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

Authors:
Riyad Kechroud;Azzeddine Soulaimani;Yousef Saad
Affiliations:
Département de Génie Mécanique, École de technologie supérieure, Montréal, Québec, Canada;Département de Génie Mécanique, École de technologie supérieure, Montréal, Québec, Canada;Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
Year:
2003

Citing 4
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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, specifically 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.