Improvement of accuracy of the spectral element method for elastic wave computation using modified numerical integration operators

TL;DR

This paper presents a modified spectral element method with new numerical integration operators that cancel dispersion errors, resulting in higher accuracy for elastic wave simulations without significant additional computational cost.

Contribution

Introduction of new numerical integration operators that improve spectral element method accuracy by canceling dispersion errors, effectively adding two orders of accuracy.

Findings

Two extra-orders of accuracy achieved

Numerical dispersion analysis confirms theoretical improvements

Waveform computations demonstrate enhanced precision

Abstract

We introduce new numerical integration operators which compose the mass and stiffness matrices of a modified spectral element method for simulation of elastic wave propagation. While these operators use the same quadrature nodes as does the original spectral element method, they are designed in order that their harmonic responses have errors of the same ratio, and that the respective dispersion errors of the mass and stiffness matrices cancel each other. As a result, the modified spectral element method yields two extra-orders of accuracy, and is comparable to the original method of one order higher. The theoretical results are confirmed by numerical dispersion analysis and examples of computation of waveforms using our operators. Replacing the ordinary operators by those proposed in this study could be a non-expensive solution to improve the accuracy.