Scattering Of Acoustic And Elastic Waves Using A 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 homogeneous regions which are possibly unbounded. The finite element (FE) method is used to calculate the scattered fields in heterogeneous but bounded scatterers. As the MMP method requires, the different regions and methods are coupled together in the least squares sense. For some examples, the scattered fields are calculated and compared to the analytical solutions. Finally, the seismograms are calculated for a scattering problem with several scatterers, and complex geometries. Thus, the hybrid MMP-FEM technique is a very general and useful tool to solve complex, two-dimensional scattering problems.