fourier coefficients u_n and of the error
of the partial Fourier approximation are given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-14
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501145
Preprintreihe des Chemnitzer SFB 393, 98-26
eng
Preprintreihe des Chemnitzer SFB 393, 98-26
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18362/zip/
urn:nbn:de:swb:ch1-200501145
oai:qucosa:de:qucosa:18363
2021-03-29T09:44:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Some remarks to large deformation elasto-plasticity (continuum formulation)
Detlef
Michael
Mathias
Meisel
510
510
Elastizitätstheorie
Finite-Elemente-Methode
Plastizitätstheorie
continuum theory
large deformation elasto-plasticity
The continuum theory of large deformation elasto-plasticity is summarized as far as it is necessary for the numerical treatment with the Finite-Element-Method. Using the calculus of modern differential geometry and functional analysis, the fundamental equations are derived and the proof of most of them is shortly outlined. It was not our aim to give a contribution to the development of the theory, rather to show the theoretical background and the assumptions to be made in state of the art elasto-plasticity.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-09-14
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501150
Preprintreihe des Chemnitzer SFB 393, 98-28
eng
Preprintreihe des Chemnitzer SFB 393, 98-28
info:eu-repo/semantics/openAccess
3
https://monarch.qucosa.de/api/qucosa%3A18363/zip/
urn:nbn:de:swb:ch1-200501150
oai:qucosa:de:qucosa:18393
2021-03-29T09:45:12Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:620
ddc:621.3
openaire
Implementation Issues on MEMS - A Study on System Identification
Heiko
Wolfram
620
620
Identifikation
Kapazitiver Sensor
MEMS
Mikrospiegel
Nichtlinearität
A nonlinear identification scheme is provided for a LTI-system with a feedback-nonlinearity, which depends on the input and LTI-system output. This is especially the case for MEMS, where the electrostatic field depends on the displacement and input voltage. The fact, that the algorithm only requires a matrix inversion and singular value decomposition, makes it possible to use the identification scheme for online-estimation. There is also no other a-priori knowledge about the system, except the order, needed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2005-10-28
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501442
eng
info:eu-repo/semantics/openAccess
11
https://monarch.qucosa.de/api/qucosa%3A18393/zip/
urn:nbn:de:swb:ch1-200501442
oai:qucosa:de:qucosa:18412
2021-03-29T09:45:27Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:620
ddc:621.3
openaire
Part-load operation of mini cogeneration plants in medium voltage grids
Eva Marie
Linne
Dipl.-Ing.
620
620
Blockheizkraftwerk
Brennstoffzelle
Mittelspannungsnetz
Teillastbetrieb
Wirkungsgrad
This paper deals with control strategies for mini cogeneration plants (short: CGP) in medium voltage grids. The aim of the paper is to explain and to minimize the trade-off between highest electrical efficiency in electrical energy production and the needs of energy reserve caused by uncertain load estimation. In general, high energy reserve means low electrical efficiency in electricity production. But fuel cells offer a high electrical efficiency in a relatively wide control range.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
University of West Bohemia in Pilsen, Departement of Electrical Power Engineering and Ecology
Chemnitz
Chemnitz
2005-12-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501638
80-7043-371-X
Distributed Power Generation Systems 2005
eng
Distributed Power Generation Systems 2005
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18412/zip/
urn:nbn:de:swb:ch1-200501638
oai:qucosa:de:qucosa:18440
2021-03-29T09:45:50Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:620
ddc:621.3
openaire
Model Building, Control Design and Practical Implementation of a High Precision, High Dynamical MEMS Acceleration Sensor
Heiko
Wolfram
620
620
Kapazitiver Sensor
Mathematisches Modell
Regelungstechnik
Acceleration Sensor
H-infinity Control
Identification
Mixed-Sensitivity Approach
Model Building
This paper presents the whole process of building up a high precision, high dynamical MEMS acceleration sensor. The first samples have achieved a resolution of better than 500 micro g and a bandwidth of more than 200 Hz. The sensor fabrication technology is shortly covered in the paper. A theoretical model is built from the physical principles of the complete sensor system, consisting of the MEMS sensor, the charge amplifier and the PWM driver for the sensor element. The mathematical modeling also covers problems during startup. A reduced order model of the entire system is used to design a robust control with the Mixed-Sensitivity H-infinity Approach. Since the system has an unstable pole, imposed by the electrostatic field and time delay, caused by A/D-D/A conversation delay and DSP computing time, limitations for the control design are given. The theoretical model might be inaccurate or lacks of completeness, because the parameters for the theoretical model building vary from sample to sample or might be not known. A new identification scheme for open or closed-loop operation is deployed to obtain directly from the samples the parameters of the mechanical system and the voltage dependent gains. The focus of this paper is the complete system development and identification process including practical tests in a DSP TI-TMS320C3000 environment.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Society of Photo-Optical Instrumentation Engineers (SPIE)
Chemnitz
Chemnitz
2005-12-22
2021-03-29
preprint
urn:nbn:de:swb:ch1-200501921
0-8194-5831-7
Proceedings of SPIE
eng
Proceedings of SPIE
info:eu-repo/semantics/openAccess
6
https://monarch.qucosa.de/api/qucosa%3A18440/zip/
urn:nbn:de:swb:ch1-200501921
oai:qucosa:de:qucosa:18482
2021-03-29T09:46:24Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Visualization Tools for 2D and 3D Finite Element Programs - User's Manual
Matthias
Pester
510
510
Finite-Elemente-Methode
Parallelverarbeitung / Programmierung
Visualisierung
computer graphics
numerical algorithms
This paper deals with the visualization of
numerical results as a very convenient method to
understand and evaluate a solution which has been
calculated as a set of millions of numerical values.
One of the central research fields of the Chemnitz
SFB 393 is the analysis of parallel numerical
algorithms for large systems of linear equations
arising from differential equations (e.g. in solid
and fluid mechanics). Solving large problems on
massively parallel computers makes it more and
more impossible to store numerical data from the
distributed memory of the parallel computer to
the disk for later postprocessing. However, the
developer of algorithms is interested in an
on-line response of his algorithms. Both visual
and numerical response of the running program may
be evaluated by the user for a decision how to
switch or adjust interactively certain parameters
that may influence the solution process.
The paper gives a survey of current programmer
and user interfaces that are used in our various
2D and 3D parallel finite element programs for
the visualization of the solution.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-04
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600436
Preprintreihe des Chemnitzer SFB 393, 02-02
eng
Preprintreihe des Chemnitzer SFB 393, 02-02
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18482/zip/
urn:nbn:de:swb:ch1-200600436
oai:qucosa:de:qucosa:18483
2021-03-29T09:46:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Fully Discrete Wavelet Galerkin Schemes
Helmut
Harbrecht
Michael
Konik
Reinhold
Schneider
510
510
Galerkin-Methode
Galerkin-Methode
Wavelet
boundary elements
matrix compression
The present paper is intended to give a survey of the developments of the wavelet Galerkin boundary element method. Using appropriate wavelet bases for the discretization of boundary integral operators yields numerically sparse system matrices. These system matrices can be compressed to O(N_j) nonzero matrix entries without loss of accuracy of the underlying Galerkin scheme. Herein, O(N_j) denotes the number of unknowns. As we show in the present paper, the assembly of the compressed system matrix can be performed within optimal complexity. By numerical experiments we provide examples which corroborate the theory.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-04
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600441
Preprintreihe des Chemnitzer SFB 393, 02-03
eng
Preprintreihe des Chemnitzer SFB 393, 02-03
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18483/zip/
urn:nbn:de:swb:ch1-200600441
oai:qucosa:de:qucosa:18484
2021-03-29T09:46:26Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Wavelet Galerkin Schemes for 3D-BEM
Helmut
Harbrecht
Reinhold
Schneider
510
510
Galerkin-Methode
Integralgleichung
Wavelet
3D-BEM
boundary elements
This paper is intended to present wavelet Galerkin
schemes for the boundary element method.
Wavelet Galerkin schemes employ appropriate
wavelet bases for the discretization of boundary
integral operators. This yields quasisparse system
matrices which can be compressed to O(N_J)
relevant matrix entries without compromising the
accuracy of the underlying Galerkin scheme.
Herein, O(N_J) denotes the number of unknowns.
The assembly of the compressed system matrix
can be performed in O(N_J) operations. Therefore,
we arrive at an algorithm which solves boundary
integral equations within optimal complexity.
By numerical experiments we provide results which
corroborate the theory.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-04
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600452
Preprintreihe des Chemnitzer SFB 393, 02-05
eng
Preprintreihe des Chemnitzer SFB 393, 02-05
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18484/zip/
urn:nbn:de:swb:ch1-200600452
oai:qucosa:de:qucosa:18486
2021-03-29T09:46:28Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Robust local problem error estimation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes
Serguei
Grosman
510
510
Anisotropie
Finite-Elemente-Methode
Reaktions-Diffusionsgleichung
a posteriori error estimation
singular perturbations
stretched elements
Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, e.g. strong boundary and/or interior layers. This anisotropy is reflected in the discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the a posteriori error estimator with respect to both the perturbation parameters of the problem and the anisotropy of the mesh. An estimator that has shown to be one of the most reliable for reaction-diffusion problem is the <i>equilibrated residual method</i> and its modification done by Ainsworth and Babuška for singularly perturbed problem. However, even the modified method is not robust in the case of anisotropic meshes. The present work modifies the equilibrated residual method for anisotropic meshes. The resulting error estimator is equivalent to the equilibrated residual method in the case of isotropic meshes and is proved to be robust on anisotropic meshes as well. A numerical example confirms the theory.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-05
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600475
Preprintreihe des Chemnitzer SFB 393, 02-07
eng
Preprintreihe des Chemnitzer SFB 393, 02-07
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18486/zip/
urn:nbn:de:swb:ch1-200600475
oai:qucosa:de:qucosa:18485
2021-03-29T09:46:27Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Compression Techniques for Boundary Integral Equations - Optimal Complexity Estimates
Wolfgang
Dahmen
Helmut
Harbrecht
Reinhold
Schneider
510
510
Integralgleichung
Randintegral
Wavelet
a-posteriori compression
asymptotic complexity estimates
multilevel preconditioning
norm equivalences
In this paper matrix compression techniques in the
context of wavelet Galerkin schemes for boundary
integral equations are developed and analyzed that
exhibit optimal complexity in the following sense.
The fully discrete scheme produces approximate
solutions within discretization error accuracy
offered by the underlying Galerkin method at a
computational expense that is proven to stay
proportional to the number of unknowns.
Key issues are the second compression, that
reduces the near field complexity significantly,
and an additional a-posteriori compression.
The latter one is based on a general result
concerning an optimal work balance, that applies,
in particular, to the quadrature used to compute
the compressed stiffness matrix with sufficient
accuracy in linear time. The theoretical results
are illustrated by a 3D example on a nontrivial
domain.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-05
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600464
Preprintreihe des Chemnitzer SFB 393, 02-06
eng
Preprintreihe des Chemnitzer SFB 393, 02-06
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18485/zip/
urn:nbn:de:swb:ch1-200600464
oai:qucosa:de:qucosa:18490
2021-03-29T09:46:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallel implementation of curve reconstruction from noisy samples
Maharavo
Randrianarivony
Guido
Brunnett
510
510
B-Spline
Geometrie
Parallelverarbeitung
curve reconstruction
noisy samples
nonlinear optimization
This paper is concerned with approximating noisy
samples by non-uniform rational B-spline curves
with special emphasis on free knots. We show how to
set up the problem such that nonlinear optimization
methods can be applied efficiently. This involves
the introduction of penalizing terms in order to
avoid undesired knot positions. We report on our
implementation of the nonlinear optimization and we
show a way to implement the program in parallel.
Parallel performance results are described. Our
experiments show that our program has a linear
speedup and an efficiency value close to unity.
Runtime results on a parallel computer are
displayed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600519
Preprintreihe des Chemnitzer SFB 393, 02-15
eng
Preprintreihe des Chemnitzer SFB 393, 02-15
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18490/zip/
urn:nbn:de:swb:ch1-200600519
oai:qucosa:de:qucosa:18488
2021-03-29T09:46:29Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:620
ddc:621.3
openaire
Identifikation schädigungsmechanischer Materialparameter mit Hilfe nichtlinearer Optimierungsverfahren am Beispiel des Rousselier Modells
Marcel
Springmann
Meinhard
Kuna
620
620
Optimierung
Parameteridentifikation
Sensitivitätsanalyse
Rousselier Modell
Schädigungsmechanik
Der vorliegende Beitrag befasst sich mit der
Identifikation von Parametern schädigungsmechanischer
Materialgesetze. In diesem Zusammenhang wird für
die Lösung des nichtlinearen Rand- und Anfangswertproblems
das finite Element System SPC-PMHP verwendet.
Die duktile Schädigung wird durch das Modell von
Rousselier beschrieben. Neben den Materialgleichungen
wird der Algorithmus zur numerischen Integration des
Materialgesetzes vorgestellt. Die zur
Materialparameteridentifikation erforderliche Lösung
der inversen Aufgabenstellung wird mit einem
nichtlinearen Optimierungsverfahren realisiert.
Die quadratische Abweichung zwischen gemessenen
und simulierten Verschiebungsfeldern wird als
Zielfunktion gewählt, deren Minimierung auf die
gesuchten Parameter führt. Im Rahmen der
deterministischen Optimierungsprozeduren wird zur
Bestimmung des Gradienten der Zielfunktion ein
impliziter Algorithmus - die sogenannte
semianalytische Sensitivitätsanalyse - angewandt.
Synthetisch erzeugte inhomogene Verschiebungsfelder
dienen als Messwerte und werden den berechneten
Verschiebungen gegenübergestellt. Mit verschiedenen
numerischen Experimenten wird am Beispiel einer
Scheibe mit Loch die Anwendbarkeit des Verfahrens
getestet.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-05
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600490
Preprintreihe des Chemnitzer SFB 393, 02-08
ger
Preprintreihe des Chemnitzer SFB 393, 02-08
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18488/zip/
urn:nbn:de:swb:ch1-200600490
oai:qucosa:de:qucosa:18489
2021-03-29T09:46:30Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Multiresolution weighted norm equivalences and applications
Sven
Beuchler
Reinhold
Schneider
Christoph
Schwab
510
510
Norm <Mathematik>
Wavelet
fast solvers
norm equivalences
weighted norms
We establish multiresolution norm equivalences in
weighted spaces <i>L<sup>2</sup><sub>w</sub></i>((0,1))
with possibly singular weight functions <i>w(x)</i>≥0
in (0,1).
Our analysis exploits the locality of the
biorthogonal wavelet basis and its dual basis
functions. The discrete norms are sums of wavelet
coefficients which are weighted with respect to the
collocated weight function <i>w(x)</i> within each scale.
