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Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks
Joint Authors
Lee, Ming-Gong
Li, Zi-Cai
Huang, Hung-Tsai
Chiang, John Y.
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-10
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Huang, Hung-Tsai& Lee, Ming-Gong& Li, Zi-Cai& Chiang, John Y.. 2013. Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-508823
Modern Language Association (MLA)
Huang, Hung-Tsai…[et al.]. Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks. Abstract and Applied Analysis No. 2013 (2013), pp.1-15.
https://search.emarefa.net/detail/BIM-508823
American Medical Association (AMA)
Huang, Hung-Tsai& Lee, Ming-Gong& Li, Zi-Cai& Chiang, John Y.. Null Field and Interior Field Methods for Laplace’s Equation in Actually Punctured Disks. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-15.
https://search.emarefa.net/detail/BIM-508823
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-508823