Multigrid-based ‘shifted-Laplacian’ preconditioning for the time-harmonic elastic wave equation

Gabrio Rizzuti, Wim Mulder

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)


We investigate the numerical performance of an iterative solver for a frequency-domain finite-difference discretization of the isotropic elastic wave equation. The solver is based on the ‘shifted-Laplacian’ preconditioner, originally designed for the acoustic wave equation. This preconditioner represents a discretization of a heavily damped wave equation and can be efficiently inverted by a multigrid iteration. However, the application of multigrid to the elastic case is not straightforward because standard methods, such as point-Jacobi, fail to smooth the S-wave wavenumber components of the error when high P-to-S velocity ratios are present. We consider line smoothers as an alternative and apply local-mode analysis to evaluate the performance of the various components of the multigrid preconditioner. Numerical examples in 2-D demonstrate the efficacy of our method.
Original languageEnglish
Pages (from-to)47-65
Number of pages19
JournalJournal of Computational Physics
Issue numberJuly
Publication statusPublished - 27 Apr 2016


  • Multigrid
  • Elastic
  • Wave equation
  • Frequency domain
  • Finite-difference


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