A new BEM–FEM coupling strategy for two-dimensional fluid–solid interaction problems

We present a numerical method to solve a fluid–solid interaction problem posed in the plane. In this scheme, we use a finite element method to approximate the solid vibrations and the near wave field. The far field effects are taken into account by means of boundary integral equations posed on an artificial interface that contains the obstacle. The boundary unknown involved in our formulation is approximated by a spectral method. We obtain a fully discrete Galerkin procedure whose main advantage is the simplicity of the quadratures used to approximate the weakly singular boundary integrals. We provide numerical results that illustrate the accuracy of our method and the stability of the algorithm used to solve the linear systems of equations that arise from this discretization technique.