Overlapped BEM-FEM for some Helmholtz transmission problems (Q870287)

The authors introduce and analyze a fairly sophisticated numerical method in order to solve some Helmholtz transmission problems in 2D and 3D bounded domains with polygonal/polyhedral boundaries. They use finite elements to approximate the solution and Petrov-Galerkin boundary elements to approximate the two densities defined on the interface of the two subdomains. Thus they consider a boundary element method (BEM) module for the exterior transmission problem, a finite element method (FEM) module for the Helmholtz problem on the whole domain, with mixed boundary conditions, and a smoother for the finite element solution of homogeneous elliptic problems. A 2D numerical experiment is carried out in order to underline the capabilities of the method.