Ulrike Baur, Peter Benner

Gramian-Based Model Reduction for Data-Sparse Systems

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Hinweis

Bitte nutzen Sie beim Zitieren immer folgende Url:

http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200701952

Kurzfassung in Englisch

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.

weitere Metadaten

Titel der Schriftenreihe
(Englisch)
Chemnitz Scientific Computing Preprints ; 07-01
Schlagwörter
balanced truncation
Schlagwörter
large-scale Lyapunov equation
Schlagwörter
model reduction
SWD SchlagworteLjapunov-Gleichung
SWD SchlagworteOrdnungsreduktion
DDC Klassifikation510
Institution(en) 
HochschuleTU Chemnitz
FakultätFakultät für Mathematik
DokumententypPreprint
SpracheEnglisch
Veröffentlichungsdatum (online)27.11.2007
persistente URNurn:nbn:de:bsz:ch1-200701952
ISSN1864-0087
Externe Referenzhttp://www.tu-chemnitz.de/mathematik/csc/preprints.php

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