1 - Parallel direct solver for finite element modeling of manufacturing processes

Abstract

This chapter describes and evaluates the parallelization of a direct equation solver for implementation in the finite element modeling of manufacturing processes. The parallel solver is implemented in an existing three-dimensional finite element computer program for problems including large deformations, contact development, and electrical and thermal fields. Speed-up and efficiency are evaluated on a standard personal computer. Considerable time savings are achieved, allowing computations to take place in industry within reasonable computation time without access to any kind of supercomputers or clusters. The direct equation solver is parallelized for shared memory platforms by OpenMP instructions, and it can be directly implemented in existing finite element codes utilizing skyline matrix storage, no matter the physical dimensions of the problems dealt with. Only the call to the existing solver has to be substituted by a call to the proposed parallel solver. The modification of the parallel direct equation solver to be applied as preconditioner of iterative equation solvers is also discussed. The FORTRAN source code is provided in the Appendix.