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

Cody Lorton; Ryan Severance

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arXiv · 1905.00411

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

Cody Lorton·Ryan Severance

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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.

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Cody Lorton, Ryan Severance. 2019-05-01. An analysis of sparsity preserving pivot strategies for discontinuous Galerkin methods applied to acoustic scattering. https://arxiv.org/abs/1905.00411

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