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

Authors:
Riyad Kechroud;Azzeddine Soulaimani;Yousef Saad;Shivaraju Gowda
Affiliations:
Dé/partement de Gé/nie Mé/canique, É/cole de Technologie Supé/rieure/ 1100 Notre-Dame Ouest, Montré/al, Que., Canada H3C 1K3;Dé/partement de Gé/nie Mé/canique, É/cole de Technologie Supé/rieure/ 1100 Notre-Dame Ouest, Montré/al, Que., Canada H3C 1K3;Department of Computer Science and Engineering, University of Minnesota, 4-192 EE/CS Building, 200 Union Street S.E., Minneapolis, MN;Department of Computer Science and Engineering, University of Minnesota, 4-192 EE/CS Building, 200 Union Street S.E., Minneapolis, MN
Venue:
Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
Year:
2004

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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 ILUO, are tested to enhance convergence.