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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:341

Article

Chaillat, Stephanie¹  Darbas, Marion²  Le Louer, Frederique³ 

[1] Univ Paris Saclay, CNRS, INRIA, ENSTA,Lab POEMS,UMA, 828 Bd Marechaux, F-91762 Palaiseau, France

[2] Univ Picardie Jules Verne, LAMFA UMR CNRS 7352, 33 Rue St Leu, F-80039 Amiens, France

[3] Univ Technol Compiegne, Sorbonne Univ, LMAC EA 2222, CS 60319, F-60203 Compiegne, France

关键词: Scattering;    Time-harmonic elastic waves;    Boundary element method;    Fast multipole method;    Analytical preconditioner;    Approximate local DtN map;   

DOI  :  10.1016/j.jcp.2017.04.020

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

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