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

Abstract

Multigrid is a popular solution method for the set of linear algebraic equations that arise from PDEs discretized with the finite element method. The application of multigrid to unstructured grid problems, however, is not well developed. 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 use maximal independent sets (MISs) as a mechanism to automatically coarsen unstructured grids; the inherent flexibility in the selection of an MIS allows for the use of heuristics to improve their effectiveness for a multigrid solver. We present parallel algorithms, based on geometric heuristics, to optimize the quality of MISs and the meshes constructed from them, for use in multigrid solvers for 3D unstructured problems. We discuss parallel issues of our algorithms, multigrid solvers in general, and the parallel finite element application that we have developed to test our solver on challenging problems. We show that our solver, and parallel finite element architecture, does indeed scale well, with test problems in 3D large deformation elasticity and plasticity, with 40 million degree of freedom problem on 240 IBM four‐way SMP PowerPC nodes. Copyright © 2000 John Wiley & Sons, Ltd.

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