A novel multigrid based preconditioner for heterogeneous Helmholtz problems

Y. A. Erlangga, C. W. Oosterlee, C. Vuik

Research output: Contribution to journalArticle

191 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1471-1492
Number of pages22
JournalSIAM Journal on Scientific Computing
Volume27
Issue number4
DOIs
Publication statusPublished - 2006
Externally publishedYes

Fingerprint

Helmholtz equation
Fourier analysis
Hermann Von Helmholtz
Preconditioner
Experiments
Krylov Subspace Methods
Heterogeneous Media
Fourier Analysis
Iterative Solution
Helmholtz Equation
Preconditioning
Differential operator
Numerical Experiment
Iteration
Term

Keywords

  • Complex multigrid preconditioner
  • Fourier analysis
  • Helmholtz equation
  • Nonconstant high wavenumber

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A novel multigrid based preconditioner for heterogeneous Helmholtz problems. / Erlangga, Y. A.; Oosterlee, C. W.; Vuik, C.

In: SIAM Journal on Scientific Computing, Vol. 27, No. 4, 2006, p. 1471-1492.

Research output: Contribution to journalArticle

Erlangga, Y. A. ; Oosterlee, C. W. ; Vuik, C. / A novel multigrid based preconditioner for heterogeneous Helmholtz problems. In: SIAM Journal on Scientific Computing. 2006 ; Vol. 27, No. 4. pp. 1471-1492.
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