Title
A new level-dependent coarse grid correction scheme for indefinite Helmholtz problems A new level-dependent coarse grid correction scheme for indefinite Helmholtz problems
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Chichester :Wiley ,
Subject
Mathematics
Source (journal)
Numerical linear algebra with applications. - Chichester
Volume/pages
21(2014) :4 , p. 513-533
ISSN
1070-5325
ISI
000339432400003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In this paper, we construct and analyze a level-dependent coarse grid correction scheme for indefinite Helmholtz problems. This adapted multigrid (MG) method is capable of solving the Helmholtz equation on the finest grid using a series of MG cycles with a grid-dependent complex shift, leading to a stable correction scheme on all levels. It is rigorously shown that the adaptation of the complex shift throughout the MG cycle maintains the functionality of the two-grid correction scheme, as no smooth modes are amplified in or added to the error. In addition, a sufficiently smoothing relaxation scheme should be applied to ensure damping of the oscillatory error components. Numerical experiments on various benchmark problems show the method to be competitive with or even outperform the current state-of-the-art MG-preconditioned Krylov methods, for example, complex shifted Laplacian preconditioned flexible GMRES.
E-info
https://repository.uantwerpen.be/docman/iruaauth/7ef846/9873debe739.pdf
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