Dispersion analysis of spectral element methods for elastic wave propagation

Abstract

We study the numerical dispersion of spectral element methods of arbitrary order for the isotropic elastic wave equation in two and three dimensions by a simplified modal analysis of the discrete wave operators. This analysis is based on a Rayleigh quotient approximation of the eigenvalue problem that characterizes the dispersion relation. This approximation takes full advantage of the tensor product representation of the spectral element matrices. We compute dispersion graphs that show the dependence of the phase/group velocity, the polarization error, and the numerical anisotropy on the grid resolution as well as the polynomial degree with both Gauss–Lobatto–Chebyshev and Gauss–Lobatto–Legendre collocation points.