Preconditionning Techniques for the Solution of the Helmholtz Equation by the Finite Element Method

  • Riyad Kechroud
  • Azzeddine Soulaimani
  • Yousef Saad
Conference paper

DOI: 10.1007/3-540-44843-8_92

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2668)
Cite this paper as:
Kechroud R., Soulaimani A., Saad Y. (2003) Preconditionning Techniques for the Solution of the Helmholtz Equation by the Finite Element Method. In: Kumar V., Gavrilova M.L., Tan C.J.K., L’Ecuyer P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2668. Springer, Berlin, Heidelberg

Abstract

This paper discusses 2D solutions of the 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, speci.cally a preconditioned GMRES iteration. The stabilization paremeter associated to GLS is computed using a new formula. Two types of preconditioners, ILUT and ILU0, are tested to enhance convergence.

Key words

Helmholtz Equation acoustic scattering DtN technique Finite element method GMRES iterative method Incomplete factorization ILUT ILU0 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Riyad Kechroud
    • 1
    • 2
  • Azzeddine Soulaimani
    • 1
    • 2
  • Yousef Saad
    • 3
  1. 1.Département de Génie MécaniqueÉcole de technologie supérieureMontréalCanada
  2. 2.École de technologie supérieureMontréalCanada
  3. 3.Department of Computer Science and EngineeringUniversity of MinnesotaMinneapolis

Personalised recommendations