A novel multigrid based preconditioner for heterogeneous Helmholtz problems

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

Research output: Contribution to journalArticlepeer-review

211 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2006


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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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