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 2006, Vol.27 (4), p.1471-1492
Hauptverfasser:	ERLANGGA, Y. A, OOSTERLEE, C. W, VUIK, C
Format:	Artikel
Sprache:	eng
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
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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.
ISSN:	1064-8275 1095-7197
DOI:	10.1137/040615195