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Estimation of the optimal shift for the discrete Helmholtz operator preconditioned with a shifted Laplacian
Author(s) -
Gijzen M.B. van,
Erlangga Y.A.,
Vuik C.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700481
Subject(s) - helmholtz equation , laplace operator , convergence (economics) , operator (biology) , laplace transform , helmholtz free energy , mathematics , mathematical analysis , mathematical optimization , physics , chemistry , boundary value problem , thermodynamics , biochemistry , repressor , transcription factor , economics , gene , economic growth
Shifted Laplace preconditioners have attracted considerable attention as a technique to speed up convergence of iterative solution methods for the Helmholtz equation. In this paper we present an approach to determine a near‐optimal value for the shift. We illustrate our results with a geophysical test problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)