Since norm equivalences for Sobolev norms are by now
well-known, our result can also be applied to
weighted Sobolev norms. We apply our theory to
the problem of preconditioning <i>p</i>-Version FEM
and wavelet discretizations of degenerate
elliptic problems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-05
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600503
Preprintreihe des Chemnitzer SFB 393, 02-09
eng
Preprintreihe des Chemnitzer SFB 393, 02-09
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18489/zip/
urn:nbn:de:swb:ch1-200600503
oai:qucosa:de:qucosa:18492
2021-03-29T09:46:32Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallel implementation of surface reconstruction from noisy samples
Maharavo
Randrianarivony
Guido
Brunnett
510
510
Geometrie
Parallelverarbeitung
Rationaler B-Spline
noisy samples
nonlinear optimization
surface reconstruction
We consider the problem of reconstructing a surface from noisy samples by approximating the point set with non-uniform rational B-spline surfaces. We focus on the fact that the knot sequences should also be part of the unknown variables that include the control points and the weights in order to find their optimal positions. We show how to set up the free knot problem such that constrained nonlinear optimization can be applied efficiently. We describe in detail a parallel implementation of our approach that give almost linear speedup. Finally, we provide numerical results obtained on the Chemnitzer Linux Cluster supercomputer.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600524
Preprintreihe des Chemnitzer SFB 393, 02-16
eng
Preprintreihe des Chemnitzer SFB 393, 02-16
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18492/zip/
urn:nbn:de:swb:ch1-200600524
oai:qucosa:de:qucosa:18493
2021-03-29T09:46:33Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:004
openaire
Task Pool Teams for Implementing Irregular Algorithms on Clusters of SMPs
Judith
Hippold
Gudula
Rünger
004
004
Coupled Cluster
Parallelverarbeitung / Programmierung
Radiosity
Verteilter Speicher
irregular algorithms
task pool teams
The characteristics of irregular algorithms make a parallel implementation difficult, especially for PC clusters or clusters of SMPs. These characteristics may include an unpredictable access behavior to dynamically changing data structures or strong irregular coupling of computations. Problems are an unknown load distribution and expensive irregular communication patterns for data accesses and redistributions. Thus the parallel implementation of irregular algorithms on distributed memory machines and clusters requires a special organizational mechanism for a dynamic load balance while keeping the communication and administration overhead low. We propose task pool teams for implementing irregular algorithms on clusters of PCs or SMPs. A task pool team combines multithreaded programming using task pools on single nodes with explicit message passing between different nodes. The dynamic load balance mechanism of task pools is generalized to a dynamic load balance scheme for all distributed nodes. We have implemented and compared several versions for task pool teams. As application example, we use the hierarchical radiosity algorithm, which is based on dynamically growing quadtree data structures annotated by varying interaction lists expressing the irregular coupling between the quadtrees. Experiments are performed on a PC cluster and a cluster of SMPs.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600537
Preprintreihe des Chemnitzer SFB 393, 02-18
eng
Preprintreihe des Chemnitzer SFB 393, 02-18
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18493/zip/
urn:nbn:de:swb:ch1-200600537
oai:qucosa:de:qucosa:18495
2021-03-29T09:46:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Adaptive Wavelet Galerkin BEM
Helmut
Harbrecht
Reinhold
Schneider
510
510
Galerkin-Methode
Randintegral
Wavelet
adaptive methods
biorthogonal wavelet bases
The wavelet Galerkin scheme for the fast solution of boundary integral equations produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that stays proportional to the number of unknowns. In this paper we present an adaptive version of the scheme which preserves the super-convergence of the Galerkin method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600559
Preprintreihe des Chemnitzer SFB 393, 02-20
eng
Preprintreihe des Chemnitzer SFB 393, 02-20
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18495/zip/
urn:nbn:de:swb:ch1-200600559
oai:qucosa:de:qucosa:18494
2021-03-29T09:46:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Wavelets for the fast solution of boundary integral equations
Helmut
Harbrecht
Reinhold
Schneider
510
510
Randintegral
Wavelet
boundary element method
matrix compression
wavelet bases
This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasi-sparse system matrices which can be compressed to O(N_J) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(N_J) denotes the number of unknowns. The assembly of the compressed system matrix can be performed in O(N_J) operations. Therefore, we arrive at an algorithm which solves boundary integral equations within optimal complexity. By numerical experiments we provide results which corroborate the theory.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600540
Preprintreihe des Chemnitzer SFB 393, 02-19
eng
Preprintreihe des Chemnitzer SFB 393, 02-19
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18494/zip/
urn:nbn:de:swb:ch1-200600540
oai:qucosa:de:qucosa:18496
2021-03-29T09:46:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Wavelet Galerkin Schemes for Boundary Integral Equations - Implementation and Quadrature
Helmut
Harbrecht
Reinhold
Schneider
510
510
Galerkin-Methode
Numerische Integration
Randintegral
Wavelet
biorthogonal wavelet bases
matrix compression
In this paper we consider the fully discrete wavelet Galerkin scheme for the fast solution of boundary integral equations in three dimensions. It produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that stays proportional to the number of unknowns. We focus on implementational details of the scheme, in particular on numerical integration of relevant matrix coefficients. We illustrate the proposed algorithms by numerical results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600560
Preprintreihe des Chemnitzer SFB 393, 02-21
eng
Preprintreihe des Chemnitzer SFB 393, 02-21
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18496/zip/
urn:nbn:de:swb:ch1-200600560
oai:qucosa:de:qucosa:18500
2021-03-29T09:46:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Wavelet preconditioners for the p-version of the fem
Sven
Beuchler
510
510
Finite-Elemente-Methode
Wavelet
Multigrid methods
Preconditioning
p-version
In this paper, we consider domain decomposition preconditioners for a system of linear algebraic equations arising from the <i>p</i>-version of the fem. We propose several multi-level preconditioners for the Dirichlet problems in the sub-domains in two and three dimensions. It is proved that the condition number of the preconditioned system is bounded by a constant independent of the polynomial degree. The proof uses interpretations of the <i>p</i>-version element stiffness matrix and mass matrix on [-1,1] as <i>h</i>-version stiffness matrix and weighted mass matrix. The analysis requires wavelet methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600607
Preprintreihe des Chemnitzer SFB 393, 03-03
eng
Preprintreihe des Chemnitzer SFB 393, 03-03
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18500/zip/
urn:nbn:de:swb:ch1-200600607
oai:qucosa:de:qucosa:18499
2021-03-29T09:46:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Existence of the guided modes of an optical fiber
Sergey I.
Solov'ëv
510
510
Eigenwertproblem
Glasfaser
Minimax-Prinzip
guided modes
optical fiber
The present paper is devoted to the investigation of the guided wave problem. This problem is formulated as the eigenvalue problem with a compact self-adjoint operator pencil. Applying the minimax principle for the compact operators in the Hilbert space we obtain a necessary and sufficient condition for the existence of a preassigned number of linearly independent guided modes. As a consequence of this result we also derive simple sufficient conditions, which can be easily applied in practice. We give a statement of the problem in a bounded domain and propose an efficient method for solving the problem.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600594
Preprintreihe des Chemnitzer SFB 393, 03-02
eng
Preprintreihe des Chemnitzer SFB 393, 03-02
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18499/zip/
urn:nbn:de:swb:ch1-200600594
oai:qucosa:de:qucosa:18501
2021-03-29T09:46:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Fast solvers for degenerated problems
Sven
Beuchler
510
510
Finite-Elemente-Methode
Numerische Mathematik / Algorithmus
Multigrid
Preconditioning
multi-level method
In this paper, finite element discretizations of the
degenerated operator
-ω<sup>2</sup>(y) u<sub>xx</sub>-ω<sup>2</sup>(x)u<sub>yy</sub>=g
in the unit square are investigated, where the
weight function satisfies ω(ξ)=ξ<sup>α</sup>
with α ≥ 0.
We propose two multi-level methods in order to
solve the resulting system of linear algebraic
equations. The first method is a multi-grid
algorithm with line-smoother.
A proof of the smoothing property is given.
The second method is a BPX-like preconditioner
which we call MTS-BPX preconditioner.
We show that the upper eigenvalue bound of the
MTS-BPX preconditioned system matrix grows
proportionally to the level number.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600611
Preprintreihe des Chemnitzer SFB 393, 03-04
eng
Preprintreihe des Chemnitzer SFB 393, 03-04
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18501/zip/
urn:nbn:de:swb:ch1-200600611
oai:qucosa:de:qucosa:18503
2021-03-29T09:46:41Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Wavelet based fast solution of boundary integral equations
Helmut
Harbrecht
Reinhold
Schneider
510
510
Galerkin-Methode
Wavelet
adaptive methods
matrix compression
This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators which yields quasi-sparse system matrices. These matrices can be compressed such that the complexity for solving a boundary integral equation scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. Based on the wavelet Galerkin scheme we present also an adaptive algorithm. By numerical experiments we provide results which demonstrate the performance of our algorithm.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600649
Preprintreihe des Chemnitzer SFB 393, 03-07
eng
Preprintreihe des Chemnitzer SFB 393, 03-07
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18503/zip/
urn:nbn:de:swb:ch1-200600649
oai:qucosa:de:qucosa:18502
2021-03-29T09:46:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Stable evaluation of the Jacobians for curved triangles
Arnd
Meyer
510
510
Finite-Elemente-Methode
Numerische Mathematik / Algorithmus
Jacobian matrix
adaptive methods
stable calculation
In the adaptive finite element method, the solution of a p.d.e. is approximated
from finer and finer meshes, which are controlled by error estimators. So,
starting from a given coarse mesh, some elements are subdivided a couple of
times. We investigate the question of avoiding instabilities which limit this
process from the fact that nodal coordinates of one element coincide in more
and more leading digits. In a previous paper the stable calculation of the
Jacobian matrices of the element mapping was given for straight line triangles,
quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and
quadratic triangles on curved boundaries.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600629
Preprintreihe des Chemnitzer SFB 393, 03-05
eng
Preprintreihe des Chemnitzer SFB 393, 03-05
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18502/zip/
urn:nbn:de:swb:ch1-200600629
oai:qucosa:de:qucosa:18504
2021-03-29T09:46:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Preconditioned iterative methods for monotone nonlinear eigenvalue problems
Sergey I.
Solov'ëv
510
510
Iterativ
Nichtlineares Eigenwertproblem
conjugate gradient method
preconditioning
steepest descent method
This paper proposes new iterative methods for the efficient computation of the smallest eigenvalue of the symmetric nonlinear matrix eigenvalue problems of large order with a monotone dependence on the spectral parameter. Monotone nonlinear eigenvalue problems for differential equations have important applications in mechanics and physics. The discretization of these eigenvalue problems leads to ill-conditioned nonlinear eigenvalue problems with very large sparse matrices monotone depending on the spectral parameter. To compute the smallest eigenvalue of large matrix nonlinear eigenvalue problem, we suggest preconditioned iterative methods: preconditioned simple iteration method, preconditioned steepest descent method, and preconditioned conjugate gradient method. These methods use only matrix-vector multiplications, preconditioner-vector multiplications, linear operations with vectors and inner products of vectors. We investigate the convergence and derive grid-independent error estimates of these methods for computing eigenvalues. Numerical experiments demonstrate practical effectiveness of the proposed methods for a class of mechanical problems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-04-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200600657
Preprintreihe des Chemnitzer SFB 393, 03-08
eng
Preprintreihe des Chemnitzer SFB 393, 03-08
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18504/zip/
urn:nbn:de:swb:ch1-200600657
oai:qucosa:de:qucosa:18568
2021-03-29T09:47:34Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Transformation of hexahedral finite element meshes into tetrahedral meshes according to quality criteria
Thomas
Apel
Nico
Düvelmeyer
510
510
Finite-Elemente-Methode
Gittererzeugung
Tetraedergitter
Hexaedergitter
mesh transformation
The paper is concerned with algorithms for transforming hexahedral finite element meshes into tetrahedral meshes without introducing new nodes. Known algorithms use only the topological structure of the hexahedral mesh but no geometry information. The paper provides another algorithm which can be extented such that quality criteria for the splitting of faces are respected.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601295
Preprintreihe des Chemnitzer SFB 393, 03-09
eng
Preprintreihe des Chemnitzer SFB 393, 03-09
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18568/zip/
urn:nbn:de:swb:ch1-200601295
oai:qucosa:de:qucosa:18571
2021-03-29T09:47:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A Dirichlet-Dirichlet DD-pre-conditioner for p-FEM
Sven
Beuchler
510
510
Finite-Elemente-Methode
Randwertproblem
numerical results
preconditioning
second order problem
In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet-Dirichlet domain decomposition pre-conditioner for the system of linear algebraic equations is investigated. The solver for the problem in the sub-domains and a pre-conditioner for the Schur-complement are proposed as ingredients for the inexact DD-pre-conditioner. Finally, several numerical experiments are given.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601329
Preprintreihe des Chemnitzer SFB 393, 03-12; Numerische Ergebnisse (Computerpraktikum)
eng
Preprintreihe des Chemnitzer SFB 393, 03-12; Numerische Ergebnisse (Computerpraktikum)
info:eu-repo/semantics/openAccess
145
https://monarch.qucosa.de/api/qucosa%3A18571/zip/
urn:nbn:de:swb:ch1-200601329
oai:qucosa:de:qucosa:18569
2021-03-29T09:47:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Biorthogonal wavelet bases for the boundary element method
Helmut
Harbrecht
Reinhold
Schneider
510
510
Biorthogonale Wavelet-Basis
Integralgleichung
Randelemente-Methode
cancellation property
norm equivalences
As shown by Dahmen, Harbrecht and Schneider, the fully discrete wavelet Galerkin scheme for boundary integral equations scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. The supposition is a wavelet basis with a sufficiently large number of vanishing moments. In this paper we present several constructions of appropriate wavelet bases on manifolds based on the biorthogonal spline wavelets of A. Cohen, I. Daubechies and J.-C. Feauveau. By numerical experiments we demonstrate that it is worthwhile to spent effort on their construction to increase the performance of the wavelet Galerkin scheme considerably.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601308
Preprintreihe des Chemnitzer SFB 393, 03-10
eng
Preprintreihe des Chemnitzer SFB 393, 03-10
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18569/zip/
urn:nbn:de:swb:ch1-200601308
oai:qucosa:de:qucosa:18572
2021-03-29T09:47:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Clément-type interpolation on spherical domains - interpolation error estimates and application to a posteriori error estimation
Thomas
Apel
Cornelia
Pester
510
510
A-posteriori-Abschätzung
Finite-Elemente-Methode
Laplace-Beltrami-Operator
Clément-type interpolation
spherical domains
In this paper, a mixed boundary value problem for
the Laplace-Beltrami operator is considered for
spherical domains in $R^3$, i.e. for domains on
the unit sphere. These domains are parametrized
by spherical coordinates (\varphi, \theta),
such that functions on the unit sphere are
considered as functions in these coordinates.
Careful investigation leads to the introduction
of a proper finite element space corresponding to
an isotropic triangulation of the underlying
domain on the unit sphere. Error estimates are
proven for a Clément-type interpolation operator,
where appropriate, weighted norms are used.
The estimates are applied to the deduction of
a reliable and efficient residual error estimator
for the Laplace-Beltrami operator.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601335
eng
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18572/zip/
urn:nbn:de:swb:ch1-200601335
oai:qucosa:de:qucosa:18573
2021-03-29T09:47:38Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The inf-sup condition for the Bernardi-Fortin-Raugel element on anisotropic meshes
Thomas
Apel
Serge
Nicaise
510
510
Anisotropes Gitter
Finite-Elemente-Methode
aspect ratio
inf-sup condition
stability
On a large class of two-dimensional anisotropic meshes, the inf-sup condition (stability) is proved for the triangular and quadrilateral finite element pairs suggested by Bernardi/Raugel and Fortin. As a consequence the pairs ${\cal P}_2-{\cal P}_0$, ${\cal Q}_2-{\cal P}_0$, and ${\cal Q}_2^\prime-{\cal P}_0$ turn out to be stable independent of the aspect ratio of the elements.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601341
Preprintreihe des Chemnitzer SFB 393, 03-15
eng
Preprintreihe des Chemnitzer SFB 393, 03-15
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18573/zip/
urn:nbn:de:swb:ch1-200601341
oai:qucosa:de:qucosa:18570
2021-03-29T09:47:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Some choices of moments of refinable function and applications
Tugal
Zhanlav
510
510
Quadraturformel
Wavelet
fast wavelet transform
refinable function evaluation
wavelet approximation
We propose a recursive formula for moments of scaling function and sum rule. It is shown that some quadrature formulae has a higher degree of accuracy under proposed moment condition. On this basis we obtain higher accuracy formula for wavelet expansion coefficients which are needed to start the fast wavelet transform and estimate convergence rate of wavelet approximation and sampling of smooth functions. We also present a direct algorithm for solving refinement equation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601316
Preprintreihe des Chemnitzer SFB 393, 03-11
eng
Preprintreihe des Chemnitzer SFB 393, 03-11
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18570/zip/
urn:nbn:de:swb:ch1-200601316
oai:qucosa:de:qucosa:18574
2021-03-29T09:47:39Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A posteriori error estimation for a finite volume discretization on anisotropic meshes
Gerd
Kunert
Zoubida
Mghazli
Serge
Nicaise
510
510
Anisotropie
Fehlerabschätzung
Finite-Volumen-Methode
error bounds
singular perturbations
A singularly perturbed reaction diffusion problem is considered. The small diffusion coefficient generically leads to solutions with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution is reflected by using \emph{anisotropic meshes} which can improve the accuracy of the discretization considerably. The main focus is on \emph{a posteriori} error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect to the small perturbation parameter. The estimator is also robust with respect to the mesh anisotropy as long as the anisotropic mesh sufficiently reflects the anisotropy of the solution (which is almost always the case for sensible discretizations). Altogether, reliable and efficient \emph{a posteriori} error estimation is achieved for the finite volume method on anisotropic meshes.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601352
Preprintreihe des Chemnitzer SFB 393, 03-16
eng
Preprintreihe des Chemnitzer SFB 393, 03-16
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18574/zip/
urn:nbn:de:swb:ch1-200601352
oai:qucosa:de:qucosa:18576
2021-03-29T09:47:41Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Vibrations of plates with masses
Sergey I.
Solov'ëv
510
510
Nichtlineares Eigenwertproblem
Schwingung
eigenfunctions
numerical experiments
vibrations of plates
This paper presents the investigation of the
nonlinear eigenvalue problem describing free
vibrations of plates with elastically attached
masses. We study properties of eigenvalues and
eigenfunctions and prove the existence theorem.
Theoretical results are illustrated by numerical
experiments.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601375
Preprintreihe des Chemnitzer SFB 393, 03-18
eng
Preprintreihe des Chemnitzer SFB 393, 03-18
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18576/zip/
urn:nbn:de:swb:ch1-200601375
oai:qucosa:de:qucosa:18575
2021-03-29T09:47:40Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Nitsche type mortaring for singularly perturbed reaction-diffusion problems
Bernd
Heinrich
Kornelia
Pönitz
510
510
Finite-Elemente-Methode
Gebietszerlegungsmethode
Mortar-Element-Methode
boundary layers
non-matching meshes
The paper is concerned with the Nitsche mortaring in the framework of domain decomposition where non-matching meshes and weak continuity of the finite element approximation at the interface are admitted. The approach is applied to singularly perturbed reaction-diffusion problems in 2D. Non-matching meshes of triangles being anisotropic in the boundary layers are applied. Some properties as well as error estimates of the Nitsche mortar finite element schemes are proved. In particular, using a suitable degree of anisotropy of triangles in the boundary layers of a rectangle, we derive convergence rates as known for the conforming finite element method in presence of regular solutions. Numerical examples illustrate the approach and the results.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601364
Preprintreihe des Chemnitzer SFB 393, 03-17
eng
Preprintreihe des Chemnitzer SFB 393, 03-17
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18575/zip/
urn:nbn:de:swb:ch1-200601364
oai:qucosa:de:qucosa:18577
2021-03-29T09:47:41Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Preconditioned iterative methods for a class of nonlinear eigenvalue problems
Sergey I.
