Time-Domain Multiple Traces Boundary Integral Formulation for Acoustic Wave Scattering in 2D

TL;DR

This paper introduces a new time-domain boundary integral method for simulating acoustic wave scattering in 2D, using spectral elements and convolution quadrature to handle complex geometries with junctions.

Contribution

It develops a novel multiple traces boundary integral formulation for acoustic scattering in 2D, combining spectral element discretization and convolution quadrature for improved accuracy.

Findings

Demonstrates convergence of the method on complex domains

Validates the approach with computational experiments

Handles penetrable obstacles with junctions effectively

Abstract

We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain boundary integral formulation valid in two and three dimensions. Numerically, our two-dimensional non-conforming spatial discretization uses spectral elements based on second kind Chebyshev polynomials while a convolution quadrature scheme is performed in the complex frequency domain. Computational experiments reveal multistep and multistage convolution quadrature expected convergence results for a variety of complex domains.