Abstract
A multigrid method is described for solving history-dependent elastoplastic solid mechanics problems using the finite element method. A multigrid algorithm that solves linear matrix equations is combined with the Newton-Raphson iteration procedure. The method is implemented on shared memory parallel computers by employing an element-by-element approach to computing matrix-vector products. Some two- and three-dimensional fracture mechanics problems are used to study the behavior of the algorithm. The convergence of the linear multigrid solver deteriorates as plastic flow increases. This is a result of the effect of near incompressibility on the smoothing effect of the relaxation procedure employed; however, reasonable performance can still be achieved. The solution of some large-scale problems demonstrates the speed, storage requirements, and parallel performance of the algorithm. For example, a three-dimensional problem with 215 000 degrees-of-freedom and 10 load steps was solved in 69 100 CPU s with 108 Mbytes of storage on a single processor of a Convex C240. Maximum speed-ups of 2.96 and 4.13 were measured on a 4-processor Convex and an 8-processor Alliant, respectively, for the nonlinear algorithm.
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