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

## TL;DR

This paper analyzes how different pivoting strategies affect the sparsity of matrices in discontinuous Galerkin methods for acoustic scattering, providing insights into reducing fill-in during LU-factorization.

## Contribution

It evaluates three pivoting strategies—AMD, nested dissection, and reverse Cuthill-McKee—for their effectiveness in maintaining sparsity in IP-DG matrices.

## Key findings

- Nested dissection best reduces fill-in.
- Performance varies with mesh structure and polynomial degree.
- Numerical results validate the strategies' effectiveness.

## 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.