The Costabel-Stephan system of Boundary Integral Equations in the Time Domain

TL;DR

This paper formulates a boundary integral equation system for transient acoustic waves, analyzes a fully discrete numerical method combining Galerkin semidiscretization and Convolution Quadrature, and supports findings with numerical experiments.

Contribution

It introduces a novel formulation of the transmission problem as retarded boundary integral equations and provides a rigorous analysis of a fully discrete numerical scheme.

Findings

The method achieves stable and accurate numerical solutions.

Theoretical proofs are developed using evolution equations techniques.

Numerical experiments demonstrate the effectiveness of the approach.

Abstract

In this paper we formulate a transmission problem for the transient acoustic wave equation as a system of retarded boundary integral equations. We then analyse a fully discrete method using a general Galerkin semidiscretization-in-space and Convolution Quadrature in time. All proofs are developed using recent techniques based on the theory of evolution equations. Some numerical experiments are provided.