An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems

M.A. Botchev, G.L.G. Sleijpen, A. Sopaheluwakan

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    Abstract

    Numerical solution of the Helmholtz equation in an infinite domain often involves restriction of the domain to a bounded computational window where a numerical solution method is applied. On the boundary of the computational window artificial transparent boundary conditions are posed, for example, widely used perfectly matched layers (PMLs) or absorbing boundary conditions (ABCs). Recently proposed transparent-influx boundary conditions (TIBCs) resolve a number of drawbacks typically attributed to PMLs and ABCs, such as introduction of spurious solutions and the inability to have a tight computational window. Unlike the PMLs or ABCs, the TIBCs lead to a nonlinear dependence of the boundary integral operator on the frequency. Thus, a nonlinear Helmholtz eigenvalue problem arises. This paper presents an approach for solving such nonlinear eigenproblems which is based on a truncated singular value decomposition (SVD) polynomial approximation of the nonlinearity and subsequent solution of the obtained approximate polynomial eigenproblem with the Jacobi-Davidson method.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages14
    Publication statusPublished - Sep 2008

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1883
    ISSN (Print)1874-4850

    Keywords

    • MSC-65F15
    • MSC-35J05
    • MSC-65F30

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  • Cite this

    Botchev, M. A., Sleijpen, G. L. G., & Sopaheluwakan, A. (2008). An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems. (Memorandum / Department of Applied Mathematics; No. 1883). Enschede: University of Twente, Department of Applied Mathematics.