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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Bibliographic Details
Published in:Finite elements in analysis and design Vol. 36; no. 3; pp. 197 - 214
Main Authors: Adams, Mark, Taylor, R.L
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.11.2000
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0168-874X
1872-6925
DOI:10.1016/S0168-874X(00)00033-0