A wrapper around parallel MUMPS solver to reduce its memory usage and execution time for finite element method computations

Abstract

In this paper, we present a wrapper around MUMPS solver, called Hierarchical Solver Wrapper (HSW), that is tailored to domain decomposition-based parallel finite element method computations on distributed memory systems. It offers the same interface as parallel MUMPS with matrix entries in coordinate format provided in a distributed fashion among multiple processors. The algorithm implemented by the wrapper utilizes multiple sequential instances of MUMPS solver to compute Schur complements over subdomains. Next, it deallocates sequential MUMPS solvers and LU factors, and it calls the parallel MUMPS solver feeded with the Schur complements, stored in distributed manner. In the backward substitution stage it recomputes the local LU factors before solving the local problems. The wrapper has been tested with three-dimensional isogeometric analysis computations, and we show it reduces both the memory usage and the execution time, in comparison with a single parallel MUMPS call.