Preconditionning Techniques for the Solution of the Helmholtz Equation by the Finite Element Method
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- 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
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 wordsHelmholtz Equation acoustic scattering DtN technique Finite element method GMRES iterative method Incomplete factorization ILUT ILU0
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