Space-time stochastic Galerkin boundary elements for acoustic scattering problems

TL;DR

This paper introduces a space-time stochastic Galerkin boundary element method for solving acoustic scattering problems with uncertainties in sources and boundary conditions, demonstrating its effectiveness through numerical experiments and a traffic noise application.

Contribution

It develops a novel stochastic Galerkin boundary element approach for time domain acoustic scattering with uncertainties, incorporating polynomial chaos expansion.

Findings

The method shows good convergence in model problems.

Numerical results validate the approach's accuracy.

Application to traffic noise demonstrates practical utility.

Abstract

Acoustic emission or scattering problems naturally involve uncertainties about the sound sources or boundary conditions. This article initiates the study of time domain boundary elements for such stochastic boundary problems for the acoustic wave equation. We present a space-time stochastic Galerkin boundary element method which is applied to sound-hard, sound-soft and absorbing scatterers. Uncertainties in both the sources and the boundary conditions are considered using a polynomial chaos expansion. The numerical experiments illustrate the performance and convergence of the proposed method in model problems and present an application to a problem from traffic noise.