Multifrontal solver combined with graph partitioners

Abstract

For large-scale structural analysis, the performance of a linear equation solver is very important for the overall efficiency of the analysis code. The multifrontal solver is a very efficient direct solver for finite element analysis, By using multiple fronts, it can considerably reduce the computing time spent on solving the system of linear equations arising from flnite element analysis. To achieve good performance using the multifrontal solver, a good front partition must be obtained because the performance largely depends on the quality of the front partition, that is, the number of degrees of freedom on the partitioned fronts. In this study, graph-partitioning algorithms that are generally used to decompose a given domain for parallel computation are combined with the multifrontal solver to obtain good front partitions of irregular (unstructured) meshes. The influence of the partitioning quality on the performance of the multifrontal solver is also examined. For regular (structured) meshes, the multifrontal scheme can solve the system of linear equations much more efficiently than the single frontal scheme with the help of a simple front-partitioning algorithm. For large-scale problems with irregular meshes such as the finite element meshes of aerospace structures, the verification was made that the developed multifrontal solver combined with an efficient graph partitioner (Metis) and an appropriate mesh mapping scheme (weighted-edge mapping) shows very good performance.