PERFORMANCE OF A MULTI-FRONTAL PARALLEL DIRECT SOLVER FOR HP-FINITE ELEMENT METHOD

摘要

In this paper we present the performance of our parallelrnmulti-frontal direct solver when applied to solve linear systemsrnof equations resulting from discretizations of a hp FiniternElement Method (hp-FEM). The hp-FEM generatesrna sequence of computational meshes delivering exponentialrnconvergence of the numerical error with respect to thernmesh size (number of degrees of freedom). A sequence ofrnmeshes is obtained by performing several hp refinementsrnstarting from an arbitrary initial mesh. The solver constructsrninitial elimination tree for an arbitrary initial mesh,rnand expands the elimination tree each time the mesh is refined.rnThe solver has been tested on 3D Direct Currentrn(DC) borehole resistivity measurement simulations problems.rnWe compare the solver with two versions of thernMUMPS parallel solver: with (1) distributed entries executedrnover the entire problem, and (2) the direct substructuringrnmethod with parallel MUMPS solver utilizedrnto solve the interface problem. We show that by providingrnto the solver the knowledge about the structure of thernhp-FEM, the order of elimination is obtained straightforward,rnand leads to a better performance than by submittingrnthe entire matrix to the solver and executing a connectivityrngraph based ordering algorithm.