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Polyhedral Finite Elements Using Harmonic Basis Functions
Author(s) -
Martin Sebastian,
Kaufmann Peter,
Botsch Mario,
Wicke Martin,
Gross Markus
Publication year - 2008
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2008.01293.x
Subject(s) - hexahedron , finite element method , tetrahedron , discretization , basis (linear algebra) , computer science , basis function , computation , computational science , mesh generation , algorithm , quadrilateral , topology (electrical circuits) , mathematics , geometry , mathematical analysis , structural engineering , combinatorics , engineering
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.