Boundary and coupled boundary-finite element methods for transient wave-structure interaction

TL;DR

This paper develops and analyzes boundary integral and coupled boundary-finite element methods for simulating transient wave interactions with elastic obstacles, providing stability, error bounds, and second-order convergence results.

Contribution

It introduces new formulations for wave-structure interaction problems with explicit stability and error analysis, including coupling boundary and finite element methods with Convolution Quadrature.

Findings

Proved well-posedness and stability of the proposed methods.

Established second-order convergence in time for BDF2-CQ.

Numerical experiments confirm theoretical convergence rates.

Abstract

We propose time-domain boundary integral and coupled boundary integral and variational formulations for acoustic scattering by linearly elastic obstacles. Well posedness along with stability and error bounds with explicit time dependence are established. Full discretization is achieved coupling boundary and finite elements; Convolution Quadrature is used for time evolution in the pure BIE formulation and combined with time stepping in the coupled BEM/FEM scenario. Second order convergence in time is proven for BDF2-CQ and numerical experiments are provided for both BDF2 and Trapezoidal Rule CQ showing second order behavior for the latter as well.