Title
Analyzing the wave number dependency of the convergence rate of a multigrid preconditioned Krylov method for the Helmholtz equation with an absorbing layer Analyzing the wave number dependency of the convergence rate of a multigrid preconditioned Krylov method for the Helmholtz equation with an absorbing layer
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
19(2012) :2 , p. 232-252
ISSN
1070-5325
ISI
000299777500005
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
This paper analyzes the Krylov convergence rate of a Helmholtz problem preconditioned with multigrid. The multigrid method is applied to the Helmholtz problem formulated on a complex contour and uses the generalized minimal residual method as a smoother substitute at each level. A one-dimensional model is analyzed both in a continuous and discrete way. It is shown that the Krylov convergence rate of the continuous problem is independent of the wave number. The discrete problem, however, can deviate significantly from this bound because of a pitchfork in the spectrum. It is further shown in numerical experiments that the convergence rate of the Krylov method approaches the continuous bound as the grid distance h gets small. Copyright (C) 2012 John Wiley & Sons, Ltd.
E-info
https://repository.uantwerpen.be/docman/iruaauth/9709f9/7db1218.pdf
Full text (open access)
https://repository.uantwerpen.be/docman/irua/84cff5/3952.pdf
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