A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering
Numerical methods for computing Steklov eigenvalues have attracted the attention of academia for their important physical background and wide applications. In this article we discuss the multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inve...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-07-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0607 |
| _version_ | 1797752507366113280 |
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| author | Xie Jiali Bi Hai |
| author_facet | Xie Jiali Bi Hai |
| author_sort | Xie Jiali |
| collection | DOAJ |
| description | Numerical methods for computing Steklov eigenvalues have attracted the attention of academia for their important physical background and wide applications. In this article we discuss the multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering, and give the error estimation of the proposed scheme. In addition, on the basis of the a posteriori error indicator, we design an adaptive multigrid algorithm. Finally, we present numerical examples to show the efficiency of the proposed scheme. |
| first_indexed | 2024-03-12T17:04:23Z |
| format | Article |
| id | doaj.art-ce5142b7053b428db905941aa516fba2 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-12T17:04:23Z |
| publishDate | 2023-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-ce5142b7053b428db905941aa516fba22023-08-07T06:56:44ZengDe GruyterOpen Mathematics2391-54552023-07-0121154055810.1515/math-2022-0607A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scatteringXie Jiali0Bi Hai1School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, ChinaSchool of Mathematical Sciences, Guizhou Normal University, Guiyang, 550001, ChinaNumerical methods for computing Steklov eigenvalues have attracted the attention of academia for their important physical background and wide applications. In this article we discuss the multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering, and give the error estimation of the proposed scheme. In addition, on the basis of the a posteriori error indicator, we design an adaptive multigrid algorithm. Finally, we present numerical examples to show the efficiency of the proposed scheme.https://doi.org/10.1515/math-2022-0607steklov eigenvalue problem in inverse scatteringmultigrid discretizationthe shifted-inverse iterationerror estimationadaptive algorithm65n2565n30 |
| spellingShingle | Xie Jiali Bi Hai A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering Open Mathematics steklov eigenvalue problem in inverse scattering multigrid discretization the shifted-inverse iteration error estimation adaptive algorithm 65n25 65n30 |
| title | A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering |
| title_full | A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering |
| title_fullStr | A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering |
| title_full_unstemmed | A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering |
| title_short | A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering |
| title_sort | multigrid discretization scheme based on the shifted inverse iteration for the steklov eigenvalue problem in inverse scattering |
| topic | steklov eigenvalue problem in inverse scattering multigrid discretization the shifted-inverse iteration error estimation adaptive algorithm 65n25 65n30 |
| url | https://doi.org/10.1515/math-2022-0607 |
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