An analysis of sparsity preserving pivot strategies for discontinuous Galerkin methods applied to acoustic scattering

Abstract

In this paper we discuss and analyze the sparse structure of matrices associated to the interior penalty discontinuous Galerkin (IP-DG) method applied to the Helmholtz equation. It is well-known that LU-factorization causes fill-in and this paper discusses three pivoting strategies: approximate minimal degree (AMD), nested dissection, and reverse Cuthill-McKee, that can reduce fill-in associated to the LU-factorization. Numerical experiments are included that demonstrate the performance of these pivoting strategies. These experiments include both uniform and non-uniform mesh structures, the inclusion of a scattering boundary, and both piecewise linear and quadratic solution spaces.