A p-Multigrid Algorithm using Cubic Finite Elements for Efficient Deformation Simulation

dc.contributor.authorWeber, Danielen_US
dc.contributor.authorMueller-Roemer, Johannesen_US
dc.contributor.authorAltenhofen, Christianen_US
dc.contributor.authorStork, Andreen_US
dc.contributor.authorFellner, Dieter W.en_US
dc.contributor.editorJan Bender and Christian Duriez and Fabrice Jaillet and Gabriel Zachmannen_US
dc.date.accessioned2014-12-16T07:27:43Z
dc.date.available2014-12-16T07:27:43Z
dc.date.issued2014en_US
dc.description.abstractWe present a novel p-multigrid method for efficient simulation of co-rotational elasticity with higher-order finite elements. In contrast to other multigrid methods proposed for volumetric deformation, the resolution hierarchy is realized by varying polynomial degrees on a tetrahedral mesh. We demonstrate the efficiency of our approach and compare it to commonly used direct sparse solvers and preconditioned conjugate gradient methods. As the polynomial representation is defined w.r.t. the same mesh, the update of the matrix hierarchy necessary for co-rotational elasticity can be computed efficiently. We introduce the use of cubic finite elements for volumetric deformation and investigate different combinations of polynomial degrees for the hierarchy. We analyze the applicability of cubic finite elements for deformation simulation by comparing analytical results in a static scenario and demonstrate our algorithm in dynamic simulations with quadratic and cubic elements. Applying our method to quadratic and cubic finite elements results in speed up of up to a factor of 7 for solving the linear system.en_US
dc.description.seriesinformationWorkshop on Virtual Reality Interaction and Physical Simulationen_US
dc.identifier.isbn978-3-905674-71-2en_US
dc.identifier.urihttps://doi.org/10.2312/vriphys.20141223en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectPhysically based modelingen_US
dc.subjectI.3.7 [Computer Graphics]en_US
dc.subjectThree Dimensional Graphics and Realismen_US
dc.subjectAnimationen_US
dc.titleA p-Multigrid Algorithm using Cubic Finite Elements for Efficient Deformation Simulationen_US
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