Reducing numerical dispersion and reflections in finite element and finite difference simulation of acoustic wave propagation and scattering

Abstract

Discretization methods such as the finite element method (FEM) and the finite difference method (FDM) suffer from two types of accuracy problems: spurious wave dispersion for long-range propagation and artificial reflections from discretization of perfectly matched layers that are often used to represent the unbounded exterior. In this talk, we focus on lower-order FEM and compact FDM stencils, and show that these errors can be significantly reduced using simple measures: using modified integration rules for FEM, and modified compact stencils for FDM. It turns out that these needed corrections for reducing dispersion and reflections are in opposite directions, indicating that reducing one error results in increasing the other, which is not desirable. In this talk, we introduce a special technique that leads to reduction of both dispersion and reflection errors, and illustrate its effectiveness through theoretical analysis and numerical experiments.