Galerkin method for the scattering problem of strip gratings
Abstract In this paper, the diffraction problem of periodic strip gratings is considered. The previous study of this problem usually concentrated on the numerical method; however, we try to analyze this problem and the convergence of the numerical solution from the mathematical point of view in this...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-02-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-1999-2 |
| _version_ | 1818523971446898688 |
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| author | Enxi Zheng Yujie Wang |
| author_facet | Enxi Zheng Yujie Wang |
| author_sort | Enxi Zheng |
| collection | DOAJ |
| description | Abstract In this paper, the diffraction problem of periodic strip gratings is considered. The previous study of this problem usually concentrated on the numerical method; however, we try to analyze this problem and the convergence of the numerical solution from the mathematical point of view in this work. By use of the Dirichlet to Neumann operator on the slit between two strips, we reformulate the problem to an operator equation. The well-posedness of the solution to the operator equation is proved. The Galerkin method is applied to solve this operator equation and the convergence result of the numerical solution is also derived. Finally, some numerical experiments are presented to show the effectiveness of our method and verify the theoretical convergence result. |
| first_indexed | 2024-12-11T05:51:18Z |
| format | Article |
| id | doaj.art-451d391da2b648509bfd51b827ea91d1 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T05:51:18Z |
| publishDate | 2019-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-451d391da2b648509bfd51b827ea91d12022-12-22T01:18:49ZengSpringerOpenAdvances in Difference Equations1687-18472019-02-012019111410.1186/s13662-019-1999-2Galerkin method for the scattering problem of strip gratingsEnxi Zheng0Yujie Wang1School of Science, Dalian Maritime UniversitySchool of Science, Dalian Maritime UniversityAbstract In this paper, the diffraction problem of periodic strip gratings is considered. The previous study of this problem usually concentrated on the numerical method; however, we try to analyze this problem and the convergence of the numerical solution from the mathematical point of view in this work. By use of the Dirichlet to Neumann operator on the slit between two strips, we reformulate the problem to an operator equation. The well-posedness of the solution to the operator equation is proved. The Galerkin method is applied to solve this operator equation and the convergence result of the numerical solution is also derived. Finally, some numerical experiments are presented to show the effectiveness of our method and verify the theoretical convergence result.http://link.springer.com/article/10.1186/s13662-019-1999-2Strip gratingDirichlet to Neumann mapHelmholtz equationGalerkin method |
| spellingShingle | Enxi Zheng Yujie Wang Galerkin method for the scattering problem of strip gratings Advances in Difference Equations Strip grating Dirichlet to Neumann map Helmholtz equation Galerkin method |
| title | Galerkin method for the scattering problem of strip gratings |
| title_full | Galerkin method for the scattering problem of strip gratings |
| title_fullStr | Galerkin method for the scattering problem of strip gratings |
| title_full_unstemmed | Galerkin method for the scattering problem of strip gratings |
| title_short | Galerkin method for the scattering problem of strip gratings |
| title_sort | galerkin method for the scattering problem of strip gratings |
| topic | Strip grating Dirichlet to Neumann map Helmholtz equation Galerkin method |
| url | http://link.springer.com/article/10.1186/s13662-019-1999-2 |
| work_keys_str_mv | AT enxizheng galerkinmethodforthescatteringproblemofstripgratings AT yujiewang galerkinmethodforthescatteringproblemofstripgratings |