On the stability of time-domain integral equations for acoustic wave propagation

TL;DR

This paper presents a systematic method for choosing boundary integral representations to ensure stable solutions in time-domain acoustic wave scattering problems.

Contribution

It introduces a principled approach for selecting retarded potential representations to improve stability in solving wave scattering equations.

Findings

Provides criteria for stable boundary integral formulations

Enhances understanding of wave equation solution representations

Facilitates more reliable acoustic scattering simulations

Abstract

We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain.