Parallel multigrid solvers for 3D-unstructured large deformation elasticity and plasticity finite element problems

Multigrid is a popular solution method for the set of linear algebraic equations that arise from PDEs discretized with the finite element method. We discuss a method, that uses many of the same techniques as the finite element method itself, to apply standard multigrid algorithms to unstructured fin...

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Vydané v:	Finite elements in analysis and design Ročník 36; číslo 3; s. 197 - 214
Hlavní autori:	Adams, Mark, Taylor, R.L
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.11.2000 Elsevier
Predmet:	Algebraic multigrid Computational techniques Condensed matter: structure, mechanical and thermal properties Deformation and plasticity (including yield, ductility, and superplasticity) Exact sciences and technology Finite-element and galerkin methods Mathematical methods in physics Mechanical and acoustical properties of condensed matter Mechanical properties of solids Nonlinear solvers Parallel sparse solvers Physics Unstructured multigrid Parallel sparse solvers Nonlinear solvers Algebraic multigrid Unstructured multigrid Set point High strain Elasticity Theoretical study Numerical method Incompressible material Parallel algorithms Shape memory effects Finite element method Three dimensional model Program processors Linear equation Multigrid Heuristic method Plasticity Algebraic equation
ISSN:	0168-874X, 1872-6925
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Abstract	Multigrid is a popular solution method for the set of linear algebraic equations that arise from PDEs discretized with the finite element method. We discuss a method, that uses many of the same techniques as the finite element method itself, to apply standard multigrid algorithms to unstructured finite element problems. We present parallel algorithms, based on geometric heuristics, to optimize the quality of coarse grid point sets and the meshes constructed from them, for use in multigrid solvers for 3D-unstructured problems. We conduct scalability studies that demonstrate the effectiveness of our methods on a problem in large deformation elasticity and plasticity of up to 40 million degrees of freedom on 960 processor IBM PowerPC 4-way SMP cluster with about 60% parallel efficiency. We also investigate the effect of incompressible materials on a problem in linear elasticity.
AbstractList	Multigrid is a popular solution method for the set of linear algebraic equations that arise from PDEs discretized with the finite element method. We discuss a method, that uses many of the same techniques as the finite element method itself, to apply standard multigrid algorithms to unstructured finite element problems. We present parallel algorithms, based on geometric heuristics, to optimize the quality of coarse grid point sets and the meshes constructed from them, for use in multigrid solvers for 3D-unstructured problems. We conduct scalability studies that demonstrate the effectiveness of our methods on a problem in large deformation elasticity and plasticity of up to 40 million degrees of freedom on 960 processor IBM PowerPC 4-way SMP cluster with about 60% parallel efficiency. We also investigate the effect of incompressible materials on a problem in linear elasticity. Multigrid is a popular solution method for the set of linear algebraic equations that arise from PDEs discretized with the FEM. We discuss a method that uses many of the same techniques as the FEM itself to apply standard multigrid algorithms to unstructured finite element problems. We present parallel algorithms, based on geometric heuristics, to optimize the quality of coarse grid point sets and the meshes constructed from them, for use in multigrid solvers for 3D unstructured problems. We conduct scalability studies that demonstrate the effectiveness of our methods on a problem in large deformation elasticity and plasticity of up to 40 million DOFs on a 960 processor IBM Power PC 4-way SMP cluster with about 60 percent parallel efficiency. We also investigate the effect of incompressible materials on a problem in linear elasticity. (Author)
Author	Taylor, R.L Adams, Mark
Author_xml	– sequence: 1 givenname: Mark surname: Adams fullname: Adams, Mark email: madams@cs.berkeley.edu organization: Department of Computer Science, University of California Berkeley, Berkeley, CA 94720, USA – sequence: 2 givenname: R.L surname: Taylor fullname: Taylor, R.L organization: Department of Civil Engineering, University of California Berkeley, Berkeley, CA 94720, USA
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Cites_doi	10.1137/0215074 10.1137/0914041 10.1145/10515.10542 10.1016/0096-3003(86)90109-8 10.1002/(SICI)1097-0207(19960415)39:7<1181::AID-NME899>3.0.CO;2-Y 10.1002/nme.1620381908 10.1002/(SICI)1097-0207(19980830)42:8<1441::AID-NME428>3.0.CO;2-C 10.1007/PL00009321 10.1007/BF02238511 10.1002/nme.1620382010 10.1002/nme.1620381002 10.1016/0045-7825(93)90150-V
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Keywords	Parallel sparse solvers Nonlinear solvers Algebraic multigrid Unstructured multigrid Set point High strain Elasticity Theoretical study Numerical method Incompressible material Parallel algorithms Shape memory effects Finite element method Three dimensional model Program processors Linear equation Multigrid Heuristic method Plasticity Algebraic equation
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Snippet	Multigrid is a popular solution method for the set of linear algebraic equations that arise from PDEs discretized with the finite element method. We discuss a... Multigrid is a popular solution method for the set of linear algebraic equations that arise from PDEs discretized with the FEM. We discuss a method that uses...
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SubjectTerms	Algebraic multigrid Computational techniques Condensed matter: structure, mechanical and thermal properties Deformation and plasticity (including yield, ductility, and superplasticity) Exact sciences and technology Finite-element and galerkin methods Mathematical methods in physics Mechanical and acoustical properties of condensed matter Mechanical properties of solids Nonlinear solvers Parallel sparse solvers Physics Unstructured multigrid
Title	Parallel multigrid solvers for 3D-unstructured large deformation elasticity and plasticity finite element problems
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