Solov'ëv
510
510
Gradientenverfahren
Konjugierte-Gradienten-Methode
Nichtlineares Eigenwertproblem
Präkonditionierung
preconditioned iterative method
symmetric eigenvalue problem
In this paper we develop new preconditioned
iterative methods for solving monotone nonlinear
eigenvalue problems. We investigate the convergence
and derive grid-independent error estimates for
these methods. Numerical experiments demonstrate
the practical effectiveness of the proposed methods
for a model problem.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601389
eng
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18577/zip/
urn:nbn:de:swb:ch1-200601389
oai:qucosa:de:qucosa:18581
2021-03-29T09:47:44Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The robustness of the hierarchical a posteriori error estimator for reaction-diffusion equation on anisotropic meshes
Serguei
Grosman
510
510
A-posteriori-Abschätzung
Finite-Elemente-Methode
Robuste Schätzung
singular perturbations
stretched elements
Singularly perturbed reaction-diffusion problems
exhibit in general solutions with anisotropic
features, e.g. strong boundary and/or interior
layers. This anisotropy is reflected in the
discretization by using meshes with anisotropic
elements. The quality of the numerical solution
rests on the robustness of the a posteriori error
estimator with respect to both the perturbation
parameters of the problem and the anisotropy of the
mesh. The simplest local error estimator from the
implementation point of view is the so-called
hierarchical error estimator. The reliability
proof is usually based on two prerequisites:
the saturation assumption and the strengthened
Cauchy-Schwarz inequality. The proofs of these
facts are extended in the present work for the
case of the singularly perturbed reaction-diffusion
equation and of the meshes with anisotropic elements.
It is shown that the constants in the corresponding
estimates do neither depend on the aspect ratio
of the elements, nor on the perturbation parameters.
Utilizing the above arguments the concluding
reliability proof is provided as well as the
efficiency proof of the estimator, both
independent of the aspect ratio and perturbation
parameters.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601418
Preprintreihe des Chemnitzer SFB 393, 04-02
eng
Preprintreihe des Chemnitzer SFB 393, 04-02
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18581/zip/
urn:nbn:de:swb:ch1-200601418
oai:qucosa:de:qucosa:18579
2021-03-29T09:47:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Constructing a diffeomorphism between a trimmed domain and the unit square
Maharavo
Randrianarivony
Guido
Brunnett
Reinhold
Schneider
510
510
CAD
Diffeomorphismus
IGES
Coons patch
Gordon patch
surface decomposition
trimmed surface
This document has two objectives: decomposition of
a given trimmed surface into several four-sided
subregions and creation of a diffeomorphism from
the unit square onto each subregion. We aim at
having a diffeomorphism which is easy and fast to
evaluate. Throughout this paper one of our
objectives is to keep the shape of the curves
delineating the boundaries of the trimmed surfaces
unchanged. The approach that is used invokes the
use of transfinite interpolations. We will describe
an automatic manner to specify internal cubic
Bezier-spline curves that are to be subsequently
interpolated by a Gordon patch. Some theoretical
criterion pertaining to the control points of the
internal curves is proposed and proved so as to
ensure that the resulting Gordon patch is a
diffeomorphism. Numerical results are reported
to illustrate the approaches. Our benchmarks
include CAD objects which come directly from
IGES files.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-08-31
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601399
Preprintreihe des Chemnitzer SFB 393, 03-20
eng
Preprintreihe des Chemnitzer SFB 393, 03-20
info:eu-repo/semantics/openAccess
7
https://monarch.qucosa.de/api/qucosa%3A18579/zip/
urn:nbn:de:swb:ch1-200601399
oai:qucosa:de:qucosa:18582
2021-03-29T09:47:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Entwicklung von adaptiven Algorithmen für nichtlineare FEM
Anke
Bucher
Arnd
Meyer
Uwe-Jens
Görke
Reiner
Kreißig
510
510
Adaptives Verfahren
Finite-Elemente-Methode
Gitterverfeinerung
deformation problem in solid mechanics
nonlinear material
The development of adaptive finite element
procedures for the solution of geometrically
and physically nonlinear problems in structural
mechanics is very important for the augmentation
of the efficiency of FE-codes. In this contribution
methods of mesh refinement as well as mesh
coarsening are presented for a material model
considering finite elasto-plastic deformations.
For newly generated elements stresses, strains and
internal variables have to be calculated. This
implies the determination of the nodal values as
well as the Gaussian point values of the new
elements based on the transfer of data from the
former mesh. Analogously, the coarsening of less
important elements necessitates the determination
of these values for the newly created father
elements.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601424
Preprintreihe des Chemnitzer SFB 393, 04-03
ger
Preprintreihe des Chemnitzer SFB 393, 04-03
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18582/zip/
urn:nbn:de:swb:ch1-200601424
oai:qucosa:de:qucosa:18580
2021-03-29T09:47:44Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Efficient finite element simulation of crack propagation
Arnd
Meyer
Frank
Rabold
Matthias
Scherzer
510
510
Adaptives Gitter
Finite-Elemente-Methode
Iteration
Rissausbreitung
hierarchical preconditioners
The preprint delivers an efficient solution technique for the numerical simulation of crack propagation of 2D linear elastic formulations based on finite elements together with the conjugate gradient method in order to solve the corresponding linear equation systems. The developed iterative numerical approach using hierarchical preconditioners comprehends the interesting feature that the hierarchical data structure will not be destroyed during crack propagation. Thus, one gets the possibility to simulate crack advance in a very effective numerical manner including adaptive mesh refinement and mesh coarsening. Test examples are presented to illustrate the efficiency of the given approach. Numerical simulations of crack propagation are compared with experimental data.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601402
Preprintreihe des Chemnitzer SFB 393, 04-01
eng
Preprintreihe des Chemnitzer SFB 393, 04-01
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18580/zip/
urn:nbn:de:swb:ch1-200601402
oai:qucosa:de:qucosa:18583
2021-03-29T09:47:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Projection methods for contact problems in elasticity
Arnd
Meyer
Roman
Unger
510
510
Finite-Elemente-Methode
Kontakt <Reibung>
Projektionsverfahren
contact problems
hanging nodes
The aim of the paper is showing, how projection methods can be used for computing contact problems in elasticity for different classes of obstacles. Starting with the projection idea for handling hanging nodes in finite element discretizations the extension of the method for handling penetrated nodes in contact problems will be described for some obstacle classes.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601436
Preprintreihe des Chemnitzer SFB 393, 04-04
eng
Preprintreihe des Chemnitzer SFB 393, 04-04
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18583/zip/
urn:nbn:de:swb:ch1-200601436
oai:qucosa:de:qucosa:18586
2021-03-29T09:47:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Solving Linear Matrix Equations via Rational Iterative Schemes
Peter
Benner
Enrique
Quintana-Ortí
Gregorio
Quintana-Ortí
510
510
Ordnungsreduktion
Parallelverarbeitung
Halley's method
Newton-Schulz iteration
Sylvester equation
matrix sign function
model reduction
We investigate the numerical solution of stable Sylvester equations via iterative schemes proposed for computing the sign function of a matrix. In particular, we discuss how the rational iterations for the matrix sign function can efficiently be adapted to the special structure implied by the Sylvester equation. For Sylvester equations with factored constant term as those arising in model reduction or image restoration, we derive an algorithm that computes the solution in factored form directly. We also suggest convergence criteria for the resulting iterations and compare the accuracy and performance of the resulting methods with existing Sylvester solvers. The algorithms proposed here are easy to parallelize. We report on the parallelization of those algorithms and demonstrate their high efficiency and scalability using experimental results obtained on a cluster of Intel Pentium Xeon processors.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601460
Preprintreihe des Chemnitzer SFB 393, 04-08
eng
Preprintreihe des Chemnitzer SFB 393, 04-08
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18586/zip/
urn:nbn:de:swb:ch1-200601460
oai:qucosa:de:qucosa:18584
2021-03-29T09:47:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A local error analysis of the boundary concentrated FEM
Tino
Eibner
Jens Markus
Melenk
510
510
Elliptisches Randwertproblem
Interpolationsoperator
hp-Methode
boundary concentrated finite element method
local error
The boundary concentrated finite element method is
a variant of the hp-version of the FEM that is
particularly suited for the numerical treatment of
elliptic boundary value problems with smooth
coefficients and boundary conditions with low
regularity or non-smooth geometries. In this paper
we consider the case of the discretization of a
Dirichlet problem with exact solution
$u \in H^{1+\delta}(\Omega)$ and investigate the
local error in various norms. We show that for
a $\beta > 0$ these norms behave as
$O(N^{−\delta−\beta})$, where $N$ denotes the
dimension of the underlying finite element space.
Furthermore, we present a new Gauss-Lobatto based
interpolation operator that is adapted to the
case non-uniform polynomial degree distributions.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601440
Preprintreihe des Chemnitzer SFB 393, 04-05
eng
Preprintreihe des Chemnitzer SFB 393, 04-05
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18584/zip/
urn:nbn:de:swb:ch1-200601440
oai:qucosa:de:qucosa:18587
2021-03-29T09:47:49Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
An adaptive strategy for hp-FEM based on testing for analyticity
Tino
Eibner
Jens Markus
Melenk
510
510
Adaptives Verfahren
Finite-Elemente-Methode
Orthogonale Polynome
hp-Methode
mesh generation and refinement
We present an $hp$-adaptive strategy that is based
on estimating the decay of the expansion coefficients
when a function is expanded in $L^2$-orthogonal
polynomails on a triangle or a tetrahedron.
This method is justified by showing that the decay
of the coefficients is exponential if and only if
the function is analytic.
Numerical examples illustrate the performance of
this approach, and we compare it with two other
$hp$-adaptive strategies.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601484
Preprintreihe des Chemnitzer SFB 393, 04-10
eng
Preprintreihe des Chemnitzer SFB 393, 04-10
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18587/zip/
urn:nbn:de:swb:ch1-200601484
oai:qucosa:de:qucosa:18585
2021-03-29T09:47:48Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Wavelet Galerkin BEM on unstructured meshes
Helmut
Harbrecht
Ulf
Kähler
Reinhold
Schneider
510
510
Mehrskalenanalyse
Randelemente-Methode
Unstrukturiertes Gitter
multiscale methods
norm equivalences
The present paper is devoted to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme. On the given mesh we construct a wavelet basis providing vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates can be compressed to $\mathcal{O}(N\log N)$ relevant matrix coefficients, where $N$ denotes the number of unknowns. The compressed system matrix can be computed within suboptimal complexity by using techniques from the fast multipole method or panel clustering. Numerical results prove that we succeeded in developing a fast wavelet Galerkin scheme for solving the considered class of problems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601459
Preprintreihe des Chemnitzer SFB 393, 04-06
eng
Preprintreihe des Chemnitzer SFB 393, 04-06
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18585/zip/
urn:nbn:de:swb:ch1-200601459
oai:qucosa:de:qucosa:18588
2021-03-29T09:47:50Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Fourier-finite-element method with Nitsche-mortaring
Bernd
Heinrich
Beate
Jung
510
510
Finite-Elemente-Methode
Mortar-Element-Methode
Poisson-Gleichung
Fourier method
Nitsche-mortaring
non-matching meshes
The paper deals with a combination of the
Fourier-finite-element method with the
Nitsche-finite-element method (as a mortar method).
The approach is applied to the Dirichlet problem
of the Poisson equation in three-dimensional
axisymmetric domains $\widehat\Omega$ with
non-axisymmetric data. The approximating Fourier
method yields a splitting of the 3D-problem into
2D-problems. For solving the 2D-problems on the
meridian plane $\Omega_a$,
the Nitsche-finite-element method with
non-matching meshes is applied. Some important
properties of the approximation scheme are
derived and the rate of convergence in some
$H^1$-like norm is proved to be of the type
${\mathcal O}(h+N^{-1})$ ($h$: mesh size on
$\Omega_a$, $N$: length of the Fourier sum) in
case of a regular solution of the boundary value
problem. Finally, some numerical results are
presented.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601493
Preprintreihe des Chemnitzer SFB 393, 04-11
eng
Preprintreihe des Chemnitzer SFB 393, 04-11
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18588/zip/
urn:nbn:de:swb:ch1-200601493
oai:qucosa:de:qucosa:18590
2021-03-29T09:47:52Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the Convergence Factor in Multilevel Methods for Solving 3D Elasticity Problems
Michael
Jung
Todor D.
Todorov
510
510
Eigenwertproblem
Finite-Elemente-Methode
Mehrgitterverfahren
linear elasticity problem
strengthened Cauchy-Schwarz-Buniakowski inequality
The constant gamma in the strengthened Cauchy-Bunyakowskii-Schwarz inequality is a basic tool for constructing of two-level and multilevel preconditioning matrices. Therefore many authors consider estimates or computations of this quantity. In this paper the bilinear form arising from 3D linear elasticity problems is considered on a polyhedron. The cosine of the abstract angle between multilevel finite element subspaces is computed by a spectral analysis of a general eigenvalue problem. Octasection and bisection approaches are used for refining the triangulations. Tetrahedron, pentahedron and hexahedron meshes are considered. The dependence of the constant $\gamma$ on the Poisson ratio is presented graphically.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601510
Preprintreihe des Chemnitzer SFB 393, 04-13
eng
Preprintreihe des Chemnitzer SFB 393, 04-13
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18590/zip/
urn:nbn:de:swb:ch1-200601510
oai:qucosa:de:qucosa:18589
2021-03-29T09:47:51Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Laplace and the linear elasticity problems near polyhedral corners and associated eigenvalue problems
Arnd
Meyer
Cornelia
Pester
510
510
Eckensingularität
Eigenwertproblem
Elliptisches Randwertproblem
Laplace-Beltrami-Operator
corner singularities
linear elasticity problem
The solutions to certain elliptic boundary value problems have singularities with a typical structure near polyhedral corners. This structure can be exploited to devise an eigenvalue problem whose solution can be used to quantify the singularities of the given boundary value problem. It is necessary to parametrize a ball centered at the corner. There are different possibilities for a suitable parametrization; from the numerical point of view, spherical coordinates are not necessarily the best choice. This is why we do not specify a parametrization in this paper but present all results in a rather general form. We derive the eigenvalue problems that are associated with the Laplace and the linear elasticity problems and show interesting spectral properties. Finally, we discuss the necessity of widely accepted symmetry properties of the elasticity tensor. We show in an example that some of these properties are not only dispensable, but even invalid, although claimed in many standard books on linear elasticity.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-01
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601506
Preprintreihe des Chemnitzer SFB 393, 04-12
eng
Preprintreihe des Chemnitzer SFB 393, 04-12
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18589/zip/
urn:nbn:de:swb:ch1-200601506
oai:qucosa:de:qucosa:18595
2021-03-29T09:47:56Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parallel Order Reduction via Balanced Truncation for Optimal Cooling of Steel Profiles
José M.
Badía
Peter
Benner
Rafael
Mayo
Enrique S.
