Application of Multifrontal Method with Relaxed Supernodes for Unsymmetric Matrices

Abstract

When solving sparse matrix linear equations by direct methods, algorithms which take advantage of their sparsity are required. The multifrontal method is a parallelizable method with few fill-ins in the numerical decomposition of matrices, which is advantageous in terms of memory consumption and efficiency when dealing with large systems. Supernodes are a concept for grouping dense portions of a decomposed matrix, and are now also incorporated in the computation of the multifrontal method. In this presentation, we will consider the use of supernodes in the multifrontal methods, especially for unsymmetric matrices.