Sebastian Martin, Peter Kaufmann, Mario Botsch, Martin Wicke, Markus Gross: Polyhedral Finite Elements Using Harmonic Basis Functions. In Computer Graphics Forum 27(5) [Proceedings SGP], 2008 [Best Paper First-Authored by a Student]


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.


  author =  {Sebastian Martin and Peter Kaufmann and Mario Botsch and Martin Wicke and Markus Gross},
  title =   {Polyhedral Finite Elements Using Harmonic Basis Functions},
  journal = {Computer Graphics Forum},
  volume = {27},
  number = {5},
  year = {2008},
  pages = {1521--1529}