Quintana-Ortí
Gregorio
Quintana-Ortí
Jens
Saak
510
510
Ljapunov-Gleichung
Ordnungsreduktion
2-D heat equation
balanced truncation
dynamical linear system
generalized Lyapunov equations
We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601566
Preprintreihe des Chemnitzer SFB 393, 05-02
eng
Preprintreihe des Chemnitzer SFB 393, 05-02
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18595/zip/
urn:nbn:de:swb:ch1-200601566
oai:qucosa:de:qucosa:18594
2021-03-29T09:47:55Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A residual a posteriori error estimator for the eigenvalue problem for the Laplace-Beltrami operator
Cornelia
Pester
510
510
A-posteriori-Abschätzung
Eigenwertproblem
Laplace-Beltrami-Operator
Clément-type interpolation
spherical domains
The Laplace-Beltrami operator corresponds to the Laplace operator on curved surfaces. In this paper, we consider an eigenvalue problem for the Laplace-Beltrami operator on subdomains of the unit sphere in $\R^3$. We develop a residual a posteriori error estimator for the eigenpairs and derive a reliable estimate for the eigenvalues. A global parametrization of the spherical domains and a carefully chosen finite element discretization allows us to use an approach similar to the one for the two-dimensional case. In order to assure results in the quality of those for plane domains, weighted norms and an adapted Clément-type interpolation operator have to be introduced.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601556
Preprintreihe des Chemnitzer SFB 393, 05-01
eng
Preprintreihe des Chemnitzer SFB 393, 05-01
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18594/zip/
urn:nbn:de:swb:ch1-200601556
oai:qucosa:de:qucosa:18596
2021-03-29T09:47:57Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
CoCoS - Computation of Corner Singularities
Cornelia
Pester
510
510
Eckensingularität
Eigenwertproblem
Software
CoCoS
linear elasticity problem
This is a documentation of the software package COCOS. The purpose of COCOS is the computation of corner singularities of elliptic equations in polyhedral corners and crack tips. COCOS provides a self-contained library for the generation of structured 2D finite element meshes, including various routines for mesh manipulation, as well as several algorithms for the solution of quadratic eigenvalue problems with Hamiltonian structure. These and further features will be described in this documentation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-06
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601576
eng
Preprintreihe des Chemnitzer SFB 393, 05-03
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18596/zip/
urn:nbn:de:swb:ch1-200601576
oai:qucosa:de:qucosa:18597
2021-03-29T09:47:57Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Mindlin-Reissner-Platte: Einige Elemente, Fehlerschätzer und Ergebnisse
Arnd
Meyer
Peter
Nestler
510
510
Fehlerabschätzung
Finite-Elemente-Methode
Implementierung
Arnold Falk Element
MITC elements
Some problems and results in connection with error estimators for modern elements of the Mindlin Reissner equation for plates are discussed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-08
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601589
Preprintreihe des Chemnitzer SFB 393, 05-04
ger
Preprintreihe des Chemnitzer SFB 393, 05-04
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18597/zip/
urn:nbn:de:swb:ch1-200601589
oai:qucosa:de:qucosa:18600
2021-03-29T09:48:00Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A New Efficient Preconditioner for Crack Growth Problems
Arnd
Meyer
510
510
Finite-Elemente-Methode
Iterativ
Rissausbreitung
adaptive methods
crack growth
A new preconditioner for the quick solution of a crack growth problem in 2D adaptive finite element analysis is proposed. Numerical experiments demonstrate the power of the method.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601600
Preprintreihe des Chemnitzer SFB 393, 05-06
eng
Preprintreihe des Chemnitzer SFB 393, 05-06
info:eu-repo/semantics/openAccess
7
https://monarch.qucosa.de/api/qucosa%3A18600/zip/
urn:nbn:de:swb:ch1-200601600
oai:qucosa:de:qucosa:18598
2021-03-29T09:47:58Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Linear-Quadratic Regulator Design for Optimal Cooling of Steel Profiles
Peter
Benner
Jens
Saak
510
510
Approximationsalgorithmus
Riccati-Differentialgleichung
Wärmeleitungsgleichung
boundary control
dynamical linear systems
feedback control
We present a linear-quadratic regulator (LQR) design for a heat transfer model describing the cooling process of steel profiles in a rolling mill. Primarily we consider a feedback control approach for a linearization of the nonlinear model given there, but we will also present first ideas how to use local (in time) linearizations to treat the nonlinear equation with a regulator approach. Numerical results based on a spatial finite element discretization and a numerical algorithm for solving large-scale algebraic Riccati equations are presented both for the linear and nonlinear models.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601597
Preprintreihe des Chemnitzer SFB 393, 05-05
eng
Preprintreihe des Chemnitzer SFB 393, 05-05
info:eu-repo/semantics/openAccess
9
https://monarch.qucosa.de/api/qucosa%3A18598/zip/
urn:nbn:de:swb:ch1-200601597
oai:qucosa:de:qucosa:18601
2021-03-29T09:48:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Überlegungen zur Parameterwahl im Bramble-Pasciak-CG für gemischte FEM
Choices of the control parameters in the Bramble-Pasciak-CG for mixed problems
Arnd
Meyer
Peter
Steinhorst
510
510
Finite-Elemente-Methode
Iteration
Bramble-Pasciak CG
control parameters
mixed formulation
Variants on the choice of nessecary control parameters in the generalized Bramble-Pasciak-CG method are discussed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601612
Preprintreihe des Chemnitzer SFB 393, 05-07
ger
Preprintreihe des Chemnitzer SFB 393, 05-07
info:eu-repo/semantics/openAccess
7
https://monarch.qucosa.de/api/qucosa%3A18601/zip/
urn:nbn:de:swb:ch1-200601612
oai:qucosa:de:qucosa:18603
2021-03-29T09:48:02Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Mindlin-Reissner-Platte : Vergleich der Fehlerindikatoren in Bezug auf die Netzsteuerung
Arnd
Meyer
Peter
Nestler
510
510
Fehlerabschätzung
Finite-Elemente-Methode
Gittererzeugung
MITC elements
Mindlin-Reissner-Platte
Es werden die vorgestellten Fehlerindikatoren in Bezug auf die Netzsteuerung anhand von drei Beispielen analysiert. Im weiteren werden auch die einzelen MITC-Elemente und ihre Besonderheiten bei dieser Analyse der Netzsteuerung mit berücksichtigt. Als Abschluss werden einige spezielle Fehlerindikatoren vorgestellt, die für die weitere Entwicklung einige interessante Eigenschaften aufzeigen.
Im zweiten Teil geht es um die Auswertung mit dem speziellen Ziel der Findung einer optimalen Netzsteuerung. Dabei wird auf die Besonderheiten der Elemente eingegangen sowie auf die Plattendicke und auf ihre Wirkung bei den Fehlerindikatoren. Mit diesen Erkenntnissen wird ein spezieller Fehlerindikator vorgestellt, der die Vorteile aller Fehlerindikatoren aus Teil I vereint.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601638
Preprintreihe des Chemnitzer SFB 393, 05-09/10
ger
Preprintreihe des Chemnitzer SFB 393, 05-09/10
info:eu-repo/semantics/openAccess
10
https://monarch.qucosa.de/api/qucosa%3A18603/zip/
urn:nbn:de:swb:ch1-200601638
oai:qucosa:de:qucosa:18602
2021-03-29T09:48:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison
Tino
Eibner
Jens Markus
Melenk
510
510
Finite-Elemente-Methode
Steifigkeitsmatrix
hp-Methode
elliptic problems
matrix-vector multiplication
We analyze and compare different techniques to
set up the stiffness matrix in the hp-version
of the finite element method. The emphasis is
on methods for second order elliptic problems
posed on meshes including triangular and
tetrahedral elements. The polynomial degree
may be variable. We present a generalization
of the Spectral Galerkin Algorithm of [7],
where the shape functions are adapted to the
quadrature formula, to the case of
triangles/tetrahedra. Additionally, we study
on-the-fly matrix-vector multiplications, where
merely the matrix-vector multiplication is
realized without setting up the stiffness matrix.
Numerical studies are included.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601623
Preprintreihe des Chemnitzer SFB 393, 05-08
eng
Preprintreihe des Chemnitzer SFB 393, 05-08
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18602/zip/
urn:nbn:de:swb:ch1-200601623
oai:qucosa:de:qucosa:18608
2021-03-29T09:48:06Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Nitsche- and Fourier-finite-element method for the Poisson equation in axisymmetric domains with re-entrant edges
Bernd
Heinrich
Beate
Jung
510
510
Eckensingularität
Finite-Elemente-Methode
Poisson-Gleichung
Fourier method
Nitsche-mortaring
non-matching meshes
The paper deals with a combination of the Fourier
method with the Nitsche-finite-element method
(as a mortar method). The approach is applied to
the Dirichlet problem of the Poisson equation in
threedimensional axisymmetric domains with
reentrant edges generating singularities.
The approximating Fourier method yields a
splitting of the 3D problem into 2D problems
on the meridian plane of the given domain.
For solving the 2D problems bearing corner
singularities, the Nitsche finite-element
method with non-matching meshes and mesh
grading near reentrant corners is applied.
Using the explicit representation of singular
functions, the rate of convergence of the
Fourier-Nitsche-mortaring is estimated in some
$H^1$-like norm as well as in the $L_2$-norm.
Finally, some numerical results are presented.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601691
Preprintreihe des Chemnitzer SFB 393, 05-16
eng
Preprintreihe des Chemnitzer SFB 393, 05-16
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18608/zip/
urn:nbn:de:swb:ch1-200601691
oai:qucosa:de:qucosa:18605
2021-03-29T09:48:04Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
The Fourier Singular Complement Method for the Poisson Problem. Part III: Implementation Issues
Patrick
Ciarlet, Jr.
Beate
Jung
Samir
Kaddouri
Simon
Labrunie
Jun
Zou
510
510
Eckensingularität
Finite-Elemente-Methode
Fourier method
mesh grading
numerical experiments
singular complement method
This paper is the last part of a three-fold article
aimed at some efficient numerical methods for
solving the Poisson problem in three-dimensional
prismatic and axisymmetric domains. In the first
and second parts, the Fourier singular complement
method (FSCM) was introduced and analysed for
prismatic and axisymmetric domains with reentrant
edges, as well as for the axisymmetric domains
with sharp conical vertices. In this paper we
shall mainly conduct numerical experiments to check
and compare the accuracies and efficiencies
of FSCM and some other related numerical methods
for solving the Poisson problem in the
aforementioned domains. In the case of prismatic
domains with a reentrant edge, we shall compare
the convergence rates of three numerical methods:
3D finite element method using prismatic elements,
FSCM, and the 3D finite element method combined
with the FSCM. For axisymmetric domains with a
non-convex edge or a sharp conical vertex we
investigate the convergence rates of the
Fourier finite element method (FFEM) and the
FSCM, where the FFEM will be implemented on both
quasi-uniform meshes and locally graded meshes.
The complexities of the considered algorithms
are also analysed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601654
Preprintreihe des Chemnitzer SFB 393, 05-12; Part I: Num. Math., vol. 101, pp. 423-450, 2005; Part II: Num. Math., vol. 102, pp. 583-610, 2006
eng
Preprintreihe des Chemnitzer SFB 393, 05-12; Part I: Num. Math., vol. 101, pp. 423-450, 2005; Part II: Num. Math., vol. 102, pp. 583-610, 2006
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18605/zip/
urn:nbn:de:swb:ch1-200601654
oai:qucosa:de:qucosa:18609
2021-03-29T09:48:07Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Solving Linear-Quadratic Optimal Control Problems on Parallel Computers
Peter
Benner
Enrique S.
Quintana-Ortí
Gregorio
Quintana-Ortí
510
510
Algebraische Riccati-Gleichung
Parallelverarbeitung
disk function
linear-quadratic optimal control
sign function
We discuss a parallel library of efficient algorithms for the solution of linear-quadratic optimal control problems involving largescale systems with state-space dimension up to $O(10^4)$. We survey the numerical algorithms underlying the implementation of the chosen optimal control methods. The approaches considered here are based on invariant and deflating subspace techniques, and avoid the explicit solution of the associated algebraic Riccati equations in case of possible ill-conditioning. Still, our algorithms can also optionally compute the Riccati solution. The major computational task of finding spectral projectors onto the required invariant or deflating subspaces is implemented using iterative schemes for the sign and disk functions. Experimental results report the numerical accuracy and the parallel performance of our approach on a cluster of Intel Itanium-2 processors.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601704
Preprintreihe des Chemnitzer SFB 393, 05-19
eng
Preprintreihe des Chemnitzer SFB 393, 05-19
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18609/zip/
urn:nbn:de:swb:ch1-200601704
oai:qucosa:de:qucosa:18606
2021-03-29T09:48:05Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Multilevel preconditioning for the boundary concentrated hp-FEM
Tino
Eibner
Jens Markus
Melenk
510
510
Finite-Elemente-Methode
Gitterverfeinerung
hp-Methode
elliptic problems
multilevel preconditioning
The boundary concentrated finite element method
is a variant of the hp-version of the finite
element method that is particularly suited for
the numerical treatment of elliptic boundary
value problems with smooth coefficients and low
regularity boundary conditions. For this method
we present two multilevel preconditioners that
lead to preconditioned stiffness matrices with
condition numbers that are bounded uniformly in
the problem size N. The cost of applying the
preconditioners is O(N). Numerical examples
illustrate the efficiency of the algorithms.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601662
Preprintreihe des Chemnitzer SFB 393, 05-13
eng
Preprintreihe des Chemnitzer SFB 393, 05-13
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18606/zip/
urn:nbn:de:swb:ch1-200601662
oai:qucosa:de:qucosa:18607
2021-03-29T09:48:06Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Multilevel preconditioning operators on locally modified grids
Michael
Jung
Aleksandr M.
Matsokin
Sergey V.
Nepomnyaschikh
Yu. A.
Tkachov
510
510
Finite-Elemente-Methode
Gittererzeugung
Präkonditionierung
elliptic boundary value problem
multilevel methods
Systems of grid equations that approximate elliptic boundary value problems on locally modified grids are considered. The triangulation, which approximates the boundary with second order of accuracy, is generated from an initial uniform triangulation by shifting nodes near the boundary according to special rules. This "locally modified" grid possesses several significant features: this triangulation has a regular structure, the generation of the triangulation is rather fast, this construction allows to use multilevel preconditioning (BPX-like) methods. The proposed iterative methods for solving elliptic boundary value problems approximately are based on two approaches: The fictitious space method, i.e. the reduction of the original problem to a problem in an auxiliary (fictitious) space, and the multilevel decomposition method, i.e. the construction of preconditioners by decomposing functions on hierarchical grids. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh size. The construction of the grid and the preconditioning operator for the three dimensional problem can be done in the same way.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2006-09-11
2021-03-29
preprint
urn:nbn:de:swb:ch1-200601671
Preprintreihe des Chemnitzer SFB 393, 05-14
eng
Preprintreihe des Chemnitzer SFB 393, 05-14
info:eu-repo/semantics/openAccess
8
https://monarch.qucosa.de/api/qucosa%3A18607/zip/
urn:nbn:de:swb:ch1-200601671
oai:qucosa:de:qucosa:18671
2021-03-29T09:48:59Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:000
openaire
Software pertaining to the preparation of CAD data from IGES interface for mesh-free and mesh-based numerical solvers
IntegralCAD version 0.9.1
Maharavo
Randrianarivony
Dr.-Ing.
000
000
CAD
Gitterverfeinerung
Integralgleichung
Coons
Quadrangulation
Transfinite interpolation
Viereckige Zerlegung
We focus on the programming aspect of the treatment of digitized
geometries for subsequent use in mesh-free and mesh-based numerical
solvers. That perspective includes the description of our C/C++ implementations
which use OpenGL for the visualization and MFC classes for the user
interface. We report on our experience about implementing with the IGES
interface which serves as input for storage of geometric information. For
mesh-free numerical solvers, it is helpful to decompose the boundary of a
given solid into a set of four-sided surfaces. Additionally, we will describe
the treatment of diffeomorphisms on four-sided domains by using transfinite
interpolations. In particular, Coons and Gordon patches are appropriate for
dealing with such mappings when the equations of the delineating curves
are explicitly known. On the other hand, we show the implementation of
the mesh generation algorithms which invoke the Laplace-Beltrami operator.
We start from coarse meshes which one refine according to generalized
Delaunay techniques. Our software is also featured by its ability of treating
assembly of solids in B-Rep scheme.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-02-27
2021-03-29
preprint
urn:nbn:de:swb:ch1-200700267
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18671/zip/
urn:nbn:de:swb:ch1-200700267
oai:qucosa:de:qucosa:18670
2021-03-29T09:48:58Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:000
openaire
The ITL programming interface toolkit
(API functions Version 0.9.1)
Maharavo
Randrianarivony
Dr.-Ing.
000
000
CAD-CAM
Integralgleichung
CAD
Coons
Integral equation
Quadrangulation
Transfinite interpolation
Wavelet Galerkin
This document serves as a reference for the beta version of our evaluation
library ITL. First, it describes a library which gives an easy way for
programmers to evaluate the 3D image and the normal vector corresponding to
a parameter value which belongs to the unit square. The API functions which
are described in this document let programmers make those
evaluations without the need to understand the underlying CAD complica-
tions. As a consequence, programmers can concentrate on their own scien-
tific interests. Our second objective is to describe the input which is a set
of parametric four-sided surfaces that have the structure required by some
integral equation solvers.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-02-27
2021-03-29
preprint
urn:nbn:de:swb:ch1-200700254
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18670/zip/
urn:nbn:de:swb:ch1-200700254
oai:qucosa:de:qucosa:18812
2020-11-17T09:50:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:330
status-type:submittedVersion
openaire
Probleme der Wissensgesellschaft und ihrer Wissens-Wissenschaften Thesen zur Neukonturierung der Erwerbsarbeit
Manfred F.
Moldaschl
Prof. Dr. Dr.
Informationsgesellschaft
Wissensextraktion
Wissensintensives Unternehmen
Wissenskluft
Wissensmanagement
Wissensorganisation
Wissensproduktion
Wissenspsychologie
Wissensrepräsentation
Wissenssoziologie
330
330
Informationsgesellschaft
Wissensextraktion
Wissensintensives Unternehmen
Wissenskluft
Wissensmanagement
Wissensorganisation
Wissensproduktion
Wissenspsychologie
Wissensrepräsentation
Wissenssoziologie
Die Transformation der Industriegesellschaft zur „Wissensgesellschaft“ ist ein in vielen Punk-ten erst noch zu verstehender und zu erforschender Prozess. Man muss sich nicht lange mit der scholastischen Frage aufhalten, ob man aktuelle Umbrüche in Erwerbsarbeit und Gesell-schaft unter diesem Label angemessen zusammenfassen kann, solange man den Begriff als eine unter verschiedenen möglichen „Brillen“ betrachtet, die die Aufmerksamkeit auf be-stimmte Trends lenkt und die Annahmen bezüglich ihrer inneren Zusammenhänge klar formu-liert.
Technische Universität Chemnitz
Chemnitz
Chemnitz
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2007-11-05
2020-11-17
preprint
submittedVersion
urn:nbn:de:bsz:ch1-200701743
ger
info:eu-repo/semantics/openAccess
0
https://monarch.qucosa.de/api/qucosa%3A18812/zip/
urn:nbn:de:bsz:ch1-200701743
oai:qucosa:de:qucosa:18818
2020-11-17T09:45:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:330
status-type:submittedVersion
openaire
Institutional Reflexivity
An institutional approach to measure innovativeness
Manfred F.
Moldaschl
Prof Dr. Dr.
