Implicit/explicit, BEM/FEM coupled scheme for acoustic waves with the wave equation in the second order formulation

TL;DR

This paper presents a coupled BEM/FEM scheme for acoustic wave scattering, integrating boundary integral equations with finite element methods and analyzing stability and convergence through numerical experiments.

Contribution

It introduces a fully discrete coupled BEM/FEM scheme with a novel truncated trapezoidal rule for convolution quadrature, along with stability and convergence analysis.

Findings

Stable and convergent scheme under CFL condition

Effective implementation of convolution quadrature with new rule

Numerical experiments confirm theoretical results

Abstract

Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is described. A fully discrete system consists of spatial discretization by boundary and finite element methods (BEM/FEM), leapfrog time-stepping in the interior, and convolution quadrature for the boundary integral equations. Convolution quadrature is based on BDF2, trapezoidal rule, or a newly introduced truncated trapezoidal rule that has some favourable properties for both the implementation and quality of approximate solution. We give a stability and convergence analysis under a CFL conditon of the fully discrete system. The theoretical results are illustrated by numerical experiments in two dimensions.