Fast solution of MSC/Nastran sparse matrix problems using a multi-level approach

Clemens-August Thole, Alexander Supalov

GMD-SCAI.WR, Schloß Birlinghoven, D-53754 Sankt Augustin


Abstract

As part of the European Esprit project EUROPORT, 38 commercial and industrial simulation codes were parallelized for distributed memory architectures. As a result of the project among others the CFD codes CFX4, PHOENICS, POLYFLOW and STAR-CD as well as the structural analysis codes LS-DYNA3D, MSC/NASTRAN, PAM-CRASH, PERMAS and SAMCEF are now available for parallel architectures.

During the project sparse matrix solvers turned out to be a major obstacle for high scalability of the parallel version of several codes. The European Commission therefore launched the PARASOL project to develop fast parallel direct solvers and to test parallel iterative solvers on their applicability and robustness in an industrial framework. The industrial codes involved in this project perform structural analysis (DNV-Sesame, MSC/NASTRAN), simulation of forming processes (ARC3D, INDEED) and viscous flow (POLYFLOW). Iterative numerical methods involved are domain decomposition methods and hierarchical methods, like multigrid. For each of the industrial test cases several solvers will be evaluated with respect to performance and robustness.

This paper presents initial results using a special multi-level method as preconditioner for matrices resulting from MSC/NASTRAN structural analysis for linear test cases in three dimensions. P-elements in MSC/NASTRAN allow to specify globally or for each element the polynomial degree of the elements. Solution depended adaptive "refinement" of the p-level can be selected. Based on this approach discretisations with lower p-level can be used as coarser grids for a multi-level method (as suggested already in [1]).

Tests have been performed using such a method as preconditioner for a regular cube and a crankshaft segment, which were modeled by tetrahedrons and hexagonal elements. In both cases about 15 cg-iterations are necessary to reduce the residual by 6 orders of magnitude. For the crankshaft segment each iteration involves more smoothing steps than in the other case.
In both cases the new solver needs substantial less memory compared to the fastest solver provided by MSC/NASTRAN. Preliminary performance comparison on small test cases (about 10.000 degrees of freedom) indicate, that the multi-level approach is at least as fast as the currently available fastest MSC/NASTRAN solver. Therefore substantial performance improvements are expected for full-size industrial problems.

[1] Axelsson, O.; Gustafsson, I.: Preconditioning and two-level multigrid methods of arbitrary degree of approximation. Math. Comp., 40, pp. 219-242, 1983.