Institutional Reflexivity
Absorptive Capacity
Competence-Based View
Dynamic Capabilities
330
330
Innovationsbereitschaft
Innovationspotenzial
How can we understand the innovativeness of firms or organizations in general, and how should we assess it in terms of nontechnological innovation? My paper deals with these two questions. The “ability” of companies to adapt to new circumstances, to create new products, processes and new knowledge, has been conceptualized in many approaches. Some of them simply define a list of “(critical) success factors” or “(key) performance indica-tors”, as tools for ranking and evaluation, without any theoretical reference. Others, like the resource-based or capability-based approach(es), work with theoretical references, but are still very weak in operationalizing of what they call “capability”. My paper gives a critical description of this situation and offers a new proposal to classify and to measure the “inclination” of organizations to innovate in all dimensions. This proposal roots in pragmatistic thinking as represented in the theory of reflexive modernization and in the pragmatist version of organizational learning theory. Empirically, it has been applied merely in case studies yet. A survey project is in preparation.
Technische Universität Chemnitz
Chemnitz
Chemnitz
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2007-11-19
2020-11-17
preprint
submittedVersion
urn:nbn:de:bsz:ch1-200701809
eng
info:eu-repo/semantics/openAccess
0
https://monarch.qucosa.de/api/qucosa%3A18818/zip/
urn:nbn:de:bsz:ch1-200701809
oai:qucosa:de:qucosa:18817
2020-11-17T09:42:37Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:330
status-type:submittedVersion
openaire
Zivilisierung, Informalisierung, Individualisierung
Zur kultursoziologischen und modernisierungstheoretischen Deutung der Subjektivierung von Arbeit
Manfred F.
Moldaschl
Prof Dr. Dr.
Individualisierung
Informalisierung
Zivilisierung
330
330
Arbeitsethik
Modernisierung
Modernisierungstheorie
Soziologie
Man soll in Gesellschaft anderer besser nicht über den Tisch spucken. Dass uns dieser Rat des Erasmus von Rotterdam heute bestenfalls überflüssig vorkommt, weil über den Tisch zu spu-cken niemand mehr als „natürliches“ Bedürfnis empfindet, ist aus kulturhistorischer Sicht ein Beleg für die Wandelbarkeit menschlicher Bedürfnisse und Sitten, und aus der Sicht von Nor-bert Elias‘ Zivilisationstheorie ein Zeichen für die fortschreitende bzw. fortgeschrittene Inter-nalisierung gesellschaftlicher Regeln in die individuelle ‚Affektkontrolle‘. Ist dieser Prozess möglicherweise der generative gesellschaftliche Hintergrund für diejenigen Prozesse, die wir in der Regel nur als Folge von Veränderungen im Wirtschaftssystem betrachten, und denen wir gewissermaßen nur nachträglich eine ökonomische Rationalität zuschreiben? Können Elias‘ psychogenetische und soziogenetische Untersuchungen des Zivilisationsprozesses den kulturellen Hintergrund beleuchten, der jenen radikalen Wandel von Organisationslogiken im Feld der Wirtschaft ermöglichte, welchen wir als „Subjektivierung von Arbeit“ bezeichnen?
Technische Universität Chemnitz
Chemnitz
Chemnitz
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2007-11-19
2020-11-17
preprint
submittedVersion
urn:nbn:de:bsz:ch1-200701796
ger
info:eu-repo/semantics/openAccess
0
https://monarch.qucosa.de/api/qucosa%3A18817/zip/
urn:nbn:de:bsz:ch1-200701796
oai:qucosa:de:qucosa:18820
2020-11-17T09:46:57Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:330
status-type:submittedVersion
openaire
Institutionelle Reflexivität
Manfred F.
Moldaschl
Prof Dr. Dr.
Institutionelle
Reflexivität
lernen
330
330
Politische Institutionenlehre
Reflexivität
Während die handlungsorientierte Managementforschung und -theorie von Frage nach der bestmöglichen Orga-nisation der Produktion (im weitesten Sinne: der Leistungserstellung) ausgeht, fragt die erklärungsorientierte Organisationstheorie nach der Produktion der Organisation. Verschiedene Organisationstheorien beinhalten, in den letzten Jahren verstärkt, Aussagen und Hypothesen darüber, dass die Produktion organisationaler Regeln zunehmend reflexiv erfolge. Als Chiffre dafür etablierte sich, besonders im Anschluss an Argyris und Schön (1978) das „Organisationslernen“. Manches davon ist in anspruchsvollere Konzepte des Wissensmanagements mitgenommen worden. Gemeint ist damit, dass die Modifikation organisationaler Regeln erstens vom Ausnah-me- zum Regelfall wird, zweitens zunehmend selbst der Reflexion unterzogen wird, und dabei drittens immer wissensabhängiger wird (u. a., weil sich die Gestaltungsoptionen vervielfältigen). Fast alle Ansätze aber, die den Begriff der Reflexivität gebrauchen, tun dies mehr oder weniger en passant, und auf ein wissenschaftliches All-tagsverständnis von diesem Begriff vertrauend. In meinem Beitrag möchte ich zeigen, dass man die Kategorie der Reflexivität ernster nehmen sollte, und man damit – gewissermaßen als Lohn - ein Konzept Institutioneller Reflexivität begründen kann, das bei der Analyse und die Gestaltung von Organisation bzw. organisationalem Wandel gute Dienste leisten kann. Die Organisationstheorie muss dazu allerdings Anleihen bei der Modernisie-rungstheorie machen.
Technische Universität Chemnitz
Chemnitz
Chemnitz
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
2007-11-20
2020-11-17
preprint
submittedVersion
urn:nbn:de:bsz:ch1-200701833
ger
info:eu-repo/semantics/openAccess
0
https://monarch.qucosa.de/api/qucosa%3A18820/zip/
urn:nbn:de:bsz:ch1-200701833
oai:qucosa:de:qucosa:18829
2021-03-29T09:51:07Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the solution of the radical matrix equation $X=Q+LX^{-1}L^T$
Peter
Benner
Heike
Faßbender
510
510
Matrix <Mathematik>
Nichtlineare algebraische Gleichung
butterfly SZ algorithm
discrete-time algebraic Riccati equation
nonlinear matrix equation
We study numerical methods for finding the maximal
symmetric positive definite solution of the nonlinear matrix equation
$X = Q + LX^{-1}L^T$, where Q is symmetric positive definite and L is
nonsingular. Such equations arise for instance in the analysis of
stationary Gaussian reciprocal processes over a finite interval.
Its unique largest positive definite solution coincides with the unique
positive definite solution of a related discrete-time algebraic
Riccati equation (DARE). We discuss how to use the butterfly
SZ algorithm to solve the DARE. This approach is compared to
several fixed point type iterative methods suggested in the
literature.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-26
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701929
eng
Chemnitz Scientific Computing Preprints ; 06-02
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18829/zip/
urn:nbn:de:bsz:ch1-200701929
oai:qucosa:de:qucosa:18831
2021-03-29T09:51:09Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Balanced Truncation Model Reduction of Large and Sparse Generalized Linear Systems
José M.
Badía
Peter
Benner
Rafael
Mayo
Enrique S.
Quintana-Ortí
Gregorio
Quintana-Ortí
Alfredo
Remón
510
510
Ljapunov-Gleichung
Ordnungsreduktion
Parallelverarbeitung
balanced truncation
generalized Lyapunov equations
model reduction
We investigate model reduction of large-scale linear time-invariant systems in
generalized state-space form. We consider sparse state matrix pencils, including
pencils with banded structure. The balancing-based methods employed here are
composed of well-known linear algebra operations and have been recently shown to be
applicable to large models by exploiting the structure of the matrices defining
the dynamics of the system.
In this paper we propose a modification of the LR-ADI iteration to solve
large-scale generalized Lyapunov equations together with a practical
convergence criterion, and several other implementation refinements.
Using kernels from several serial and parallel linear algebra libraries,
we have developed a parallel package for model reduction, SpaRed, extending
the applicability of balanced truncation to sparse systems with up to
$O(10^5)$ states.
Experiments on an SMP parallel architecture consisting of Intel Itanium 2 processors
illustrate the numerical performance of this approach and the potential of the
parallel algorithms for model reduction of large-scale sparse systems.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-26
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701947
Chemnitz Scientific Computing Preprints
eng
Chemnitz Scientific Computing Preprints
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18831/zip/
urn:nbn:de:bsz:ch1-200701947
oai:qucosa:de:qucosa:18832
2021-03-29T09:51:10Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Gramian-Based Model Reduction for Data-Sparse Systems
Ulrike
Baur
Peter
Benner
510
510
Ljapunov-Gleichung
Ordnungsreduktion
balanced truncation
large-scale Lyapunov equation
model reduction
Model reduction is a common theme within the simulation, control and
optimization of complex dynamical systems. For instance, in control
problems for partial differential equations, the associated large-scale
systems have to be solved very often. To attack these problems in
reasonable time it is absolutely necessary to reduce the dimension of the
underlying system. We focus on model reduction by balanced truncation
where a system theoretical background provides some desirable properties
of the reduced-order system. The major computational task in
balanced truncation is the solution of large-scale Lyapunov equations,
thus the method is of limited use for really large-scale applications.
We develop an effective implementation of balancing-related model reduction
methods in exploiting the structure of the underlying problem.
This is done by a data-sparse approximation of the large-scale state
matrix A using the hierarchical matrix format. Furthermore, we integrate
the corresponding formatted arithmetic in the sign function method
for computing approximate solution factors of the Lyapunov equations.
This approach is well-suited for a class of practical relevant problems
and allows the application of balanced truncation and related methods
to systems coming from 2D and 3D FEM and BEM discretizations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-27
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701952
eng
Chemnitz Scientific Computing Preprints ; 07-01
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18832/zip/
urn:nbn:de:bsz:ch1-200701952
oai:qucosa:de:qucosa:18830
2021-03-29T09:51:08Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the Parameter Selection Problem in the Newton-ADI Iteration for Large Scale Riccati Equations
Peter
Benner
Hermann
Mena
Jens
Saak
510
510
Linearquadratische Kontrolltheorie
Parabolische Differentialgleichung
Riccati-Differentialgleichung
Newton-ADI iteration
large scale differential Riccati equation
The numerical treatment of linear-quadratic regulator problems for
parabolic partial differential equations (PDEs) on infinite time horizons
requires the solution of large scale algebraic Riccati equations (ARE).
The Newton-ADI iteration is an efficient numerical method for this task.
It includes the solution of a Lyapunov equation by the alternating directions
implicit (ADI) algorithm in each iteration step. On finite time
intervals the solution of a large scale differential Riccati equation is required.
This can be solved by a backward differentiation formula (BDF)
method, which needs to solve an ARE in each time step.
Here, we study the selection of shift parameters for the ADI method.
This leads to a rational min-max-problem which has been considered by
many authors. Since knowledge about the complete complex spectrum
is crucial for computing the optimal solution, this is infeasible for the
large scale systems arising from finite element discretization of PDEs.
Therefore several alternatives for computing suboptimal parameters are
discussed and compared for numerical examples.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-26
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701930
eng
Chemnitz Scientific Computing Preprints ; 06-03
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18830/zip/
urn:nbn:de:bsz:ch1-200701930
oai:qucosa:de:qucosa:18833
2021-03-29T09:51:11Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Rotationssymmetrie für piezoelektrische Probleme
Rotational Symmetry for Piezoelectric Problems
Peter
Steinhorst
510
510
Adaptives Verfahren
Finite-Elemente-Methode
Piezoelektrizität
Rotationssymmetrie
Zylinderkoordinaten
Ausgehend von bekannten Grundlagen zu Rotationssymmetrie und linearer Elektromechanik, wird eine Vorlage für die Simulation piezoelektrischer Probleme mit FEM im rotationssymmetrischen Fall hergeleitet. Dabei wird insbesondere die Berechnung der Integrale in den Bilinearformen mittels erweiterter 2D-Methoden beschrieben. Außerdem wird kurz auf notwendige Modifikationen am Fehlerschätzer sowie auf die Behandlung der Randbedingungen eingegangen. Ein Experimentalprogramm mit einigen gerechneten Testbeispielen zeigt die prinzipielle Umsetzbarkeit der vorgestellten Theorie und ermöglicht den Abgleich mit anderen Methoden.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701978
ger
Chemnitz Scientific Computing Preprints ; 07-03
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18833/zip/
urn:nbn:de:bsz:ch1-200701978
oai:qucosa:de:qucosa:18836
2021-03-29T09:51:13Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Primal and Dual Interface Concentrated Iterative Substructuring Methods
Sven
Beuchler
Tino
Eibner
Ulrich
Langer
510
510
Finite-Elemente-Methode
Gebietszerlegungsmethode
Parallelverarbeitung
Substruktur
boundary concentrated
interface concentrated
This paper is devoted to the fast solution of interface concentrated finite element
equations. The interface concentrated finite element schemes are constructed
on the basis of a non-overlapping domain decomposition where a conforming
boundary concentrated finite element approximation is used in every subdomain.
Similar to data-sparse boundary element domain decomposition methods
the total number of unknowns per subdomain behaves like $O((H/h)^{d−1})$,
where H, h, and d denote the usual scaling parameter of the subdomains, the
average discretization parameter of the subdomain boundaries, and the spatial
dimension, respectively. We propose and analyze primal and dual substructuring
iterative methods which asymptotically exhibit the same or at least almost
the same complexity as the number of unknowns. In particular, the so-called
All-Floating Finite Element Tearing and Interconnecting solvers are
highly parallel and very robust with respect to large coefficient jumps.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200701990
eng
Chemnitz Scientific Computing Preprints ; 07-04
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18836/zip/
urn:nbn:de:bsz:ch1-200701990
oai:qucosa:de:qucosa:18837
2021-03-29T09:51:14Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Simultane Identifikation voneinander unabhängiger Materialparameter - numerische Studien
Torsten
Hein
Marcus
Meyer
510
510
Elliptische Differentialgleichung
Fallstudie
Parameteridentifikation
Identifizierbarkeit
Modellproblem
In einem Modellproblem wird die Aufgabe der gleichzeitigen Identifikation
zweier unabhängiger Parameterfunktionen bei elliptischen Differentialgleichungen
untersucht. Es werden Parameterfunktionen betrachtet,
die stückweise konstant sind. In einer ausführlichen Fallstudie
wird auf unterschiedliche Fragestellungen eingegangen.
Hierbei handelt es sich zum einen um den Vergleich von
verschiedenen bekannten Lösungsalgorithmen, um für dieses Problem geeignete
Varianten auszuwählen. Des Weiteren wurden der Einfluss von Messfehlern auf
die Qualität der Lösung sowie die Wahl von Schranken für die zu ermittelnden
Parameter untersucht. Darüber hinaus wird die Wirkung der konkreten Wahl
der Randbedingungen auf die Identifizierbarkeit der zu bestimmenden
Werte untersucht.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200702000
Chemnitz Scientific Computing Preprints, 07-05
ger
Chemnitz Scientific Computing Preprints, 07-05
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18837/zip/
urn:nbn:de:bsz:ch1-200702000
oai:qucosa:de:qucosa:18838
2021-03-29T09:51:15Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Ein Beitrag zur adaptiven gemischten Finite-Elemente-Formulierung der nahezu inkompressiblen Elastizität bei großen Verzerrungen
A contribution to adaptive mixed finite element formulations of nearly incompressible elasticity at finite defomations
Anke
Bucher
Uwe-Jens
Görke
Peter
Steinhorst
Reiner
Kreißig
Arnd
Meyer
510
510
Adaptives Verfahren
Finite-Elemente-Methode
Mehrfeldproblem
Hyperelastizität
stabile Elementklassen
In dieser Publikation werden konstitutive Gleichungen für die Modellierung großer, nahezu inkompressibler hyperelastischer Verzerrungen sowie deren numerische Realiserung im Rahmen einer adaptiven gemischten Finite-Elemente-Formulierung beschrieben. Mit dieser Problemklasse werden Methoden und Algorithmen zur numerischen Lösung direkter und inverser Aufgaben aus dem so genannten multiphysics-Bereich bereit gestellt. Dabei handelt es sich um Mehrfeldprobleme, deren gekoppelte Behandlung eine wachsende Rolle bei der hochgenauen Simulation realer physikalischer Vorgänge spielt. Der vorgestellte konstitutive Ansatz beruht auf einer multiplikativen Zerlegung des Deformationsgradienten und einer additiven Zerlegung der freien Helmholtz-Energiedichte, die auf eine Zweifeldformulierung mit den Verschiebungen und dem Druck als Knotenvariablen führen. Die linearisierten Feldgleichungen werden aus dem Impulssatz und der Inkompressibilitätsbedingung hergeleitet und im Inkrement mit einem effektiven iterativen Löser mit hierarchischer Vorkonditionierung gleichzeitig gelöst. Zur adaptiven Steuerung der Netzverfeinerung bzw. -vergröberung wird ein residualer a posteriori Fehlerschätzer genutzt. Effizienz und Genauigkeit der numerischen Algorithmen werden an einem illustrativen Beispiel demonstriert.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200702017
ger
Chemnitz Scientific Computing Preprints ; 07-06
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18838/zip/
urn:nbn:de:bsz:ch1-200702017
oai:qucosa:de:qucosa:18841
2021-03-29T09:51:17Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Identification of material parameters in linear elasticity - some numerical results
Torsten
Hein
Marcus
Meyer
510
510
Inverses Problem
Lineare Elastizitätstheorie
Parameteridentifikation
experimental design
small deformation
In this paper we present some numerical results concerning the identification of material parameters in linear elasticity by dealing with small deformations. On the basis of a precise example different aspects of the parameter estimation problem are considered. We deal with practical questions such as the experimental design for obtaining sufficient data for recovering the unknown parameters as well as questions of treating the corresponding inverse problems numerically. Two algorithms for solving these problems can be introduced and extensive numerical case studies are presented and discussed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200702040
Chemnitz Scientific Computing Preprints, 07-09
eng
Chemnitz Scientific Computing Preprints, 07-09
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18841/zip/
urn:nbn:de:bsz:ch1-200702040
oai:qucosa:de:qucosa:18839
2021-03-29T09:51:15Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Zur Numerik der inversen Aufgabe für gemischte (u/p) Formulierungen am Beispiel der nahezu inkompressiblen Elastizität bei großen Verzerrungen
About the Numerics of the Inverse Problem Considering Mixed (u/p) Formulations on the Example of Nearly Incompressible Elasticity at Finite Strains
Uwe-Jens
Görke
Anke
Bucher
Reiner
Kreißig
510
510
Finite-Elemente-Methode
Inkompressibilität
Nichtlineare Elastizitätstheorie
Sensitivitätsanalyse
mixed formulation
In dieser Publikation werden ein numerisches
Verfahren zur Kalibrierung von Materialmodellen
für die Simulation großer, nahezu inkompressibler
hyperelastischer Verzerrungen sowie dessen
numerische Realiserung im Rahmen einer gemischten
Finite Elemente Formulierung vorgestellt.
