# Fast multipole method applied to 3D frequency domain elastodynamics

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 multi-level 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 recent 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 $O(10^{5})$ BEM unknowns, which show in particular that, as expected, the proposed FM-BEM is much faster than the traditional BEM, and that the GMRES iteration count is significantly reduced when the SPAI preconditioner is used.
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Journal articles
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Cited literature [26 references]

https://hal.archives-ouvertes.fr/hal-00310458
Contributor : Marc Bonnet <>
Submitted on : Thursday, August 28, 2008 - 12:43:01 PM
Last modification on : Wednesday, March 27, 2019 - 4:16:22 PM
Long-term archiving on : Tuesday, September 21, 2010 - 5:15:18 PM

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### Citation

Jose Antonio Sanz, Marc Bonnet, Jose Dominguez. Fast multipole method applied to 3D frequency domain elastodynamics. Engineering Analysis with Boundary Elements, Elsevier, 2008, 32, pp.787-795. ⟨10.1016/j.enganabound.2008.03.002⟩. ⟨hal-00310458v2⟩

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