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

摘要

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 Power PC 4-way SMP cluster with about 60/100 parallel efficiency. We also investigate the effect of incompressible materials on a problem in linear elasticity.