Dispersion Properties of Explicit Finite Element Methods for Wave Propagation Modelling on Tetrahedral Meshes
It offers practical guidelines for selecting numerical methods in computational wave propagation, but the analysis is incremental and domain-specific.
This paper analyzes the dispersion properties of mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods for wave propagation on tetrahedral meshes, providing guidance on efficiency, required elements per wavelength, and sensitivity to element shape.
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.