Scattering of acoustic and elastic waves using hybrid multiple multipole expansions—Finite element technique

Abstract

In this paper, two different methods to solve scattering problems in acoustic or elastic media are coupled to enhance their usefulness. The multiple multipole (MMP) expansions are used to solve for the scattered fields in unbounded homogeneous regions. The finite element (FE) method is used to calculate the scattered fields in bounded, heterogeneous regions. Applying the boundary conditions, the different regions and methods are coupled together in the least squares sense as the MMP method requires. By construction, the scattered field in the homogeneous regions is decomposed into P and S modes for the elastic case. In some examples, the scattered fields are calculated and compared to the analytical solutions. Additionally, the seismograms are calculated for a few scattering problems with one or several heterogeneous scatterers of complex geometries. The hybrid MMP–FEM technique proves to be a rather general and useful tool to solve complex, two-dimensional scattering problems.