Wave scattering using a hybrid MMP–FE technique

Among the methods amendable to solve acoustic or elastic scattering problems are the finite elements method (FEM) and multiple multipole (MMP) expansions [M. G. Imhof, J. Acoust. Soc. Am. 97, 754–763 (1995)]. Among the difficulties the FEM encounters are long calculation times, large memory requirements, and the need for absorbing boundary conditions. On the other hand, the FEM is perfectly suited for heterogeneous media because it automatically accounts for changes in material properties. In contrast, the computational cost of MMP expansions is independent of the source–receiver geometry. An unbounded domain poses no difficulty since the expansion functions account automatically for the radiation condition. MMP expansions often converge with very few terms and therefore reduce the computational effort. Unfortunately, expansion functions for heterogeneous media are difficult to find. Scattering problems with heterogeneous scatterers embedded in a homogeneous background are difficult (FEM) or impossible (MMP) to solve with either of these techniques alone. Therefore, the MMP expansions are coupled with the FE method. For a cylindrical scattering problem, the resulting solution is compared to the analytical one. Results for multiple inhomogeneous scatterers embedded in a homogeneous media are presented.