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Sebastian Martin, Peter Kaufmann, Mario Botsch, Martin Wicke, Markus Gross
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.
- S. Martin, P. Kaufmann, M. Botsch, M. Wicke, M. Gross, Polyhedral Finite Elements Using Harmonic Basis Functions, Proceedings of Eurographics Symposium on Geometry Processing (Copenhagen, Denmark, July 2-4, 2008), Computer Graphics Forum, vol. 27, no. 5, 2008, pp. 1521-1529
[Abstract]
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