Fast multipole method applied to 3-D frequency domain elastodynamics

  • Sanz J
  • Bonnet M
  • Dominguez J
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Abstract

This article is concerned with the formulation and implementation of a fast multipole-accelerated BEM for 3-D elastodynamics in the frequency domain, based on the so-called diagonal form for the expansion of the elastodynamic fundamental solution, a multilevel strategy. As usual with the FM-BEM, the linear system of BEM equations is solved by GMRES, and the matrix is never explicitly formed. The truncation parameter in the multipole expansion is adjusted to the level, a feature known from recently published studies for the Maxwell equations. A preconditioning strategy based on the concept of sparse approximate inverse (SPAI) is presented and implemented. The proposed formulation is assessed on numerical examples involving O (105) BEM unknowns, which show in particular that, as expected, the proposed FM-BEM is much faster than the BEM traditional, and that the GMRES iteration count is significantly reduced when the SPAI preconditioner is used. © 2008 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • 3-D elastodynamics
  • Boundary element method
  • Fast multipole method

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Authors

  • J. A. Sanz

  • M. Bonnet

  • J. Dominguez

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