Weber, Daniel ; Mueller-Roemer, Johannes ; Altenhofen, Christian ; Stork, André ; Fellner, Dieter W. (2014)
A p-Multigrid Algorithm using Cubic Finite Elements for Efficient Deformation Simulation.
VRIPHYS 14: 11th Workshop in Virtual Reality Interactions and Physical Simulations.
doi: 10.2312/vriphys.20141223
Konferenzveröffentlichung, Bibliographie
Kurzbeschreibung (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.
| Typ des Eintrags: | Konferenzveröffentlichung |
|---|---|
| Erschienen: | 2014 |
| Autor(en): | Weber, Daniel ; Mueller-Roemer, Johannes ; Altenhofen, Christian ; Stork, André ; Fellner, Dieter W. |
| Art des Eintrags: | Bibliographie |
| Titel: | A p-Multigrid Algorithm using Cubic Finite Elements for Efficient Deformation Simulation |
| Sprache: | Englisch |
| Publikationsjahr: | 2014 |
| Verlag: | Eurographics Association, Goslar |
| Veranstaltungstitel: | VRIPHYS 14: 11th Workshop in Virtual Reality Interactions and Physical Simulations |
| DOI: | 10.2312/vriphys.20141223 |
| Kurzbeschreibung (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. |
| Freie Schlagworte: | Business Field: Virtual engineering, Research Area: (Interactive) simulation (SIM), Forschungsgruppe Semantic Models, Immersive Systems (SMIS), Physically based simulation, Finite elements, Multigrid |
| Fachbereich(e)/-gebiet(e): | 20 Fachbereich Informatik 20 Fachbereich Informatik > Graphisch-Interaktive Systeme |
| Hinterlegungsdatum: | 12 Nov 2018 11:16 |
| Letzte Änderung: | 04 Feb 2022 12:40 |
| PPN: | |
| Export: | |
| Suche nach Titel in: | TUfind oder in Google |
 |
Frage zum Eintrag |
Optionen (nur für Redakteure)
 |
Redaktionelle Details anzeigen |
Drucken
Impressum