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

Zydrunas Gimbutas, Leslie Greengard

Research output: Contribution to journalArticle

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 (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.

Original languageEnglish (US)
Pages (from-to)175-198
Number of pages24
JournalAdvances in Computational Mathematics
Volume42
Issue number1
DOIs
StatePublished - Feb 1 2016

Fingerprint

Fast multipole Method
Elastostatics
Green's function
Half-space
Elasticity
Evaluation
Zero
Explicit Solution
Plane Wave
Physics
Standards

Keywords

  • Fast multipole method
  • Linear elasticity
  • Mindlin’s solution

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

A fast multipole method for the evaluation of elastostatic fields in a half-space with zero normal stress. / Gimbutas, Zydrunas; Greengard, Leslie.

In: Advances in Computational Mathematics, Vol. 42, No. 1, 01.02.2016, p. 175-198.

Research output: Contribution to journalArticle

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