A study into the feasibility of using two parallel sparse direct solvers for the Helmholtz equation on Linux clusters

Abstract

Two state-of-the-art parallel software packages for the direct solution of sparse linear systems based on LU-decomposition, MUMPS and SuperLU_DIST have been tested as black-box solvers on problems derived from finite difference discretizations of the Helmholtz equation. The target architecture has been Linux clusters, for which no consistent set of tests of the algorithms implemented in these packages has been published. The investigation consists of series of memory and time scalability checks and has focused on examining the applicability of the algorithms when processing very large sparse matrices on Linux cluster platforms. Special emphasis has been put on monitoring the behaviour of the packages when the equation systems need to be solved for multiple right-hand sides, which is the case, for instance, when modelling a seismic survey. The outcome of the tests points at poor efficiency of the tested algorithms during application of the LU-factors in the solution phase on this type of architecture, where the communication acts as an impasse. Copyright © 2005 John Wiley & Sons, Ltd.