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A p-multigrid algorithm using cubic finite elements for efficient deformation simulation

: Weber, Daniel; Müller-Römer, Johannes; Altenhofen, Christian; Stork, André; Fellner, Dieter W.


Bender, Jan (Ed.) ; European Association for Computer Graphics -EUROGRAPHICS-:
VRIPHYS 2014, 11th Workshop on Virtual Reality Interactions and Physical Simulations : Bremen, Germany, September 24 - 25, 2014
Goslar: Eurographics Association, 2014
ISBN: 978-3-905674-71-2
Workshop on Virtual Reality Interaction and Physical Simulations (VRIPHYS) <11, 2014, Bremen>
Conference Paper
Fraunhofer IGD ()
physically based simulation; Finite Elements; multigrid; Business Field: Virtual engineering; Research Area: (Interactive) Simulation (SIM)

We 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.