Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics - Archive ouverte HAL Access content directly
Journal Articles Journal of Computational Physics Year : 2017

Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics

Abstract

The fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles.
Fichier principal
Vignette du fichier
chaillat_2017.pdf (1.41 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01523020 , version 1 (15-05-2017)

Identifiers

Cite

Stéphanie Chaillat, Marion Darbas, Frédérique Le Louër. Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics. Journal of Computational Physics, 2017, 341, pp.429 - 446. ⟨10.1016/j.jcp.2017.04.020⟩. ⟨hal-01523020⟩
282 View
454 Download

Altmetric

Share

Gmail Facebook X LinkedIn More