マルチフロンタル法の並列実装および効率評価

Abstract

To numerically solve linear equations with large sparse matrices derived by the finite element method, a solution method that can be computed in parallel is required to take advantage of their sparsity. Iterative methods are one group of available methods, but they may not converge. In contrast, direct methods can solve such equations. We can use the multifrontal method as a part of a direct method to utilize two factors mentioned above. This paper explores how to implement the method that incorporates parallelization using MPI to achieve efficient solution in a variety of environments. Numerical experiments using sequential calculations were conducted as a preparatory step for parallelization. The results showed that there was still a large difference in execution time between the existing library and the application created here, especially in the factorization, which is the core of the multifrontal method. Therefore, it is necessary to parallelize the factorization operation to achieve efficient computation and to address bottlenecks that cannot be parallelized in the future.