Dispersion Properties of Explicit Finite Element Methods for Wave Propagation Modelling on Tetrahedral Meshes

TL;DR

This paper analyzes the dispersion properties of explicit finite element methods, specifically mass-lumped and discontinuous Galerkin methods, for wave propagation on tetrahedral meshes, providing insights into their efficiency and accuracy sensitivity.

Contribution

It offers a semi-analytical dispersion analysis of two finite element methods for wave modeling on tetrahedral meshes, guiding method selection and mesh design.

Findings

Mass-lumped methods require fewer elements per wavelength for similar accuracy.

Discontinuous Galerkin methods are more sensitive to poorly shaped elements.

The analysis indicates optimal method choices based on accuracy and mesh quality.

Abstract

We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax--Wendroff time integration scheme. The dispersion properties are obtained semi-analytically using standard Fourier analysis. Based on the dispersion analysis, we give an indication of which method is the most efficient for a given accuracy, how many elements per wavelength are required for a given accuracy, and how sensitive the accuracy of the method is to poorly shaped elements.