A symmetric boundary integral formulation for time-domain acoustic-elastic scattering

TL;DR

This paper develops a symmetric boundary integral formulation for transient acoustic-elastic scattering, enabling efficient and modular numerical simulations by combining acoustic and elastic wave models through a coupled integral system.

Contribution

It introduces a novel symmetric integral formulation with a mortar variable, facilitating non-intrusive numerical implementation for acoustic-elastic scattering problems.

Findings

Formulation is well-suited for existing acoustic and elastic codes.

Analysis conducted via Laplace domain and convolution quadrature.

Ensures stable and accurate time-domain simulations.

Abstract

A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented through a direct integral representation, resulting in a coupled system of interior/exterior integral equations that is symmetrized through the introduction of an auxiliary mortar variable. The analysis of each system and of its Galerkin discretization is done through the passage to the Laplace domain, which allows for the use of convolution quadrature for time discretization. Since the operators of the acustic and elastic Calder\'on calculus appear independently of each other, the formulation is well suited for non-intrusive numerical impementations (i.e. existing codes for acoustic and elastic problems can be used without any modification).