M.Sc. Maharavo Randrianarivony

Geometric processing of CAD data and meshes as input of integral equation solvers

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Kurzfassung in Englisch

Among the presently known numerical solvers of integral equations, two main
categories of approaches can be traced: mesh-free approaches, mesh-based approaches.
We will propose some techniques to process geometric data so that they can
be efficiently used in subsequent numerical treatments of integral equations. In
order to prepare geometric information so that the above two approaches can be
automatically applied, we need the following items:
(1) Splitting a given surface into several four-sided patches,
(2) Generating a diffeomorphism from the unit square to a foursided patch,
(3) Generating a mesh M on a given surface,
(4) Patching of a given triangulation.
In order to have a splitting, we need to approximate the surfaces
first by polygonal regions. We use afterwards quadrangulation techniques by
removing quadrilaterals repeatedly. We will generate the diffeomorphisms by
means of transfinite interpolations of Coons and Gordon types.
The generation of a mesh M from a piecewise Riemannian surface will use some
generalized Delaunay techniques in which the mesh size will be determined with
the help of the Laplace-Beltrami operator.
We will describe our experiences with the IGES format because of two reasons.
First, most of our implementations have been done with it. Next, some of the
proposed methodologies assume that the curve and surface representations are
similar to those of IGES.
Patching a mesh consists in approximating or interpolating it by a set of practical
surfaces such as B-spline patches. That approach proves useful when we want to
utilize a mesh-free integral equation solver but the input geometry is represented
as a mesh.

weitere Metadaten

Foursided decomposition
Transfinite Interpolation
SWD SchlagworteB-Spline
SWD SchlagworteCAD
SWD SchlagworteDiffeomorphismus
SWD SchlagworteGittererzeugung
SWD SchlagworteIGES
SWD SchlagworteIntegralgleichung
SWD SchlagworteMannigfaltigkeit
SWD SchlagworteViereck
DDC Klassifikation000
DDC Klassifikation500
HochschuleTU Chemnitz
FakultätFakultät für Informatik
BetreuerProf. Guido Brunnett
GutachterProf. G. Brunnett
Prof. H. Hagen
Prof. R. Schneider
Tag d. Einreichung (bei der Fakultät)25.06.2006
Tag d. Verteidigung / Kolloquiums / Prüfung30.09.2006
Veröffentlichungsdatum (online)23.11.2006
persistente URNurn:nbn:de:swb:ch1-200601972

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