High Order Finite Difference Schemes for the Elastic Wave Equation in Discontinuous Media

TL;DR

This paper introduces high-order finite difference schemes with specialized interface treatments for simulating elastic waves in media with discontinuities, ensuring stability and high accuracy at material interfaces.

Contribution

The paper develops and analyzes finite difference schemes using compatible and fully compatible operators with a penalty method for interface conditions, demonstrating their stability and accuracy.

Findings

Fully compatible operators yield equal or better accuracy.

Numerical experiments confirm scheme stability and effectiveness.

Methods effectively simulate elastic wave interface phenomena.

Abstract

Finite difference schemes for the simulation of elastic waves in materi- als with jump discontinuities are presented. The key feature is the highly accurate treatment of interfaces where media discontinuities arise. The schemes are constructed using finite difference operators satisfying a sum- mation - by - parts property together with a penalty technique to impose interface conditions at the material discontinuity. Two types of opera- tors are used, termed fully compatible or compatible. Stability is proved for the first case by bounding the numerical solution by initial data in a suitably constructed semi - norm. Numerical experiments indicate that the schemes using compatible operators are also stable. However, the nu- merical studies suggests that fully compatible operators give identical or better convergence and accuracy properties. The numerical experiments are also constructed to illustrate the usefulness of the proposed method to simulations involving typical interface phenomena in elastic materials.