A fully discrete BEM-FEM scheme for transient acoustic waves

TL;DR

This paper presents a symmetric BEM-FEM coupling scheme for transient acoustic wave scattering by inhomogeneous obstacles, combining boundary and finite element methods with convolution quadrature for stable, convergent simulations.

Contribution

The paper introduces a novel symmetric coupling formulation for transient acoustic scattering, integrating boundary elements and finite elements with time discretization techniques.

Findings

The scheme is proven to generate a C_0 group of isometries ensuring stability.

Numerical experiments validate the convergence and flexibility of the proposed method.

The method effectively handles inhomogeneous anisotropic obstacles in acoustic scattering.

Abstract

We study a symmetric BEM-FEM coupling scheme for the scattering of transient acoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneous field. An incident wave in free space interacts with the obstacles and produces a combination of transmission and scattering. The transmitted part of the wave is discretized in space by finite elements while the scattered wave is reduced to two fields defined on the boundary of the obstacles and is discretized in space with boundary elements. We choose a coupling formulation that leads to a symmetric system of integro-differential equations. The retarded boundary integral equations are discretized in time by Convolution Quadrature, and the interior field is discretized in time with the trapezoidal rule. We show that the scattering problem generates a C_0 group of isometries in a Hilbert space, and use associated estimates to derive stability and convergence results. We provide numerical experiments and simulations to validate our results and demonstrate the flexibility of the method.