Polyhedral Finite Elements Using Harmonic Basis Functions

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dc.contributor.authorMartin, Sebastianen_US
dc.contributor.authorKaufmann, Peteren_US
dc.contributor.authorBotsch, Marioen_US
dc.contributor.authorWicke, Martinen_US
dc.contributor.authorGross, Markusen_US
dc.date.accessioned2015-02-21T17:32:38Z
dc.date.available2015-02-21T17:32:38Z
dc.date.issued2008en_US
dc.description.abstractFinite 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.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume27en_US
dc.identifier.doi10.1111/j.1467-8659.2008.01293.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1521-1529en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2008.01293.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titlePolyhedral Finite Elements Using Harmonic Basis Functionsen_US
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27-Issue 5
SGP08: Eurographics Symposium on Geometry Processing