An analysis of the BEM-FEM non-overlapping domain decomposition method for a scattering problem

In this paper, we analyse the BEM-FEM non-overlapping domain decomposition method introduced in [4] and improved in [7,3]. The transmission conditions used in this method produce an iteration operator which does not satisfy the isometric property. Therefore, the approach of B. Després to establish convergence [16] cannot be adapted. However, we show that convergence can be established when the geometry allows for a decomposition of the solution into propagating and evanescent portions with a methodology based on modal analysis. Here, we exemplify this in the case of circular cylindrical geometries where the derivations can be based on properties of Bessel functions.