Computing the elastic scattering from inclusions using the multiple multipoles method in three dimensions

Abstract

The paper extends the multiple multipole method (MMP) to compute the multiple scattering effects from inclusions in a homogeneous full-space from two dimensions to three dimensions. MMP methods are based on a scattered wavefield model where the unknown weighting coefficients are determined from satisfying the boundary conditions at discrete matching points. The wavefield model is most commonly constructed from multiple spherical wavefunctions with different expansion centres, but any solution or approximation to the wave equation may also be used. Such an expansion is non-orthogonal and requires use of overdetermined matrix systems, but this system can be constructed rapidly because simple point matching without costly integration is sufficient. Furthermore, irregularities of the boundary are resolved locally from the nearest centre of expansion, which decouples different parts of the boundary, and thus, promotes rapid conversion with small numbers of expansion functions. The resulting algorithm is a very general tool to solve relatively large and complex 3-D scattering problems.