The Costabel-Stephan system of Boundary Integral Equations in the Time Domain
This work provides a theoretical and numerical framework for solving transient acoustic wave transmission problems via boundary integral equations, but the results are incremental and domain-specific.
The paper formulates a transmission problem for the transient acoustic wave equation as a system of retarded boundary integral equations and analyzes a fully discrete method using Galerkin semidiscretization and Convolution Quadrature, with numerical experiments provided.
In this paper we formulate a transmission problem for the transient acoustic wave equation as a system of retarded boundary integral equations. We then analyse a fully discrete method using a general Galerkin semidiscretization-in-space and Convolution Quadrature in time. All proofs are developed using recent techniques based on the theory of evolution equations. Some numerical experiments are provided.