Polyhedral Finite Elements Using Harmonic Basis Functions
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Date
2008
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd
Abstract
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.
Description
@article{10.1111:j.1467-8659.2008.01293.x,
journal = {Computer Graphics Forum},
title = {{Polyhedral Finite Elements Using Harmonic Basis Functions}},
author = {Martin, Sebastian and Kaufmann, Peter and Botsch, Mario and Wicke, Martin and Gross, Markus},
year = {2008},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2008.01293.x}
}