Dabei werden die Parameter der konstitutiven
Beziehungen auf der Grundlage experimentell erfasster
Verschiebungsfelder (vorzugsweise inhomogener)
bzw. globaler Informationen ermittelt. Dieses
inkorrekte, inverse Problem wird mit Hilfe eines
deterministischen Optimierungsverfahrens vom
trust-region-Typ gelöst. Wesentlicher Bestandteil
ist dabei die halbanalytische Sensitivitätsanalyse,
die ein effizientes und hochgenaues Verfahren zur
Ermittlung des Gradienten der Zielfunktion darstellt.
Sie erfordert die einmalige Lösung eines zur direkten
Aufgabe analogen Gleichungssystems pro Parameter und
Lastschritt und basiert auf der impliziten
Differentiation der schwachen Formulierung des
gemischten Randwertproblems nach den
Materialparametern. Genauigkeit und Konvergenzverhalten
der numerischen Algorithmen werden an illustrativen
Beispielen mit synthetischen Messwerten demonstriert.
Im Mittelpunkt stehen dabei Untersuchungen zur
Abhängigkeit des Optimierungsergebnisses von den
Startwerten für unterschiedliche konstitutive
Ansätze der kompressiblen und nahezu
inkompressiblen Elastizität.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200702023
Chemnitz Scientific Computing Preprints, 07-07
ger
Chemnitz Scientific Computing Preprints, 07-07
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18839/zip/
urn:nbn:de:bsz:ch1-200702023
oai:qucosa:de:qucosa:18842
2021-03-29T09:51:18Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
p-FEM quadrature error analysis on tetrahedra
Tino
Eibner
Jens Markus
Melenk
510
510
Fehleranalyse
Finite-Elemente-Methode
Numerische Integration
Tetraedergitter
p-Methode
adapted shape functions
discrete stability
In this paper we consider the p-FEM for elliptic boundary value problems on tetrahedral meshes where the entries of the stiffness matrix are evaluated by numerical quadrature. Such a quadrature can be done by mapping the tetrahedron to a hexahedron via the Duffy transformation.
We show that for tensor product Gauss-Lobatto-Jacobi quadrature formulas with q+1=p+1 points in each direction and shape functions that are adapted to the quadrature formula, one again has discrete stability for the fully discrete p-FEM.
The present error analysis complements the work [Eibner/Melenk 2005] for the p-FEM on triangles/tetrahedra where it is shown that by adapting the shape functions to the quadrature formula, the stiffness matrix can be set up in optimal complexity.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-30
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200702059
eng
Chemnitz Scientific Computing Preprints, CSC/06-01
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18842/zip/
urn:nbn:de:bsz:ch1-200702059
oai:qucosa:de:qucosa:18840
2021-03-29T09:51:16Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Betrachtungen zur Spektraläquivalenz für das Schurkomplement im Bramble-Pasciak-CG bei piezoelektrischen Problemen
Examining spectral equivalence of the Schur complement in the Bramble-Pasciak-CG in the case of piezoelectric problems
Arnd
Meyer
Peter
Steinhorst
510
510
Finite-Elemente-Methode
Konjugierte-Gradienten-Methode
Piezoelektrizität
Präkonditionierung
Bramble-Pasciak-CG
Der Einsatz der Finite-Element-Methode bei linearen piezoelektrischen Problemen führt auf eine Systemmatrix der Struktur \[\left( \begin{array}{lr} C & B \\ B^T & -K \end{array} \right)\] mit positiv definiten Blockmatrizen C und K. Zur Lösung indefiniter Gleichungssysteme, die diese symmetrische Blockstruktur besitzen, kann der Bramble--Pasciak--CG eingesetzt werden. Entscheidend für eine schnelle Lösung ist es dabei, gute Vorkonditionierer für den Block C sowie für ein inexaktes Schurkomplement zu finden. Nachfolgend wird das Schurkomplement auf Spektraläquivalenz zur Blockmatrix K untersucht, für welche gute Vorkonditionierer bekannt sind.
Using the Finite-Element-Method with linear piezoelectric problems leads to a linear system of the structure \[\left( \begin{array}{lr} C & B \\ B^T & -K \end{array} \right)\] with symmetric positive definite matrix blocks C and K. The Bramble--Pasciak--CG is a possible solver for indefinite linear systems of equations with this special symmetric block structure. Essential for fast solving are good preconditioners for the block C as well as for an inexact Schur complement. In the following, the Schur complement is examined to spectral equivalence with the matrix K. For K quite good preconditioners are known.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-11-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200702036
ger
Chemnitz Scientific Computing Preprints ; 07-08
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18840/zip/
urn:nbn:de:bsz:ch1-200702036
oai:qucosa:de:qucosa:18851
2021-03-29T09:51:25Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On solving implicitly defined inverse problems by SQP-approaches
Torsten
Hein
510
510
Elliptische Differentialgleichung
Finite-Elemente-Methode
Inverses Problem
Parameteridentifikation
Regularisierung
SQP-Methode
In this paper two basic SQP-approaches for solving implicitly defined inverse problems are presented. Such problems often arises in parameter identification for differential equations. We also include regularization strategies which differ from similar problems in Optimal control. The main focus is on formulating saddle point problems for calculating the next iterate. Conditions for the unique and stable solvability of these problems are presented. The analytical considerations are illustrated by two examples including their discretizations and a numerical case study.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2007-12-18
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200702148
eng
Chemnitz Scientific Computing Preprints ; 07-10
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18851/zip/
urn:nbn:de:bsz:ch1-200702148
oai:qucosa:de:qucosa:18910
2021-03-29T09:52:12Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:300
openaire
Die dunkle Seite des Netzwerkmanagements
Von der Kunst, ein funktionierendes Netzwerk zu zerstören
Steffen
Roth
Dipl.-Soz.
300
300
Hanse
Netzwerk
Netzwerkmanagement
Soziologie
Terrorismus
Zerstörung
Dieser Aufsatz beschäftigt sich mit der Zerstörung netzförmiger Organisationen, und wählt damit einen bislang beispiellosen und vor allem unpopulären Zugang zum Thema Netzwerk: In den Sozial- und Wirtschaftswissenschaften begreifen wir Vernetzung heute fast ausschließlich als Ermöglichungshorizont. Aber auch die wenigen pessimistischen Einschätzungen beschreiben konsequent die Unausweichlichkeit der kritisierten Entwicklung. Wir wollen dennoch zeigen, dass es sowohl notwendig als auch fruchtbar ist, sich auch in den genannten Disziplinen mit der Zerstörung von Netzwerken auseinander zu setzen. Zum einen aus Gründen der Prävention. In der Hauptsache aber, weil der strategische Zugang zu einer eigenen Form von Präzision zwingt. Bevor wir also auf Grundlage eines erweiterten transaktionskostentheoretischen Netzwerkverständnisses Strategien der Zerstörung identifizieren konnten, mussten wir den aktuellen Diskurs entlang der an dieser Stelle populär formulierten Frage strukturieren, warum ein Technologiedienstleister wie SISCO mittlerweile bundesweit für selbstschützende Netzwerke wirbt, während der sozial- und wirtschaftswissenschaftliche Diskurs (erfolgreiche) Angriffe auf Netzwerke nicht thematisiert. Hinter dem selektiven Desinteresse vermuten wir seither Struktur.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-05-19
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200800643
ger
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18910/zip/
urn:nbn:de:bsz:ch1-200800643
oai:qucosa:de:qucosa:18971
2021-03-29T09:53:00Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A fast and efficient algorithm to compute BPX- and overlapping preconditioner for adaptive 3D-FEM
Tino
Eibner
510
510
Adaptives Verfahren
Finite-Elemente-Methode
Präkonditionierung
Additive-Schwarz-preconditioner
BPX-preconditioner
In this paper we consider the well-known BPX-preconditioner in
conjunction with adaptive FEM. We present an algorithm which enables
us to compute the preconditioner with optimal complexity by a total of
only O(DoF) additional memory. Furthermore, we show how to combine
the BPX-preconditioner with an overlapping Additive-Schwarz-preconditioner
to obtain a preconditioner for finite element spaces with
arbitrary polynomial degree distributions. Numerical examples
illustrate the efficiency of the algorithms.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-09-17
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200801271
eng
Chemnitz Scientific Computing Preprints ; 08-02
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18971/zip/
urn:nbn:de:bsz:ch1-200801271
oai:qucosa:de:qucosa:18972
2021-03-29T09:53:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Hierarchical Preconditioners and Adaptivity for Kirchhoff-Plates
Arnd
Meyer
510
510
Deformation
Dünne Schale
Finite-Elemente-Methode
Plattengleichung
Kirchhoff-plate equation
We describe a preconditioner for the Kirchhoff plate equation
for use of Bogner-Fox-Schmidt finite elements based on a
hierarchical technique.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-09-17
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200801284
eng
Chemnitz Scientific Computing Preprints : 08-03
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A18972/zip/
urn:nbn:de:bsz:ch1-200801284
oai:qucosa:de:qucosa:19044
2021-03-29T09:54:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
ddc:620
ddc:621.3
openaire
Ein numerischer Vergleich alternativer Formulierungen des Materialmodells der anisotropen Elastoplastizität bei großen Verzerrungen
A numerical study on alternative formulations of the material model of anisotropic elastoplasticity for large strains
Uwe-Jens
Görke
Anke
Bucher
Reiner
Kreißig
510
510
620
620
Anfangswertproblem
Anisotropie
Elastoplastizität
Finite-Elemente-Methode
Large Strains
Material Modelling
Following generally accepted axioms and assumptions the authors developed a phenomenological, thermodynamically
consistent material model for large anisotropic elastoplastic deformations based on a substructure concept.
The material model originally includes a stress relation in rate formulation, evolutional equations for the
internal variables modeling the hardening behavior, and the yield condition. Due to the necessary time
discretization solving the initial value problem (IVP) this approach is associated with an incremental
stress computation. It will be shown that, within this context, the accuracy of stress values
essentially deteriorates with increasing load steps. Consequently, the authors substitute the usual
stress relation including the symmetric plastic strain tensor of right Cauchy-Green type instead of the
stress tensor into the set of unknown constitutive variables. Stresses are explicitly computed from a
hyperelastic material law depending on the elastic strain tensor. Furthermore, as an alternative to the
plastic strain tensor the solution of the IVP considering an
evolutional equation for the plastic part of the deformation gradient has been studied.
This procedure simplifies the mathematical structure of the system to be solved as well
as the computation of substructure-based variables which are suitable for the analysis
of texture development. The presented numerical strategies were implemented into an in-house FE-code.
Some examples illustrating their accuracy, stability as well as efficiency are discussed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-12-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200802001
Chemnitz Scientific Computing Preprints, 08-04
ger
Chemnitz Scientific Computing Preprints, 08-04
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19044/zip/
urn:nbn:de:bsz:ch1-200802001
oai:qucosa:de:qucosa:19045
2021-03-29T09:54:02Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
ddc:620
ddc:621.3
openaire
Thermodynamisch konsistente Formulierung des gekoppelten Systems der Thermoelastoplastizität bei großen Verzerrungen auf der Basis eines Substrukturkonzepts
Thermodynamically consistent formulation of the coupled system of thermoelastoplasticity at large strains based on a substructure concept
Uwe-Jens
Görke
Ralf
Landgraf
Reiner
Kreißig
510
510
620
620
Finite-Elemente-Methode
Gekoppeltes System
Thermoelastizität
Large Strains
Material Modelling
Multiphysics
Non-negligible coupled thermal and mechanical
effects occur in several physical and industrial
procedures, e.g. warm for ming processes.
The authors present the theoretical background of
a phenomenological thermoelastoplastic material
model at large strains as well as its numerical
realization within the context of appropriate
finite element formulations. As usual, the presented
thermodynamical consistent constitutive approach is
based on the multiplicative decomposition of
the deformation gradient, and a corresponding
additive decomposition of the free Helmholtz
energy density. For the numerical treatment of
thermoelastoplastic problems within a finite
element approach, weak formulations of the balance
equation of momentum and the heat conduction
equation in material description are developed.
For the solution of non-linear boundary value
problems the linearization of the weak formulations
is presented. Within the context of the mechanical
problem the temperature dependence of material
parameters as well as the thermal expansion are
considered. The temperature evolution will be
affected by non-thermal phenomena like the
thermoelastic effect and plastic dissipation.
Several numerical procedures for the solution of
the coupled thermomechanical problem are
discussed.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-12-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200802018
Chemnitz Scientific Computing Preprints, 08-05
ger
Chemnitz Scientific Computing Preprints, 08-05
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19045/zip/
urn:nbn:de:bsz:ch1-200802018
oai:qucosa:de:qucosa:19046
2021-03-29T09:54:03Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Identification of mechanical strains by measurements of a deformed electrical potential field
Marcus
Meyer
Julia
Müller
510
510
Gauß-Newton-Methode
Inverses Problem
Laplace-Gleichung
Parameteridentifikation
nonlinear minimization
In this paper we discuss the inverse problem of the identification of mechanical stresses by measuring the deformation of an electric potential field in a so called differential strain gauge (D-DMS). We derive a mathematical model, where the forward operator is given in terms of an elliptic boundary value problem. Derivatives of the forward operator are considered and the solution of the inverse problem via a least-squares minimization is introduced. Here, the discretized problem is solved with the Gauss-Newton method. Numerical studies of practical interest are presented.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-12-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200802027
eng
Chemnitz Scientific Computing Preprints ; 08-06
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19046/zip/
urn:nbn:de:bsz:ch1-200802027
oai:qucosa:de:qucosa:19047
2021-03-29T09:54:03Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Model order reduction of nonlinear systems: status, open issues, and applications
Michael
Striebel
Joost
Rommes
510
510
Nichtlineares Gleichungssystem
Ordnungsreduktion
Circuit Simulation
Proper Orthogonal Decomposition
Trajectory Piecewise Linearisation
In this document we review the status of existing techniques for nonlinear model order reduction by investigating how well these techniques perform for typical industrial needs. In particular the TPWL-method (Trajectory Piecewise Linear-method) and the POD-approach (Proper Orthogonal Decomposion) is taken under consideration. We address several questions that are (closely) related to both the theory and application of nonlinear model order reduction techniques. The goal of this document is to provide an overview of available methods together with a classification of nonlinear problems that in principle could be handled by these methods.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2008-12-16
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200802036
eng
Chemnitz Scientific Computing Preprints ; 08-07
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19047/zip/
urn:nbn:de:bsz:ch1-200802036
oai:qucosa:de:qucosa:19050
2021-03-29T09:54:06Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
A rational SHIRA method for the Hamiltonian eigenvalue problem
Peter
Benner
Cedric
Effenberger
510
510
Eigenwertproblem
Hamiltonian matrix
eigenvalue problem
rational Krylov subspace method
shift-and-invert Arnoldi
skew-Hamiltonian matrix
The SHIRA method of Mehrmann and Watkins belongs among the structure preserving Krylov subspace methods for solving skew-Hamiltonian eigenvalue problems. It can also be applied to Hamiltonian eigenproblems by considering a suitable transformation. Structure induced shift-and-invert techniques are employed to steer the algorithm towards the interesting region of the spectrum. However, the shift cannot be altered in the middle of the computation without discarding the information that has been accumulated so far. This paper shows how SHIRA can be combined with ideas from Ruhe's Rational Krylov algorithm to yield a method that permits an adjustment of shift after every step of the computation, adding greatly to the flexibility of the algorithm. We call this new method rational SHIRA. A numerical example is presented to demonstrate its efficiency.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-01-07
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200900026
eng
Chemnitz Scientific Computing Preprints ; 08-08
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19050/zip/
urn:nbn:de:bsz:ch1-200900026
oai:qucosa:de:qucosa:19068
2021-03-29T09:54:21Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Obstacle Description with Radial Basis Functions for Contact Problems in Elasticity
Roman
Unger
510
510
Elastizitätstheorie
Finite-Elemente-Methode
Projektionsverfahren
Contact Problems
Radial Basis Functions
In this paper the obstacle description with Radial Basis
Functions for contact problems in three dimensional elasticity
will be done. A short Introduction of the idea of Radial Basis
Functions will be followed by the usage of Radial Basis
Functions for approximation of isosurfaces.
