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

Riyad Kechroud, Azzeddine Soulaimani, Yousef Saad and Shivaraju Gowda

Mathematics and Computers in Simulation (MATCOM), 2004, vol. 65, issue 4, 303-321

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.

Keywords: Helmholtz equation; Acoustic scattering; DtN technique; Finite element method; GMRES iterative method; Incomplete factorization; ILUT; ILUTC; ILU0 (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:65:y:2004:i:4:p:303-321

DOI: 10.1016/j.matcom.2004.01.004

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