Estimation of the optimal shift for the discrete Helmholtz operator preconditioned with a shifted Laplacian | Zendy

Gijzen M.B. van | Zendy; Erlangga Y.A. | Zendy; Vuik C. | Zendy

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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)

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