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

Mikhail A. Bochev, G.L.G. Sleijpen, A. Sopaheluwakan

    Research output: Book/ReportReportProfessional

    49 Downloads (Pure)

    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 languageUndefined
    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.Supplement/1883
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • IR-65013
    • MSC-65F15
    • METIS-251205
    • EWI-13530
    • MSC-35J05
    • MSC-65F30

    Cite this

    Bochev, 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. Supplement/1883). Enschede: University of Twente, Department of Applied Mathematics.
    Bochev, Mikhail A. ; Sleijpen, G.L.G. ; Sopaheluwakan, A. / An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems. Enschede : University of Twente, Department of Applied Mathematics, 2008. 14 p. (Memorandum / Department of Applied Mathematics; Supplement/1883).
    @book{c270faf3b5eb47e2b03f6b142ad4afdf,
    title = "An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems",
    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.",
    keywords = "IR-65013, MSC-65F15, METIS-251205, EWI-13530, MSC-35J05, MSC-65F30",
    author = "Bochev, {Mikhail A.} and G.L.G. Sleijpen and A. Sopaheluwakan",
    note = "Please note different possible spellings of the first author name: {"}Bochev{"} or {"}Botchev{"}.",
    year = "2008",
    month = "9",
    language = "Undefined",
    series = "Memorandum / Department of Applied Mathematics",
    publisher = "University of Twente, Department of Applied Mathematics",
    number = "Supplement/1883",

    }

    Bochev, MA, Sleijpen, GLG & Sopaheluwakan, A 2008, An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems. Memorandum / Department of Applied Mathematics, no. Supplement/1883, University of Twente, Department of Applied Mathematics, Enschede.

    An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems. / Bochev, Mikhail A.; Sleijpen, G.L.G.; Sopaheluwakan, A.

    Enschede : University of Twente, Department of Applied Mathematics, 2008. 14 p. (Memorandum / Department of Applied Mathematics; No. Supplement/1883).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems

    AU - Bochev, Mikhail A.

    AU - Sleijpen, G.L.G.

    AU - Sopaheluwakan, A.

    N1 - Please note different possible spellings of the first author name: "Bochev" or "Botchev".

    PY - 2008/9

    Y1 - 2008/9

    N2 - 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.

    AB - 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.

    KW - IR-65013

    KW - MSC-65F15

    KW - METIS-251205

    KW - EWI-13530

    KW - MSC-35J05

    KW - MSC-65F30

    M3 - Report

    T3 - Memorandum / Department of Applied Mathematics

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

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Bochev MA, Sleijpen GLG, Sopaheluwakan A. An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems. Enschede: University of Twente, Department of Applied Mathematics, 2008. 14 p. (Memorandum / Department of Applied Mathematics; Supplement/1883).