A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems

An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner...

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Veröffentlicht in:SIAM journal on scientific computing Jg. 27; H. 4; S. 1471 - 1492
Hauptverfasser: Erlangga, Y. A., Oosterlee, C. W., Vuik, C.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2006
Schlagworte:
Accuracy
Acoustics
Aeroacoustics, atmospheric sound
Boundary conditions
Classical and quantum physics: mechanics and fields
Eigenvalues
Exact sciences and technology
Fourier analysis
Fundamental areas of phenomenology (including applications)
General theory of scattering
Helmholtz equations
Mathematics
Methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations, boundary value problems
Physics
Radiation
Sciences and techniques of general use
78A45
Initial value problem
Decomposition method
Helmholtz equation
Krylov subspace method
Fourier analysis
Iterative method
Iteration
Nonconstant high wavenumber
Partial differential equation
Numerical analysis
Boundary value problem
complex multigrid preconditioner
Scientific computation
65F10
Multigrid
76Q05
Complex matrix
Domain decomposition
Preconditioning
65N22
65N55
ISSN:1064-8275, 1095-7197
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner. The choice of multigrid components for the corresponding preconditioning matrix with a complex diagonal is validated with Fourier analysis. Multigrid analysis results are verified by numerical experiments. High wavenumber Helmholtz problems in heterogeneous media are solved indicating the performance of the preconditioner.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1064-8275
1095-7197
DOI:10.1137/040615195