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Preconditionning Techniques for the Solution of the Helmholtz Equation by the Finite Element Method

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Book cover Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

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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, 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.

This research has been funded by the National Sciences and Engineering Research Council of Canada (NSERC), by the Army Research Office under grant DAAD19-00-1-0485, and by NSF. Support was also provided by the Minnesota Supercomputing Institute.

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Author information

Authors and Affiliations

  1. Département de Génie Mécanique, École de technologie supérieure, 1100 Notre-Dame Ouest, Montréal, (Québec), H3C 1K3, Canada

    Riyad Kechroud & Azzeddine Soulaimani

  2. École de technologie supérieure, 1100 Notre-Dame Ouest, Montréal, (Québec), H3C 1K3, Canada

    Riyad Kechroud & Azzeddine Soulaimani

  3. Department of Computer Science and Engineering, University of Minnesota, 4-192 EE/CS Building, 200 Union Street S.E., Minneapolis, MN, 55455

    Yousef Saad

Authors
  1. Riyad Kechroud
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  2. Azzeddine Soulaimani
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  3. Yousef Saad
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA

    Vipin Kumar

  2. Department of Computer Science and Engineering, University of Minessota, MN, 55455, USA

    Vipin Kumar

  3. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  4. Heuchera Technologies Inc., 122 9251-8 Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  5. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland, UK

    Chih Jeng Kenneth Tan

  6. Département d’informatique et de recherche opérationelle, Université de Montréal, Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/3-540-44843-8_92

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  • DOI: https://doi.org/10.1007/3-540-44843-8_92

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40161-2

  • Online ISBN: 978-3-540-44843-3

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