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

Riyad Kechroud; Azzeddine Soulaimani; Yousef Saad

doi:10.1007/3-540-44843-8_92

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

Riyad Kechroud, Azzeddine Soulaimani, Yousef Saad

Computer Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter

2 Scopus citations

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.

Original language	English (US)
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Vipin Kumar, Vipin Kumar, Marina L. Gavrilova, Chih Jeng Kenneth Tan, Chih Jeng Kenneth Tan, Pierre L’Ecuyer
Publisher	Springer Verlag
Pages	847-858
Number of pages	12
ISBN (Print)	354040161X
DOIs	https://doi.org/10.1007/3-540-44843-8_92
State	Published - 2003

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2668
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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10.1007/3-540-44843-8_92

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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 V. Kumar, V. Kumar, M. L. Gavrilova, C. J. K. Tan, C. J. K. Tan, & P. L’Ecuyer (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 847-858). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2668). Springer Verlag. https://doi.org/10.1007/3-540-44843-8_92

Preconditionning techniques for the solution of the Helmholtz equation by the finite element method. / Kechroud, Riyad; Soulaimani, Azzeddine; Saad, Yousef.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Vipin Kumar; Vipin Kumar; Marina L. Gavrilova; Chih Jeng Kenneth Tan; Chih Jeng Kenneth Tan; Pierre L’Ecuyer. Springer Verlag, 2003. p. 847-858 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2668).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Kechroud, R, Soulaimani, A & Saad, Y 2003, Preconditionning techniques for the solution of the Helmholtz equation by the finite element method. in V Kumar, V Kumar, ML Gavrilova, CJK Tan, CJK Tan & P L’Ecuyer (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2668, Springer Verlag, pp. 847-858. https://doi.org/10.1007/3-540-44843-8_92

Kechroud R, Soulaimani A, Saad Y. Preconditionning techniques for the solution of the Helmholtz equation by the finite element method. In Kumar V, Kumar V, Gavrilova ML, Tan CJK, Tan CJK, L’Ecuyer P, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 847-858. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44843-8_92

Kechroud, Riyad ; Soulaimani, Azzeddine ; Saad, Yousef. / Preconditionning techniques for the solution of the Helmholtz equation by the finite element method. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Vipin Kumar ; Vipin Kumar ; Marina L. Gavrilova ; Chih Jeng Kenneth Tan ; Chih Jeng Kenneth Tan ; Pierre L’Ecuyer. Springer Verlag, 2003. pp. 847-858 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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

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