Time domain boundary integral equations and convolution quadrature for scattering by composite media (extended preprint)

TL;DR

This paper develops a numerical method combining boundary element and convolution quadrature techniques to simulate acoustic scattering in heterogeneous media, providing theoretical guarantees for stability and convergence.

Contribution

It introduces a novel combination of Galerkin boundary elements and Runge-Kutta convolution quadrature for scattering problems in composite media, with rigorous analysis.

Findings

Proved well-posedness of the discretized scheme

Established a priori convergence estimates in space and time

Validated the method's stability and accuracy

Abstract

We consider acoustic scattering in heterogeneous media with piecewise constant wave number. The discretization is carried out using a Galerkin boundary element method in space and Runge-Kutta convolution quadrature in time. We prove well-posedness of the scheme and provide a priori estimates for the convergence in space and time.