A Static Parallel Multifrontal Solver for Finite Element Meshes

We present a static parallel implementation of themultifrontal method to solve unsymmetric sparse linear systems on distributed-memory architectures. We target Finite Element (FE) applications where numerical pivoting can be avoided, since an implicit minimum-degree ordering based on the FE mesh topology suffices to achieve numerical stability. Our strategy is static in the sense that work distribution and communication patterns are determined in a preprocessing phase preceding the actual numerical computation. To balance the load among the processors, we devise a simple model-driven partitioning strategy to precompute a high-quality balancing for a large family of structured meshes. The resulting approach is proved to be considerably more efficient than the strategies implemented byMUMPS and SuperLU DIST, two state-of-the-art parallel multifrontal solvers.