A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation

  • Authors:

  • C. D. Riyanti;A. Kononov;Y. A. Erlangga;C. Vuik;C. W. Oosterlee;R. -E. Plessix;W. A. Mulder

  • Affiliations:

  • Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;Computational Physics Group, Delft University of Technology, The Netherlands;Scientific Computing, Technical University, Berlin, Germany;Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;Shell International E&P, P.O. Box 60, 2280 AB Rijswijk, The Netherlands;Shell International E&P, P.O. Box 60, 2280 AB Rijswijk, The Netherlands

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a complex shifted-Laplace preconditioner combined with the Bi-CGSTAB iterative method and use a multigrid method to approximate the inverse of the resulting preconditioning operator. A 3D multigrid method with 2D semi-coarsening is employed. We show numerical results for large problems arising in geophysical applications.