Theory and implementation of H-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels

JOURNAL OF COMPUTATIONAL PHYSICS

卷:351

Article

Chaillat, Stephanie¹  Desiderio, Luca¹  Ciarlet, Patrick¹ 

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

关键词: Time-harmonic elastic waves;    H-matrices;    Low-rank approximations;    Estimators;    Algorithmic complexity;    Fast BEMs;   

DOI  :  10.1016/j.jcp.2017.09.013

来源: Elsevier

【 摘 要 】

In this work, we study the accuracy and efficiency of hierarchical matrix (H-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard H-matrix based methods, although very efficient tools for asymptotically smooth kernels, are not optimal for oscillatory kernels. H-2-matrix and directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard H-matrix representation. The central questions we address are twofold. (i) What is the frequency-range in which the H-matrix format is an efficient representation for 3D elastodynamic problems? (ii) What can be expected of such an approach to model problems in mechanical engineering? We show that even though the method is not optimal (in the sense that more involved representations can lead to faster algorithms) an efficient solver can be easily developed. The capabilities of the method are illustrated on numerical examples using the Boundary Element Method. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free