Performance of Multi Level Parallel Direct Solver for hp Finite Element Method

Abstract

The paper presents theoretical evaluation and numerical measurements of a performance of a new parallel direct solver implemented for hp Finite Element Method (FEM). The solver utilizes the substructuring method over the non-overlapping sub-domains, which consists in elimination of the sub-domains internal d.o.f. with respect to the interface d.o.f., then solving the interface problem, finally solving back the internal problems by backward substitution on each subdomain. The interface problem is solved by recursive execution of the direct substructuring method on the tree of separators associated with the subdomains on which the Schur complement approach was applied. We show that the efficiency of the solver is growing when the accuracy of the FEM solution is increased by performing hp refinements on the computational mesh. The h refinements consists in breaking some finite elements into smaller son elements, the p refinements consists in increasing the polynomial order of approximation on some finite elements edges, faces and interiors.