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

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

Research output: Book/ReportReport

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.
LanguageUndefined
Place of PublicationEnschede
PublisherDepartment of Applied Mathematics, University of Twente
Number of pages14
StatePublished - 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: Department of Applied Mathematics, University of Twente.
Bochev, Mikhail A. ; Sleijpen, G.L.G. ; Sopaheluwakan, A./ An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems. Enschede : Department of Applied Mathematics, University of Twente, 2008. 14 p. (Memorandum / Department of Applied Mathematics; Supplement/1883).
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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.",
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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, Department of Applied Mathematics, University of Twente, Enschede.

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

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

Research output: Book/ReportReport

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

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