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

Published

April 30, 2015

Author(s)

Zydrunas Gimbutas, Leslie Greengard

Abstract

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 (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.

Citation

Advances in Computational Mathematics

Volume

42

Issue

1

Pub Type

Journals

Download Paper

https://doi.org/10.1007/s10444-015-9416-1

Keywords

fast multipole method, linear elasticity, Mindlin's solution

Citation

Gimbutas, Z. and Greengard, L. (2015), A fast multipole method for the evaluation of elastostatic fields in a half-space with zero normal stress, Advances in Computational Mathematics, [online], https://doi.org/10.1007/s10444-015-9416-1 (Accessed October 10, 2025)