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

✍ Scribed by Riyad Kechroud; Azzeddine Soulaimani; Yousef Saad; Shivaraju Gowda

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
175 KB
Volume
65
Category
Article
ISSN
0378-4754

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✦ Synopsis

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.

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