A portable and scalable multigrid solver for nonlinear structural mechanics problems

A portable and scalable multigrid method is described to solve nonlinear structural mechanics problems discretized with the finite element method. The nonlinear multigrid algorithm combines the incremental Newton solution procedure with a linear multigrid solver. The details of multigrid parallelization on distributed systems are described. A domain decomposition strategy is adopted to parallelize the multigrid algorithm used in the implicit finite element solution method. This entails partitioning the finite element mesh into a number of domains and assigning the domains to individual processors of the parallel machine. The multigrid components are examined to detect the primary operations that require parallelization. Correct parallel algorithms for different stages of multigrid solution are developed using a suitable algebraic framework. This includes development of appropriate algorithms for inter-domain data transfers. The implementation of multigrid components in the element-by-element framework is described.; The message passing interface (MPI) is used to implement the proposed parallel multigrid method, which ensures the portability of the code. The object-based programming model adopted for this work is also described. The performance of the parallel algorithm is studied using two sets of benchmark problems: fixed-size problems and scaled-size problems. In order to demonstrate portability, three widely used parallel systems; an IBM SP2, an SGI Origin2000 and a CRAY T3E are employed. The obtained results shows that the proposed parallel algorithm is highly scalable and can efficiently solve large scale problems on a large number of processors.