Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics

  • Authors:

  • I. Duff;S. Gratton;X. Pinel;X. Vasseur

  • Affiliations:

  • CERFACS, France;CERFACS, France;CERFACS, France;CERFACS, France

  • Venue:
  • International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
  • Year:
  • 2007

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Abstract

We study methods for the numerical solution of the Helmholtz equation for two-dimensional applications in geophysics. The common framework of the iterative methods in our study is a combination of an inner iteration with a geometric multigrid method used as a preconditioner and an outer iteration with a Krylov subspace method. The preconditioning system is based on either a pure or shifted Helmholtz operator. A multigrid iteration is used to approximate the inverse of this operator. The proposed solution methods are evaluated on a complex benchmark in geophysics involving highly variable coefficients and high wavenumbers. We compare this preconditioned iterative method with a direct method and a hybrid method that combines our iterative approach with a direct method on a reduced problem. We see that the hybrid method outperforms both the iterative and the direct approach.