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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200601972 |
| Date | 23 November 2006 |
| Creators | Randrianarivony, Maharavo |
| Contributors | TU Chemnitz, Fakultät für Informatik, Prof. Guido Brunnett, Prof. G. Brunnett, Prof. H. Hagen, Prof. R. Schneider |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf, text/plain, application/zip |
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