Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method
The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method. First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the Gordo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/780769 |
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| _version_ | 1832552392678178816 |
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| author | Peyman Hessari Sang Dong Kim Byeong-Chun Shin |
| author_facet | Peyman Hessari Sang Dong Kim Byeong-Chun Shin |
| author_sort | Peyman Hessari |
| collection | DOAJ |
| description | The aim of this paper is to solve an elliptic interface problem
with a discontinuous coefficient and a singular source term by the spectral collocation method.
First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the
Gordon-Hall transformation, we generalize it to a domain with a curve boundary and a curve interface.
The spectral element collocation method is then employed to complex geometries; that is,
we decompose the domain into some nonoverlaping subdomains and the spectral collocation solution is sought in each subdomain.
We give some numerical experiments to show efficiency of our algorithm and its spectral convergence. |
| format | Article |
| id | doaj-art-d0976787887e47b2be37869ee6cfedc3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d0976787887e47b2be37869ee6cfedc32025-02-03T05:58:53ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/780769780769Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation MethodPeyman Hessari0Sang Dong Kim1Byeong-Chun Shin2Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan 689-798, Republic of KoreaDepartment of Mathematics, Kyungpook National University, Daegu 702-701, Republic of KoreaDepartment of Mathematics, Chonnam National University, Gwangju 500-757, Republic of KoreaThe aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method. First, we develop an algorithm for the elliptic interface problem defined in a rectangular domain with a line interface. By using the Gordon-Hall transformation, we generalize it to a domain with a curve boundary and a curve interface. The spectral element collocation method is then employed to complex geometries; that is, we decompose the domain into some nonoverlaping subdomains and the spectral collocation solution is sought in each subdomain. We give some numerical experiments to show efficiency of our algorithm and its spectral convergence.http://dx.doi.org/10.1155/2014/780769 |
| spellingShingle | Peyman Hessari Sang Dong Kim Byeong-Chun Shin Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method Abstract and Applied Analysis |
| title | Numerical Solution for Elliptic Interface Problems Using Spectral
Element Collocation Method |
| title_full | Numerical Solution for Elliptic Interface Problems Using Spectral
Element Collocation Method |
| title_fullStr | Numerical Solution for Elliptic Interface Problems Using Spectral
Element Collocation Method |
| title_full_unstemmed | Numerical Solution for Elliptic Interface Problems Using Spectral
Element Collocation Method |
| title_short | Numerical Solution for Elliptic Interface Problems Using Spectral
Element Collocation Method |
| title_sort | numerical solution for elliptic interface problems using spectral element collocation method |
| url | http://dx.doi.org/10.1155/2014/780769 |
| work_keys_str_mv | AT peymanhessari numericalsolutionforellipticinterfaceproblemsusingspectralelementcollocationmethod AT sangdongkim numericalsolutionforellipticinterfaceproblemsusingspectralelementcollocationmethod AT byeongchunshin numericalsolutionforellipticinterfaceproblemsusingspectralelementcollocationmethod |