Fourier method for approximating eigenvalues of indefinite stekloff operator

Yangqingxiang Wu, Ludmil Zikatanov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We introduce an efficient method for computing the Stekloff eigenvalues associated with the indefinite Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition repeatedly. We propose solving the discretized problem with Fast Fourier Transform (FFT) based on carefully designed extensions and restrictions operators. The proposed Fourier method, combined with proper eigensolver, results in an efficient and easy approach for computing the Stekloff eigenvalues.

Original languageEnglish (US)
Title of host publicationHigh Performance Computing in Science and Engineering - 3rd International Conference, HPCSE 2017, Revised Selected Papers
EditorsJakub Sistek, Petr Tichy, Tomas Kozubek, Martin Cermak, Dalibor Lukas, Jiri Jaros, Radim Blaheta
PublisherSpringer Verlag
Pages34-46
Number of pages13
ISBN (Print)9783319971353
DOIs
StatePublished - Jan 1 2018
Event3rd International Conference on High Performance Computing in Science and Engineering, HPCSE 2017 - Karolinka, Czech Republic
Duration: May 22 2017May 25 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11087 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other3rd International Conference on High Performance Computing in Science and Engineering, HPCSE 2017
CountryCzech Republic
CityKarolinka
Period5/22/175/25/17

Fingerprint

Helmholtz equation
Fourier Method
Helmholtz Equation
Eigenvalue
Computing
Fast Fourier transform
Operator
Neumann Boundary Conditions
Fast Fourier transforms
Dirichlet
Eigenvalue Problem
Boundary conditions
Restriction

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Wu, Y., & Zikatanov, L. (2018). Fourier method for approximating eigenvalues of indefinite stekloff operator. In J. Sistek, P. Tichy, T. Kozubek, M. Cermak, D. Lukas, J. Jaros, & R. Blaheta (Eds.), High Performance Computing in Science and Engineering - 3rd International Conference, HPCSE 2017, Revised Selected Papers (pp. 34-46). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11087 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-97136-0_3
Wu, Yangqingxiang ; Zikatanov, Ludmil. / Fourier method for approximating eigenvalues of indefinite stekloff operator. High Performance Computing in Science and Engineering - 3rd International Conference, HPCSE 2017, Revised Selected Papers. editor / Jakub Sistek ; Petr Tichy ; Tomas Kozubek ; Martin Cermak ; Dalibor Lukas ; Jiri Jaros ; Radim Blaheta. Springer Verlag, 2018. pp. 34-46 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Wu, Y & Zikatanov, L 2018, Fourier method for approximating eigenvalues of indefinite stekloff operator. in J Sistek, P Tichy, T Kozubek, M Cermak, D Lukas, J Jaros & R Blaheta (eds), High Performance Computing in Science and Engineering - 3rd International Conference, HPCSE 2017, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11087 LNCS, Springer Verlag, pp. 34-46, 3rd International Conference on High Performance Computing in Science and Engineering, HPCSE 2017, Karolinka, Czech Republic, 5/22/17. https://doi.org/10.1007/978-3-319-97136-0_3

Fourier method for approximating eigenvalues of indefinite stekloff operator. / Wu, Yangqingxiang; Zikatanov, Ludmil.

High Performance Computing in Science and Engineering - 3rd International Conference, HPCSE 2017, Revised Selected Papers. ed. / Jakub Sistek; Petr Tichy; Tomas Kozubek; Martin Cermak; Dalibor Lukas; Jiri Jaros; Radim Blaheta. Springer Verlag, 2018. p. 34-46 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11087 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Wu Y, Zikatanov L. Fourier method for approximating eigenvalues of indefinite stekloff operator. In Sistek J, Tichy P, Kozubek T, Cermak M, Lukas D, Jaros J, Blaheta R, editors, High Performance Computing in Science and Engineering - 3rd International Conference, HPCSE 2017, Revised Selected Papers. Springer Verlag. 2018. p. 34-46. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-97136-0_3