TU Darmstadt / ULB / TUbiblio

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

Weber, Daniel and Mueller-Roemer, Johannes and Altenhofen, Christian and Stork, André and Fellner, Dieter W. (2014):
A p-Multigrid Algorithm using Cubic Finite Elements for Efficient Deformation Simulation.
Eurographics Association, Goslar, In: VRIPHYS 14: 11th Workshop in Virtual Reality Interactions and Physical Simulations, pp. 49-58, DOI: 10.2312/vriphys.20141223,
[Conference or Workshop Item]

Abstract

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.

Item Type: Conference or Workshop Item
Erschienen: 2014
Creators: Weber, Daniel and Mueller-Roemer, Johannes and Altenhofen, Christian and Stork, André and Fellner, Dieter W.
Title: A p-Multigrid Algorithm using Cubic Finite Elements for Efficient Deformation Simulation
Language: English
Abstract:

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.

Publisher: Eurographics Association, Goslar
Uncontrolled Keywords: Business Field: Virtual engineering, Research Area: (Interactive) simulation (SIM), Forschungsgruppe Semantic Models, Immersive Systems (SMIS), Physically based simulation, Finite elements, Multigrid
Divisions: 20 Department of Computer Science
20 Department of Computer Science > Interactive Graphics Systems
Event Title: VRIPHYS 14: 11th Workshop in Virtual Reality Interactions and Physical Simulations
Date Deposited: 12 Nov 2018 11:16
DOI: 10.2312/vriphys.20141223
Export:
Suche nach Titel in: TUfind oder in Google
Send an inquiry Send an inquiry

Options (only for editors)

View Item View Item