Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics

Stéphanie Chaillat (1) , Marc Bonnet (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

This article is mainly devoted to a review on fast BEMs for elastodynamics, with particular attention on time-harmonic fast multipole methods (FMMs). It also includes original results that complete a very recent study on the FMM for elastodynamic problems in semi-infinite media. The main concepts underlying fast elastodynamic BEMs and the kernel-dependent elastodynamic FM-BEM based on the diagonal-form kernel decomposition are reviewed. An elastodynamic FM-BEM based on the half-space Green's tensor suitable for semi-infinite media, and in particular on the fast evaluation of the corresponding governing double-layer integral operator involved in the BIE formulation of wave scattering by underground cavities, is then presented. Results on numerical tests for the multipole evaluation of the half-space traction Green's tensor and the FMM treatment of a sample 3D problem involving wave scattering by an underground cavity demonstrate the accuracy of the proposed approach. The article concludes with a discussion of several topics open to further investigation, with relevant published work surveyed in the process.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Stéphanie Chaillat, Marc Bonnet. Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics. Wave Motion, 2013, 50, pp.1090-1104. ⟨10.1016/j.wavemoti.2013.03.008⟩. ⟨hal-00805764⟩