Coupling of boundary integral equation and finite element methods for transmission problems in acoustics

In this paper, we propose a coupling of finite element method (FEM) and boundary integral equation (BIE) method for solving acoustic transmission problems in two dimensions. The original transmission problem is firstly reduced to a nonlocal boundary value problem by introducing an artificial boundary and defining a transparent boundary condition from the relation between Dirichlet data and Neumann data on the artificial boundary. In this work, such relationship is described in terms of boundary integral operators. Then, essential mathematical analysis for the weak formulation corresponding to the nonlocal boundary value problem is discussed. Three different algorithms are utilized for the solution of boundary integral equations to be involved in the computational formulations, and numerical results are presented to demonstrate the efficiency and accuracy of the schemes.