Then these isosurfaces are used for the obstacle-description
in three dimensional elasticity contact problems.
In the last part some computational examples will be shown.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-02-03
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200900206
eng
Chemnitz Scientific Computing Preprints ; 09-01
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19068/zip/
urn:nbn:de:bsz:ch1-200900206
oai:qucosa:de:qucosa:19069
2021-03-29T09:54:21Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Kurzvorstellung der 3D-FEM Software SPC-PM3AdH-XX
Janine
Glänzel
510
510
Bedienungsanleitung
Dreidimensionale Software
Finite-Elemente-Methode
Lineare Elastizitätstheorie
Einprozessorvariante
Mehrprozessorvariante
In diesem Preprint wird die Weiterentwicklung der 3D-FEM Software SPC-PM3Adh-XX kurz vorgestellt. Die Einleitung beschreibt schematisch den Ablauf des Programms und sechs Programmversionen. Weiterhin werden die allgemeinen Bedienungsanleitungen und die Funktionalität der einzelnen Versionen aufgeführt. Im letzten Abschnitt, dem Anhang, werden kurz das Standardfile und das Radiale Basisfunktionen-Datenfile erklärt.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-02-03
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200900211
ger
Chemnitz Scientific Computing Preprints ; 09-03
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19069/zip/
urn:nbn:de:bsz:ch1-200900211
oai:qucosa:de:qucosa:19099
2021-03-29T09:54:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:300
ddc:320
ddc:330
openaire
Neu für wen?
Erste Aufnahmen aus der Sozialdimension der Innovation
Steffen
Roth
330
330
300
300
320
320
Innovation
Sozialinnovation
Nicht-technische Innovation
Nicht-ökonomische Innovation
Open Innovation
Robuste Innovation
Sozialdimension
Systemtheorie
Innovation assoziieren wir mit Technologie und Wirtschaft. Begriffliche Alternativen wie die „nicht-technologischen“ oder „sozialen Innovationen“ verweisen in der Regel auf eine Residualkategorie nicht-ökonomischer Randbedingungen des wirtschaftlichen Erfolgs von Innovationen, oder werden so allgemein verwandt, dass sie als unterdefinierte Container-Begriffe zu kaum mehr als zum Transport unterschiedlichster ökonomisierungsskeptischer Ressentiments taugen. Insgesamt ist schliesslich immer wieder unklar, ob der Begriff auf neue Objekte oder den Prozess der Neuerung angewandt werden soll, oder er erst dann Sinn macht, wenn das Neue weite Teile der Gesellschaft und hier vorzugsweise eben wieder den ökonomischen Markt erreicht hat. Entsprechend spricht man mitunter von der Innovation als Paradoxon (John 2005).
Vor diesem Hintergrund verfolgt die vorliegende Arbeit zwei Anliegen: Zum wird in Anwendung der Theo-rie sozialer Systeme (Luhmann 1987, 1997) ein dreidimensionales Modell entwickelt das den Umgang mit dem paradoxen Phänomen erheblich erleichtert: wie alles das Sinn macht hat Innovation demnach eine Sach-, eine Zeit- und eine Sozialdimension, und erscheint entsprechend sowohl als sachliche Neuheit, als zeitlicher Wandel und als sozialer Vorteil. Zum anderen wird die Sozialdimension der Innovation als For-schungslücke vorgestellt, die auch von Innovationssoziologen bislang nicht systematisch bearbeitet wird. Im Sinne erster Aufnahmen aus der bislang unterbelichteten Sozialdimension werden Grundtypen sozialer Beziehungen entwickelt und der Unterschied aufgezeigt, den die Innovation als Vorteil im jeweiligen Fall macht. Hochauflösendere Bilder scheitern dabei allerdings am Fehlen einer spezifischen Soziologie des Vorteils.
Immerhin aber gelingt noch ein überraschender Schnappschuss: Da es neben ökonomischen noch eine ganze Reihe weiterer Vorteile gibt, können wir die wirtschaftliche Innovation als Sonderfall der Innovation präsentieren. Entsprechend lassen sich nun auch robuste Innovationen vorstellen, die in mehr als einer Wettbewerbssphäre der Gesellschaft Vorteile bringen und die uns als besonders nachhaltige und profit-able Form von Innovation gelten können.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Leading Systems, Preprints of the Competence Center for Management at the Berne School of Business and Administration
Chemnitz
Chemnitz
2009-03-11
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200900518
ger
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19099/zip/
urn:nbn:de:bsz:ch1-200900518
oai:qucosa:de:qucosa:19117
2021-03-29T09:55:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
ddc:620
ddc:621.3
openaire
Ein Beitrag zur gemischten Finite-Elemente-Formulierung der Theorie gesättigter poröser Medien bei großen Verzerrungen
A contribution to the finite element formulation of the theory of saturated porous media at large strains
Uwe-Jens
Görke
Sonja
Kaiser
Anke
Bucher
Reiner
Kreißig
510
510
620
620
Finite-Elemente-Methode
Poröser Stoff
Large Strains
Mixed formulation
Poroelasticity
Porous media
This paper presents the theoretical background of
a phenomenological biphasic material approach at
large strains based on the theory of porous media
as well as its numerical realization within the
context of an adaptive mixed finite element formulation.
The study is aimed at the simulation of coupled
multiphysics problems with special focus on biomechanics.
As the materials of interest can be considered as
a mixture of two immiscible components (solid and
fluid phases), they can be modeled as saturated
porous media. For the numerical treatment of according
problems within a finite element approach, weak
formulations of the balance equations of momentum
and volume of the mixture are developed. Within this
context, a generalized Lagrangean approach is
preferred assuming the initial configuration of
the solid phase as reference configuration of the
mixture. The transient problem results in weak
formulations with respect to the displacement and
pore pressure fields as well as their time derivatives.
Therefore special linearization techniques are applied,
and after spatial discretization a global system for the
incremental solution of the initial boundary value
problem within the framework of a stable mixed U/p-c
finite element approach is defined. The global system
is solved using an iterative solver with hierarchical
preconditioning. Adaptive mesh evolution is controlled
by a residual a posteriori error estimator.
The accuracy and the efficiency of the numerical
algorithms are demonstrated on a typical example.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-04-24
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200900691
Chemnitz Scientific Computing Preprints, 09-02
ger
Chemnitz Scientific Computing Preprints, 09-02
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19117/zip/
urn:nbn:de:bsz:ch1-200900691
oai:qucosa:de:qucosa:19189
2021-03-29T09:56:00Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:000
ddc:500
ddc:600
openaire
Optimisation of food overloading at long distance flights
Karl-Heinz
Eger
Prof. Dr.
Tudevdagva
Uranchimeg
Prof. Dr.
600
600
000
000
500
500
Operations Research
Statistische Analyse
applied statistics
method of least squares
optimisation
parameter estimation
This paper deals with optimisation of food overloading
at long distance flights. It is described how in case of two
offered meals and two several passenger groups reserve meals
are to distribute to both meals such that the probability that
each passenger will get the meal of its choice is maximised.
A statistical procedure is presented for estimation of needed
demand probabilities.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-08-22
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200901418
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19189/zip/
urn:nbn:de:bsz:ch1-200901418
oai:qucosa:de:qucosa:19190
2021-03-29T09:56:01Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the QR Decomposition of H-Matrices
Peter
Benner
Thomas
Mach
510
510
Hierarchische Matrix
Orthogonalisierung
HQR decomposition
QR decomposition
least squares problem
matrix factorisation
The hierarchical (<i>H-</i>) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix-matrix and matrix-vector products, matrix inversion and LU decomposition can be implemented efficiently using the <i>H</i>-matrix format. Due to its importance in solving many problems in numerical linear algebra like least-squares problems, it is also desirable to have an efficient QR decomposition of <i>H</i>-matrices. In the past, two different approaches for this task have been suggested. We will review the resulting methods and suggest a new algorithm to compute the QR decomposition of an <i>H</i>-matrix. Like other <i>H</i>-arithmetic operations the <i>H</i>QR decomposition is of linear-polylogarithmic complexity. We will compare our new algorithm with the older ones by using two series of test examples and discuss benefits and drawbacks of the new approach.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-08-28
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200901420
eng
Chemnitz Scientific Computing Preprints ; 09-04
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19190/zip/
urn:nbn:de:bsz:ch1-200901420
oai:qucosa:de:qucosa:19233
2021-03-29T09:56:35Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parameter identification problems for elastic large deformations - Part I: model and solution of the inverse problem
Marcus
Meyer
510
510
Inverses Problem
Nichtlineare partielle Differentialgleichung
identification problem
large elastic deformations
material laws
nonlinear inverse problem
sequential quadratic programming
In this paper we discuss the identification of parameter functions in material models for elastic large deformations. A model of the the forward problem is given, where the displacement of a deformed material is found as the solution of a n onlinear PDE. Here, the crucial point is the definition of the 2nd Piola-Kirchhoff stress tensor by using several material laws including a number of material parameters. In the main part of the paper we consider the identification of such parameters from measured displacements, where the inverse problem is given as an optimal control problem. We introduce a solution of the identification problem with Lagrange and SQP methods. The presented algorithm is applied to linear elastic material with large deformations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-11-20
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200901869
eng
Chemnitz Scientific Computing Preprints ; 09-05
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19233/zip/
urn:nbn:de:bsz:ch1-200901869
oai:qucosa:de:qucosa:19230
2021-03-29T09:56:33Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
openaire
An NFFT based approach to the efficient computation of dipole-dipole interactions under different periodic boundary conditions
Franziska
Nestler
518
518
Schnelle Fourier-Transformation
Schnelle Fourier-Transformation
Ewald summation
nonequispaced fast Fourier transform
particle methods
dipole-dipole interactions
mixed periodicity
NFFT
P2NFFT
P3M
We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2015-06-11
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-171040
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnit ; 2015-07
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19230/zip/
urn:nbn:de:bsz:ch1-qucosa-171040
oai:qucosa:de:qucosa:19234
2021-03-29T09:56:36Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parameter identification problems for elastic large deformations - Part II: numerical solution and results
Marcus
Meyer
510
510
Finite-Elemente-Methode
Inverses Problem
identification problem
large elastic deformations
material laws
In this paper we continue the considerations of [5] (CSC/09-05). A numerical study for the parameter identification problem with linear elastic material and large deformations is presented. We discuss the numerical implementation in MATLAB and illustrate some results for a 2D test problem.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2009-11-20
2021-03-29
preprint
urn:nbn:de:bsz:ch1-200901876
eng
Chemnitz Scientific Computing Preprints ; 09-06
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19234/zip/
urn:nbn:de:bsz:ch1-200901876
oai:qucosa:de:qucosa:19255
2021-03-29T09:56:53Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Interpolatory Projection Methods for Parameterized Model Reduction
Ulrike
Baur
Christopher
Beattie
Peter
Benner
Serkan
Gugercin
510
510
Interpolation
Ordnungsreduktion
linear dynamical systems
parameterized model reduction
rational Krylov
We provide a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model. Moreover, we are able to give conditions under which the gradient and Hessian of the system response with respect to the system parameters is matched in the reduced-order model. We provide a systematic approach built on established interpolatory $\mathcal{H}_2$ optimal model reduction methods that will produce parameterized reduced-order models having high fidelity throughout a parameter range of interest. For single input/single output systems with parameters in the input/output maps, we provide reduced-order models that are \emph{optimal} with respect to an $\mathcal{H}_2\otimes\mathcal{L}_2$ joint error measure. The capabilities of these approaches are illustrated by several numerical examples from technical applications.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010-01-05
2021-03-29
preprint
urn:nbn:de:bsz:ch1-201000011
eng
Chemnitz Scientific Computing Preprints ; 09-08
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19255/zip/
urn:nbn:de:bsz:ch1-201000011
oai:qucosa:de:qucosa:19256
2021-03-29T09:56:54Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
RRQR-MEX - Linux and Windows 32bit MATLAB MEX-Files for the rank revealing QR factorization
Jens
Saak
Stephan
Schlömer
510
510
Compiler
Dokumentation
MATLAB
Numerische Mathematik
Software
The rank revealing QR decomposition is a special form of the well known QR decomposition of a matrix. It uses specialized pivoting strategies and allows for an easy and efficient numerical rank decision for arbitrary matrices. It is especially valuable when column compression of rectangular matrices needs to be performed. Here we provide documentation and compilation instructions for a MATLAB MEX implementation of the RRQR allowing the easy usage of this decomposition inside the MATLAB environment.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010-01-05
2021-03-29
preprint
urn:nbn:de:bsz:ch1-201000022
eng
Chemnitz Scientific Computing Preprints ; 09-09
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19256/zip/
urn:nbn:de:bsz:ch1-201000022
oai:qucosa:de:qucosa:19270
2021-03-29T09:57:05Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
On the numerical solution of large-scale sparse discrete-time Riccati equations
Peter
Benner
Heike
Faßbender
510
510
Newton-Verfahren
Riccati-Differentialgleichung
ADI iteration
Smith iteration
discrete-time control
low rank factor
sparse matrices
The numerical solution of Stein (aka discrete Lyapunov) equations is the primary step in Newton's method for the solution of discrete-time algebraic Riccati equations (DARE). Here we present a low-rank Smith method as well as a low-rank alternating-direction-implicit-iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010-03-04
2021-03-29
preprint
urn:nbn:de:bsz:ch1-201000182
eng
Chemnitz Scientific Computing Preprints ; 09-11
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19270/zip/
urn:nbn:de:bsz:ch1-201000182
oai:qucosa:de:qucosa:19275
2021-03-29T09:57:09Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Model predictive control based on an LQG design for time-varying linearizations
Peter
Benner
Sabine
Hein
510
510
Nichtlineares System
Optimale Kontrolle
LTV systems
incomplete observations
linear quadratic Gaussian design
model predictive control
noise
receding horizon control
We consider the solution of nonlinear optimal control problems subject to stochastic perturbations with incomplete observations. In particular, we generalize results obtained by Ito and Kunisch in [8] where they consider a receding horizon control (RHC) technique based on linearizing the problem on small intervals. The linear-quadratic optimal control problem for the resulting time-invariant (LTI) problem is then solved using the linear quadratic Gaussian (LQG) design. Here, we allow linearization about an instationary reference trajectory and thus obtain a linear time-varying (LTV) problem on each time horizon. Additionally, we apply a model predictive control (MPC) scheme which can be seen as a generalization of RHC and we allow covariance matrices of the noise processes not equal to the identity. We illustrate the MPC/LQG approach for a three dimensional reaction-diffusion system. In particular, we discuss the benefits of time-varying linearizations over time-invariant ones.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010-03-11
2021-03-29
preprint
urn:nbn:de:bsz:ch1-201000221
eng
Chemnitz Scientific Computing Preprints ; 09-07
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19275/zip/
urn:nbn:de:bsz:ch1-201000221
oai:qucosa:de:qucosa:19335
2021-03-29T09:57:57Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Efficiency improving implementation techniques for large scale matrix equation solvers
Martin
Köhler
Jens
Saak
510
510
Implementierung
Ljapunov-Gleichung
Numerische Mathematik
Optimale Kontrolle
Parallelisierung
Systemtheorie
We address the important field of large scale matrix based algorithms in control and model order reduction. Many important tools from theory and applications in systems theory have been widely ignored during the recent decades in the context of PDE constraint optimal control problems and simulation of electric circuits. Often this is due to the fact that large scale matrices are suspected to be unsolvable in large scale applications. Since around 2000 efficient low rank theory for matrix equation solvers exists for sparse and also data sparse systems. Unfortunately upto now only incomplete or experimental Matlab implementations of most of these solvers have existed. Here we aim on the implementation of these algorithms in a higher programming language (in our case C) that allows for a high performance solver for many matrix equations arising in the context of large scale standard and generalized state space systems. We especially focus on efficient memory saving data structures and implementation techniques as well as the shared memory parallelization of the underlying algorithms.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010-06-11
2021-03-29
preprint
urn:nbn:de:bsz:ch1-201000843
eng
Chemnitz Scientific Computing Preprints ; 09-10
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19335/zip/
urn:nbn:de:bsz:ch1-201000843
oai:qucosa:de:qucosa:19345
2021-03-29T09:58:04Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:500
ddc:600
openaire
Robustness of Sequential Probability Ratio Tests in Case of Nuisance Parameters
Karl-Heinz
Eger
Evgeni Borisovich
Tsoy
500
500
600
600
Sequentieller Test
Statistischer Test
ASN-function
Conjugated parameter pairs
Normal distribution
Nuisance parameters
OC-function
Robustness
Sequential analysis
Sequential probability ratio test
Sequential test
Wald approximations
This paper deals with the computation of OC- and ASN-function of sequential probability ratio tests in the multi-parameter case. In generalization of the method of conjugated parameter pairs Wald-like approximations are presented for the OC- and ASN-function. These characteristics can be used describing robustness properties of a sequential test in case of nuisance parameters.
