Polyhedral Finite Elements Using Harmonic Basis Functions
Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method...
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| Published in: | Computer graphics forum Vol. 27; no. 5; pp. 1521 - 1529 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford, UK
Blackwell Publishing Ltd
01.07.2008
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| Subjects: | |
| ISSN: | 0167-7055, 1467-8659 |
| Online Access: | Get full text |
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| Summary: | Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity. |
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| Bibliography: | ark:/67375/WNG-MXQJNS0L-H istex:3E9F0F5137EE09F2B0781A9689AF201F1DBD1AE6 ArticleID:CGF1293 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23 |
| ISSN: | 0167-7055 1467-8659 |
| DOI: | 10.1111/j.1467-8659.2008.01293.x |