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

Author

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  • Kechroud, Riyad
  • Soulaimani, Azzeddine
  • Saad, Yousef
  • Gowda, Shivaraju

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.

Suggested Citation

  • Kechroud, Riyad & Soulaimani, Azzeddine & Saad, Yousef & Gowda, Shivaraju, 2004. "Preconditioning techniques for the solution of the Helmholtz equation by the finite element method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(4), pages 303-321.
    • Handle: RePEc:eee:matcom:v:65:y:2004:i:4:p:303-321
    DOI: 10.1016/j.matcom.2004.01.004
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