As examples tests are considered for the mean and the variance of a normal distribution.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010-06-27
2021-03-29
preprint
urn:nbn:de:bsz:ch1-201000949
eng
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19345/zip/
urn:nbn:de:bsz:ch1-201000949
oai:qucosa:de:qucosa:19396
2021-03-29T09:58:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Numerische Simulation nahezu inkompressibler Materialien unter Verwendung von adaptiver, gemischter FEM
Numerical simulation of nearly incompressible material using adaptive, mixed FEM
Martina
Balg
Arnd
Meyer
510
510
518
518
Inkompressibilität
Finite-Elemente-Methode
Elastizität
gemischte FEM
adaptive FEM
incompressibility
elasticity
1. Einleitung
2. Grundlagen
3. Aufgabenstellung für linear elastisches Material unter kleinen Deformationen
4. Gemischte Methode der finiten Elemente
5. Herleitung der Fehlerschätzung
6. Aufgabenstellung für nichtlinear elastisches Material unter großen
Deformationen
7. Lösungsstrategie
A. Anhang
Ziel dieser Arbeit ist die Simulation der Deformation von Bauteilen, welche aus nahezu inkompressiblem Material bestehen. Dabei soll sich das Material sowohl linear als auch nichtlinear elastisch verhalten können. Zusätzlich soll die Belastung des Bauteils beliebig gewählt werden können, das heißt, es sollen kleine als auch große Deformationen möglich sein.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Spitzentechnologiecluster eniPROD
Chemnitz
Chemnitz
2010
2010-11-02
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-61993
ger
Chemnitz Scientific Computing Prerpints ; CSC/10-02
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19396/zip/
urn:nbn:de:bsz:ch1-qucosa-61993
oai:qucosa:de:qucosa:19397
2021-03-29T09:58:45Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Grundgleichungen für transversal isotropes Materialverhalten
Basic Equations for Transversely Isotropic Material
Michael
Weise
Arnd
Meyer
510
510
518
518
Finite-Elemente-Methode
Computersimulation
Faser-Kunststoff-Verbund
Materialgesetz
constitutive law
finite element method
transversal isotrop
1 Einführung
2 Energiefunktional
3 Umrechnung der Materialkonstanten
4 Elastizitätsmatrix
5 Eigenwerte
6 Ebener Verzerrungszustand
7 Ebener Spannungszustand
8 Anhang
In diesem Preprint werden grundlegende Gleichungen zur Behandlung von transversal isotropem Materialverhalten zusammengetragen. Wir betrachten ein transversal isotropes Materialgesetz mit linear elastischem Verhalten. Die angegebenen Materialgleichungen sind zur Beschreibung sowohl kleiner als auch großer Deformationen geeignet. Sie bilden eine wesentliche Grundlage zur Lösung statischer Probleme mit der Methode der finiten Elemente. Es werden Gleichungen für den ebenen Spannungszustand und den ebenen Verzerrungszustand hergeleitet.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Spitzentechnologiecluster eniPROD
Chemnitz
Chemnitz
2010
2010-11-02
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-62003
ger
Chemnitz Scientific Computing Preprints ; 10-03
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19397/zip/
urn:nbn:de:bsz:ch1-qucosa-62003
oai:qucosa:de:qucosa:19398
2021-03-29T09:58:46Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Optimal Control of the Classical Two-Phase Stefan Problem in Level Set Formulation
Martin K.
Bernauer
Roland
Herzog
510
510
Stefan-Problem
Level-Set-Methode
Freies Randwertproblem
Optimalsteuerung
optimal control
free boundary value problem
1 Introduction
2 Model Equations
3 The Optimal Control Problem and Optimality Conditions
4 Discretization of the Forward and Adjoint Systems
5 Numerical Results
6 Discussion and Conclusion
A Formal Derivation of the Optimality Conditions
B Transport Theorems and Shape Calculus
Optimal control (motion planning) of the free interface in classical two-phase Stefan problems is considered. The evolution of the free interface is modeled by a level set function. The first-order optimality system is derived on a formal basis. It provides gradient information based on the adjoint temperature and adjoint level set function. Suitable discretization schemes for the forward and adjoint systems are described. Numerical examples verify the correctness and flexibility of the proposed scheme.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010
2010-11-02
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-62014
eng
Chemnitz Scientific Computing Preprints ; 10-04
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19398/zip/
urn:nbn:de:bsz:ch1-qucosa-62014
oai:qucosa:de:qucosa:19395
2021-03-29T09:58:44Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Modellierung und Numerik wachsender Risse bei piezoelektrischem Material
Modeling and Numerics of Propagating Cracks in Piezoelectric Material
Arnd
Meyer
Peter
Steinhorst
510
510
518
518
Adaptives Verfahren
Finite-Elemente-Methode
Kontakt
Piezoelektrizität
Rissausbreitung
Risswachstum
propagating cracks
piecoelectricity
adaptive method
1 Einführung
1.1 Problembeschreibung Piezoelektrizität
1.2 Abgeleitete Größen, Materialgesetz, Gleichungen
1.3 Bilinearformen, schwache Formulierung
2 Implementierung
2.1 Sattelpunktsproblem
2.2 FE-Formulierung
2.3 Löser und Vorkonditionierung
2.4 Adaptivität
3 Besonderheiten von Randbedingungen
3.1 Konstantes Potential auf Teilrändern
3.2 Rissproblem
4 Rissschließen und Kontaktproblem
4.1 Motivation für Risskontaktbetrachtung
4.2 Bezeichnungen
4.3 Kontaktproblem für Verschiebung und Behandlung des Potentials
4.4 FEM-Implementierung des Risskontaktes
4.5 Numerische Beispiele
Zur numerischen Simulation piezoelektrischer Probleme mit linearem Materialgesetz wird die adaptive Finite-Element-Methode genutzt. Bei der Lösung der entstehenden Gleichungssysteme vom Sattelpunktstyp wird auf eine Variante des Bramble-Pasciak-CG zurückgegriffen. Die Einbettung von Projektionstechniken in den Löser erlaubt eine Behandlung von verschiedenen Problembesonderheiten, speziell wird hier auf die Fälle konstanten Potentials auf Teilrändern sowie Kontaktprobleme an wachsenden Rissen eingegangen. Erste numerische Ergebnisse werden an einigen Beispielen demonstriert.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2010-11-02
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-61981
ger
Chemnitz Scientific Computing Preprints ; 10-01
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19395/zip/
urn:nbn:de:bsz:ch1-qucosa-61981
oai:qucosa:de:qucosa:19399
2021-03-29T09:58:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Optimal rates for Lavrentiev regularization with adjoint source conditions
Robert
Plato
Prof. Dr.
Peter
Mathé
Privatdozent Dr.
Bernd
Hofmann
Prof. Dr.
510
510
Regularisierung
Lineare inkorrekte Probleme
Regularisierung
accretive Operatoren
Quellbedingungen
Konvergenzraten
Linear ill-posed problems
regularization
accretive operators
source conditions
convergence rates
There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive then Lavrentiev regularization (singular perturbation) is an immediate choice. The corresponding convergence rates for the regularization error depend on the given smoothness assumptions, and for general accretive operators these may be both with respect to the operator or its adjoint. Previous analysis revealed different convergence rates, and their optimality was unclear, specifically for adjoint source conditions. Based on the fundamental study by T. Kato, Fractional powers of dissipative operators. J. Math. Soc. Japan, 13(3):247--274, 1961, we establish power type convergence rates for this case. By measuring the optimality of such rates in terms on limit orders we exhibit optimality properties of the convergence rates, for general accretive operators under direct and adjoint source conditions, but also for the subclass of nonnegative selfadjoint operators.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Universität Siegen
Siegen
Siegen
Weierstrass Institut Berlin
Berlin
Berlin
Technische Universität Chemnitz
Chemnitz
Chemnitz
2016
2016-03-10
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-199010
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2016-03
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19399/zip/
urn:nbn:de:bsz:ch1-qucosa-199010
oai:qucosa:de:qucosa:19503
2021-03-29T10:00:11Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:600
ddc:620
ddc:621.3
openaire
ALD-grown seed layers for electrochemical copper deposition integrated with different diffusion barrier systems
Thomas
Waechtler
Shao-Feng
Ding
Lutz
Hofmann
Robert
Mothes
Qi
Xie
Steffen
Oswald
Christophe
Detavernier
Stefan E.
Schulz
Xin-Ping
Qu
Heinrich
Lang
Thomas
Gessner
600
600
620
620
621
621
Beschichten
Verkupferung
Atomlagenabscheidung
Ruthenium
Kupfer
Metallisieren
Leiterbahn
ULSI
Atomlagenabscheidung
ALD
Kupferoxid
Ruthenium
Keimschicht
Kupfer
Reduktion
Galvanik
Kupferbeschichtung
Metallisierung
Leitbahnsystem
Galvanisieren
Atomic layer deposition
ALD
Copper oxide
Reduction
Seed layer
Copper
Ruthenium
Electrochemical deposition
ECD
Interconnect
The deposition of Cu seed layers for electrochemical Cu deposition (ECD) via atomic layer deposition (ALD) of copper oxide and subsequent thermal reduction at temperatures between 110 and 120°C was studied on different diffusion barrier systems. While optimization of the process is required on TaN with respect to reduction and plating, promising results were obtained on blanket PVD Ru. The plating results on layers of ALD Cu with underlying Ru even outperformed the ones achieved on PVD Cu seed layers with respect to morphology and resistivity. Applying the processes to via and line patterns gave similar results, suggesting that a combination of ALD Cu with PVD or ALD-grown Ru could significantly improve the ECD Cu growth.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Fraunhofer-Institut für Elektronische Nanosysteme ENAS
Chemnitz
Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Fudan University
Shanghai
Shanghai
Ghent University
Ghent
Ghent
Leibniz-Institut für Festkörper- und Werkstoffforschung IFW
Dresden
Dresden
Elsevier B.V.
Amsterdam
Amsterdam
2011
2011-05-18
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-68040
Microelectronic Engineering, 88, 2011, 5, S. 684-689, DOI: 10.1016/j.mee.2010.07.004
eng
Microelectronic Engineering, 88, 2011, 5, S. 684-689, DOI: 10.1016/j.mee.2010.07.004
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19503/zip/
urn:nbn:de:bsz:ch1-qucosa-68040
oai:qucosa:de:qucosa:19570
2021-03-29T10:01:02Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
openaire
Conditional stability estimates for ill-posed PDE problems by using interpolation
Ulrich
Tautenhahn
Prof. Dr.
Uno
Hämarik
Prof. Dr.
Bernd
Hofmann
Prof. Dr.
Yuanyuan
Shao
Dipl.-Mathematikerin (FH)
515
515
Inverses Problem
Inkorrekt gestelltes Problem
Lineare partielle Differentialgleichung
Inkorrekt gestellte Probleme
Ill-posed problems
inverse problems
conditional stability estimates
interpolation
elliptic problems
parabolic problems
source problems
analytic continuation
The focus of this paper is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capability of our method is illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Hochschule Zittau/Görlitz
Zittau
Zittau
Universität Tartu - Estonia
Tartu
Tartu
2011
2011-09-06
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-72654
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnitz ; 2011-16
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19570/zip/
urn:nbn:de:bsz:ch1-qucosa-72654
oai:qucosa:de:qucosa:19592
2021-03-29T10:01:20Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
openaire
Regularizability of ill-posed problems and the modulus of continuity
Radu Ioan
Bot
PD Dr. rer. nat. habil.
Bernd
Hofmann
Prof. Dr. rer. nat. habil.
Peter
Mathe
PD Dr. rer. nat.
515
515
Regularisierung
Stetigkeitsmodul
inkorrekt gestellte Probleme
Regularisierbarkeit
ill-posed problems
regularizability
modulus of continuity
The regularization of linear ill-posed problems is based on their conditional well-posedness when restricting the problem to certain classes of solutions. Given such class one may consider several related real-valued functions, which measure the wellposedness of the problem on such class. Among those functions the modulus of continuity is best studied. For solution classes which enjoy the additional feature of being star-shaped at zero, the authors develop a series of results with focus on continuity properties of the modulus of continuity. In particular it is highlighted that the problem is conditionally well-posed if and only if the modulus of continuity is right-continuous at zero. Those results are then applied to smoothness classes in Hilbert space. This study concludes with a new perspective on a concavity problem for the modulus of continuity, recently addressed by two of the authors in "Some note on the modulus of continuity for ill-posed problems in Hilbert space", 2011.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Weierstrass-Institut für Angewandte Analysis und Stochastik
Berlin
Berlin
2011
2011-10-17
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-77342
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2011-17
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19592/zip/
urn:nbn:de:bsz:ch1-qucosa-77342
oai:qucosa:de:qucosa:19621
2021-03-29T10:01:43Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
openaire
The Main Diagonal of a Permutation Matrix
Marko
Lindner
Dr.
Gilbert
Strang
Prof.
518
518
Unendliche Matrix
Bandmatrix
Permutation
Faktorisierung
Bandmatrix
Permutation
unendliche Matrix
Hauptdiagonale
Faktorisierung
banded matrix
permutation
infinite matrix
main diagonal
factorization
15A23
47A53
47B36
By counting 1's in the "right half" of 2w consecutive rows, we locate the main diagonal of any doubly infinite permutation matrix with bandwidth w. Then the matrix can be correctly centered and factored into block-diagonal permutation matrices.
Part II of the paper discusses the same questions for the much larger class of band-dominated matrices. The main diagonal is determined by the Fredholm index of a singly infinite submatrix. Thus the main diagonal is determined "at infinity" in general, but from only 2w rows for banded permutations.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
MIT (Massachusetts Institute of Technology)
Cambridge, MA, USA
Cambridge, MA, USA
2011
2012-07-11
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-80273
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2011-20
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19621/zip/
urn:nbn:de:bsz:ch1-qucosa-80273
oai:qucosa:de:qucosa:19685
2021-03-29T10:02:31Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Stable Parameter Identification Evaluation of Volatility
Nadja
Rückert
M.Sc.
Robert S.
Anderssen
Dr.
Bernd
Hofmann
Prof. Dr. rer. nat. habil.
510
510
Volatilität
Parameteridentifikation
Black-Scholes-Modell
Parameteridentifikation
Volatilitätsfunktion
Dupire Formel
Finite Differenzen
Parameter identification
Volatility surfaces
Dupire’s equation
Finite difference
Localization approach
Using the dual Black-Scholes partial differential equation, Dupire derived an explicit formula, involving the ratio of partial derivatives of the evolving fair value of a European call option (ECO), for recovering information about its variable volatility. Because the prices, as a function of maturity and strike, are only available as discrete noisy observations, the evaluation of Dupire’s formula reduces to being an ill-posed numerical differentiation problem, complicated by the need to take the ratio of derivatives. In order to illustrate the nature of ill-posedness, a simple finite difference scheme is first used to approximate the partial derivatives.
A new method is then proposed which reformulates the determination of the volatility, from the partial differential equation defining the fair value of the ECO, as a parameter identification activity. By using the weak formulation of this equation, the problem is localized to a subregion on which the volatility surface can be approximated by a constant or a constant multiplied by some known shape function which models the local shape of the volatility function. The essential regularization is achieved through the localization, the choice of the analytic weight function, and the application of integration-by-parts to the weak formulation to transfer the differentiation of the discrete data to the differentiation of the analytic weight function.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
CSIRO Mathematical and Information Sciences
Canberra
Canberra
2012
2012-03-29
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-85402
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2012-3
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19685/zip/
urn:nbn:de:bsz:ch1-qucosa-85402
oai:qucosa:de:qucosa:19702
2021-03-29T10:02:42Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
ddc:510
openaire
Parameter choice in Banach space regularization under variational inequalities
Bernd
Hofmann
Prof. Dr.
Peter
Mathé
PD Dr.
510
510
Regularisierung
Tichonov-Regularisierung
Nichtlineare inkorrekte Probleme
inkorrekt gestellte Probleme
Banachraum-Regularisierung
Konvergenzraten
Nonlinear ill-posed problems
Banach space regularization
convergence rates
The authors study parameter choice strategies for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depend on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices under consideration include an a priori choice, the discrepancy principle as well as the Lepskii principle. For the convenience of the reader the authors review in an appendix a few instances where the validity of a variational inequality can be established.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
2012
2012-04-17
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-86241
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2012-5
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19702/zip/
urn:nbn:de:bsz:ch1-qucosa-86241
oai:qucosa:de:qucosa:19709
2021-03-29T10:02:47Z
qucosa:ubc
doc-type:preprint
has-source-swb:false
open_access
openaire
Parameter estimation for nonincreasing exponential sums by Prony-like methods
Daniel
Potts
Prof. Dr.
Manfred
Tasche
Prof. Dr.
515
515
Parameterschätzung
Hankel-Matrix
Parameterschätzung
Prony-like Methoden
Fourier Approximation
Parameter estimation
nonincreasing exponential sum
Prony-like method
exponential fitting problem
ESPRIT
matrix pencil factorization
companion matrix
Prony polynomial
eigenvalue problem
rectangular Hankel matrix
nonlinear approximation
sparse trigonometric polynomial
sparse Fourier approximation
AMS SC: 65D10
41A45
65F15
65F20
94A12
For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method.
Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation.
Universitätsbibliothek Chemnitz
Chemnitz
09107 Chemnitz
Technische Universität Chemnitz
Chemnitz
Chemnitz
Universität Rostock
Rostock
Rostock
2012
2012-05-02
2021-03-29
preprint
urn:nbn:de:bsz:ch1-qucosa-86476
eng
Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2012-4
info:eu-repo/semantics/openAccess
2
https://monarch.qucosa.de/api/qucosa%3A19709/zip/
urn:nbn:de:bsz:ch1-qucosa-86476
X1738694890/1