Preconditioning techniques for the solution of the Helmholtz equation by the finite element method

Riyad Kechroud, Azzeddine Soulaimani, Yousef Saad, Shivaraju Gowda

Research output: Contribution to journalConference articlepeer-review

24 Scopus citations

Abstract

This paper discusses 2D and 3D solutions of the harmonic Helmholtz equation by finite elements. It begins with a short survey of the absorbing and transparent boundary conditions associated with the DtN technique. The solution of the discretized system by means of a standard Galerkin or Galerkin least-squares (GLS) scheme is obtained by a preconditioned Krylov subspace technique, specifically a preconditioned GMRES iteration. The stabilization parameter associated to GLS is computed using a new formula. Three types of preconditioners: ILUT, ILUTC and ILU0, are tested to enhance convergence.

Original languageEnglish (US)
Pages (from-to)303-321
Number of pages19
JournalMathematics and Computers in Simulation
Volume65
Issue number4-5
DOIs
StatePublished - May 11 2004
EventWave Phenomena in Physisc and Engineering: New Models - Montreal, Canada
Duration: May 1 2003May 1 2003

Keywords

  • Acoustic scattering
  • DtN technique
  • Finite element method
  • GMRES iterative method
  • Helmholtz equation
  • ILU0
  • ILUT
  • ILUTC
  • Incomplete factorization

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