Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks
For solving Laplace’s equation in circular domains with circular holes, the null field method (NFM) was developed by Chen and his research group (see Chen and Shen (2009)). In Li et al. (2012) the explicit algebraic equations of the NFM were provided, where some stability analysis was made. For the...
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| Format: | Article |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/927873 |
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| author | Hung-Tsai Huang Ming-Gong Lee Zi-Cai Li John Y. Chiang |
| author_facet | Hung-Tsai Huang Ming-Gong Lee Zi-Cai Li John Y. Chiang |
| author_sort | Hung-Tsai Huang |
| collection | DOAJ |
| description | For solving Laplace’s equation in circular domains with circular holes, the null field method (NFM) was developed by Chen and his research group (see Chen and Shen (2009)). In Li et al. (2012) the explicit algebraic equations of the NFM were provided, where some stability analysis was made. For the NFM, the conservative schemes were proposed in Lee et al. (2013), and the algorithm singularity was fully investigated in Lee et al., submitted to Engineering Analysis with Boundary Elements, (2013). To target the same problems, a new interior field method (IFM) is also proposed. Besides the NFM and the IFM, the collocation Trefftz method (CTM) and the boundary integral equation method (BIE) are two effective boundary methods. This paper is devoted to a further study on NFM and IFM for three goals. The first goal is to explore their intrinsic relations. Since there exists no error analysis for the NFM, the second goal is to drive error bounds of the numerical solutions. The third goal is to apply those methods to Laplace’s equation in the domains with extremely small holes, which are called actually punctured disks. By NFM, IFM, BIE, and CTM, numerical experiments are carried out, and comparisons are provided. This paper provides an in-depth overview of four methods, the error analysis of the NFM, and the intriguing computation, which are essential for the boundary methods. |
| format | Article |
| id | doaj-art-d2b2309ab7604585a344652f21e83d51 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d2b2309ab7604585a344652f21e83d512025-02-03T01:02:46ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/927873927873Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured DisksHung-Tsai Huang0Ming-Gong Lee1Zi-Cai Li2John Y. Chiang3Department of Applied Mathematics, I-Shou University, Kaohsiung 84001, TaiwanDepartment of Leisure and Recreation Management, Ph.D. Program in Engineering Science, Chung Hua University, Hsinchu 30012, TaiwanDepartment of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, TaiwanDepartment of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung 80424, TaiwanFor solving Laplace’s equation in circular domains with circular holes, the null field method (NFM) was developed by Chen and his research group (see Chen and Shen (2009)). In Li et al. (2012) the explicit algebraic equations of the NFM were provided, where some stability analysis was made. For the NFM, the conservative schemes were proposed in Lee et al. (2013), and the algorithm singularity was fully investigated in Lee et al., submitted to Engineering Analysis with Boundary Elements, (2013). To target the same problems, a new interior field method (IFM) is also proposed. Besides the NFM and the IFM, the collocation Trefftz method (CTM) and the boundary integral equation method (BIE) are two effective boundary methods. This paper is devoted to a further study on NFM and IFM for three goals. The first goal is to explore their intrinsic relations. Since there exists no error analysis for the NFM, the second goal is to drive error bounds of the numerical solutions. The third goal is to apply those methods to Laplace’s equation in the domains with extremely small holes, which are called actually punctured disks. By NFM, IFM, BIE, and CTM, numerical experiments are carried out, and comparisons are provided. This paper provides an in-depth overview of four methods, the error analysis of the NFM, and the intriguing computation, which are essential for the boundary methods.http://dx.doi.org/10.1155/2013/927873 |
| spellingShingle | Hung-Tsai Huang Ming-Gong Lee Zi-Cai Li John Y. Chiang Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks Abstract and Applied Analysis |
| title | Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks |
| title_full | Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks |
| title_fullStr | Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks |
| title_full_unstemmed | Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks |
| title_short | Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks |
| title_sort | null field and interior field methods for laplace s equation in actually punctured disks |
| url | http://dx.doi.org/10.1155/2013/927873 |
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