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ON THE GENERATION OF HIERARCHICAL MESHES FOR MULTILEVEL FEM AND BEM SOLVERS FROM CAD DATA

  • As numerical techniques for solving PDE or integral equations become more sophisticated, treatments of the generation of the geometric inputs should also follow that numerical advancement. This document describes the preparation of CAD data so that they can later be applied to hierarchical BEM or FEM solvers. For the BEM case, the geometric data are described by surfaces which we want to decomposeAs numerical techniques for solving PDE or integral equations become more sophisticated, treatments of the generation of the geometric inputs should also follow that numerical advancement. This document describes the preparation of CAD data so that they can later be applied to hierarchical BEM or FEM solvers. For the BEM case, the geometric data are described by surfaces which we want to decompose into several curved foursided patches. We show the treatment of untrimmed and trimmed surfaces. In particular, we provide prevention of smooth corners which are bad for diffeomorphism. Additionally, we consider the problem of characterizing whether a Coons map is a diffeomorphism from the unit square onto a planar domain delineated by four given curves. We aim primarily at having not only theoretically correct conditions but also practically efficient methods. As for FEM geometric preparation, we need to decompose a 3D solid into a set of curved tetrahedra. First, we describe some method of decomposition without adding too many Steiner points (additional points not belonging to the initial boundary nodes of the boundary surface). Then, we provide a methodology for efficiently checking whether a tetrahedral transfinite interpolation is regular. That is done by a combination of degree reduction technique and subdivision. Along with the method description, we report also on some interesting practical results from real CAD data.show moreshow less

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Metadaten
Document Type:Conference Proceeding
Author: Maharavo Randrianarivony
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.2879Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-28795Cite-Link
URL:http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
ISSN:1611-4086
Editor: Klaus GürlebeckGND, Carsten KönkeORCiDGND
Language:English
Date of Publication (online):2017/03/14
Date of first Publication:2010/07/14
Release Date:2017/03/14
Publishing Institution:Bauhaus-Universität Weimar
Creating Corporation:Bauhaus-Universität Weimar
Institutes:Bauhaus-Universität Weimar / In Zusammenarbeit mit der Bauhaus-Universität Weimar
Pagenumber:20
Tag:Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
GND Keyword:Angewandte Informatik; Angewandte Mathematik; Architektur <Informatik>; Computerunterstütztes Verfahren
Dewey Decimal Classification:000 Informatik, Informationswissenschaft, allgemeine Werke / 000 Informatik, Wissen, Systeme
500 Naturwissenschaften und Mathematik / 510 Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Collections:Bauhaus-Universität Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar / Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen, IKM, Weimar, 18. 2009
Licence (German):License Logo Creative Commons 4.0 - Namensnennung-Nicht kommerziell (CC BY-NC 4.0)