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An Inexact Interior Point Method for the Large-Scale Simulation of Granular Material

  • Non-smooth contact dynamics provides an increasingly popular simulation framework for granular material. In contrast to classical discrete element methods, this approach is stable for arbitrary time steps and produces visually acceptable results in very short computing time. Yet when it comes to the prediction of draft forces, non-smooth contact dynamics is typically not accurate enough. We therefore propose to combine the method class with an interior point algorithm for higher accuracy. Our specific algorithm is based on so-called Jordan algebras and exploits the relation to symmetric cones in order to tackle the conical constraints that are intrinsic to frictional contact problems. In every interior point iteration a linear system has to be solved. We analyze how the interior point method behaves when it is combined with Krylov subspace solvers and incomplete factorizations. We show that efficient preconditioners and efficient linear solvers are essential for the method to be applicable to large-scale problems. Using BiCGstab as a linear solver and incomplete Cholesky factorizations, we substantially improve the accuracy in comparison to the projected Gauss-Jacobi solver.

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Verfasserangaben:Jan Kleinert, Bernd Simeon, Martin Obermayr
URN (Permalink):urn:nbn:de:hbz:386-kluedo-36944
Dokumentart:Preprint
Sprache der Veröffentlichung:Englisch
Veröffentlichungsdatum (online):28.01.2014
Jahr der Veröffentlichung:2013
Veröffentlichende Institution:Technische Universität Kaiserslautern
Datum der Publikation (Server):29.01.2014
Seitenzahl:21
Fachbereiche / Organisatorische Einheiten:Fachbereich Mathematik
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Klassifikation (Mathematik):65-XX NUMERICAL ANALYSIS
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012