Regular article

Computing and Visualization in Science

, Volume 11, Issue 3, pp 139-146

Open Access This content is freely available online to anyone, anywhere at any time.

Numerical performance of a parallel solution method for a heterogeneous 2D Helmholtz equation

  • A. V. KononovAffiliated withAcoustical Imaging & Sound Control, Delft University of Technology Email author 
  • , C. D. RiyantiAffiliated withNumerical Analysis Group, Delft Institute of Applied Mathematics, Delft University of Technology
  • , S. W. de LeeuwAffiliated withComputational Physics Group, PCMT, DelftChem, Delft University of Technology
  • , C. W. OosterleeAffiliated withNumerical Analysis Group, Delft Institute of Applied Mathematics, Delft University of Technology
  • , C. VuikAffiliated withNumerical Analysis Group, Delft Institute of Applied Mathematics, Delft University of Technology

Abstract

The parallel performance of a numerical solution method for the scalar 2D Helmholtz equation written for inhomogeneous media is studied. The numerical solution is obtained by an iterative method applied to the preconditioned linear system which has been derived from a finite difference discretization. The preconditioner is approximately inverted using multigrid iterations. Parallel execution is implemented using the MPI library. Only a few iterations are required to solve numerically the so-called full Marmousi problem [Bourgeois, A., et al. in The Marmousi Experience, Proceedings of the 1990 EAEG Workshop on Practical Aspects of Seismic Data Inversion: Eur. Assoc. Expl. Geophys., pp. 5–16 (1991)] for the high frequency range.