A fast multipole method for the evaluation of elastostatic fields in a half-space with zero normal stress

In this paper, we present a fast multipole method (FMM) for the half-space Green’s function in a homogeneous elastic half-space subject to zero normal stress, for which an explicit solution was given by Mindlin (Physics 7, 195–202 1936). The image structure of this Green’s function is unbounded, so that standard outgoing representations are not easily available. We introduce two such representations here, one involving an expansion in plane waves and one involving a modified multipole expansion. Both play a role in the FMM implementation.