On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Reps, Bram¹  Vanroose, Wim¹  bin Zubair, Hisham¹ 

[1] Univ Antwerp, Dept Math & Informat Technol, B-2020 Antwerp, Belgium

关键词: Complex stretched grid (CSG) preconditioner;    Complex shifted Laplacian (CSL) preconditioner;    Multigrid preconditioning (MGP);    Bi-CGSTAB;    IDR(s);    Exterior complex scaled (ECS) absorbing boundary layers;   

DOI  :  10.1016/j.jcp.2010.07.022

来源: Elsevier

【 摘 要 】

This paper paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not only the coordinates in the absorbing layer have an imaginary part, but also the coordinates in the interior region. This results into a preconditioner problem that is invertible with a multigrid cycle. We give a numerical analysis based on the eigenvalues and evaluate the performance with several numerical experiments. The method is an alternative to the complex shifted Laplacian and it gives a comparable performance for the studied model problems. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free