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NSYSU

1. Wu, Sin-Rong. The Collocation Trefftz Method for Laplace's Equation on Annular Shaped Domains, Circular and Elliptic Boundaries.

Degree: Master, Applied Mathematics, 2011, NSYSU

The collocation Trefftz method (CTM) proposed in [36] is employed to annular shaped domains, and new error analysis is made to yield the optimal convergence rates. This popular method is then applied to the special case: the Dirichlet problems on circular domains with circular holes, and comparisons are made with the null field method (NFM) proposed , and new interior field method (IFM) proposed in [35], to find out that both errors and condition numbers are smaller. Recently, for circular domains with circular holes, the null fields method (NFM) is proposed by Chen and his groups. In NFM, the fundamental solutions (FS) with the source nodes Q outside of the solution domains are used in the Green formulas, and the FS are replaced by their series expansions. The Fourier expansions of the known or the unknown Dirichlet and Neumann boundary conditions on the circular boundaries are chosen, so that the explicit discrete equations can be easily obtained by means of orthogonality of Fourier functions. The NFM has been applied to elliptic equations and eigenvalue problems in circular domains with multiple holes, reported in many papers; here we cite those for Laplace√Ęs equation only (see [18, 19, 20]). For the boundary integral equation (BIE) of the first kind, the trigonometric functions are used in Arnold [4, 5], and error analysis is made for infinite smooth solutions, to derive the exponential convergence rates. In Cheng√Ęs Dissertation [21, 22], for BIE of the first kind, the source nodes are located outside of the solution domain, the linear combination of fundamental solutions are used, and error analysis is made only for circular domains. This fact implies that not only can the CTM be applied to arbitrary domains, but also a better numerical performance is provided. Since the algorithms of the CTM is simple and its programming is easy, the CTM is strongly recommended to replace the NFM for circular domains with circular holes in engineering problems. Advisors/Committee Members: Ming-Gong Lee (chair), Jeng-Tzong Chen (chair), Zi-Cai Li (committee member), Chien-Sen Huang (chair), Tsung-Lin Lee (chair).

Subjects/Keywords: annular shaped domains; circular domains; null field method; Collocation Trefftz method; interior field method; fundamental solutions; error analysis; Dirichelet condition

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Wu, S. (2011). The Collocation Trefftz Method for Laplace's Equation on Annular Shaped Domains, Circular and Elliptic Boundaries. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819111-172202

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Wu, Sin-Rong. “The Collocation Trefftz Method for Laplace's Equation on Annular Shaped Domains, Circular and Elliptic Boundaries.” 2011. Thesis, NSYSU. Accessed August 25, 2019. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819111-172202.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Wu, Sin-Rong. “The Collocation Trefftz Method for Laplace's Equation on Annular Shaped Domains, Circular and Elliptic Boundaries.” 2011. Web. 25 Aug 2019.

Vancouver:

Wu S. The Collocation Trefftz Method for Laplace's Equation on Annular Shaped Domains, Circular and Elliptic Boundaries. [Internet] [Thesis]. NSYSU; 2011. [cited 2019 Aug 25]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819111-172202.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wu S. The Collocation Trefftz Method for Laplace's Equation on Annular Shaped Domains, Circular and Elliptic Boundaries. [Thesis]. NSYSU; 2011. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0819111-172202

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


University of North Texas

2. Finan, Marcel Basil. Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains.

Degree: 1998, University of North Texas

The aim of this work is the study of the existence and multiplicity of sign changing nonradial solutions to elliptic boundary value problems on annular domains. Advisors/Committee Members: Castro, Alfonso, 1950-, Warchall, Henry Alexander, Iaia, Joseph A..

Subjects/Keywords: annular domains; mathematics; elliptic boundaries; Nonlinear functional analysis.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Finan, M. B. (1998). Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc278251/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Finan, Marcel Basil. “Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains.” 1998. Thesis, University of North Texas. Accessed August 25, 2019. https://digital.library.unt.edu/ark:/67531/metadc278251/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Finan, Marcel Basil. “Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains.” 1998. Web. 25 Aug 2019.

Vancouver:

Finan MB. Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains. [Internet] [Thesis]. University of North Texas; 1998. [cited 2019 Aug 25]. Available from: https://digital.library.unt.edu/ark:/67531/metadc278251/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Finan MB. Existence of Many Sign Changing Non Radial Solutions for Semilinear Elliptic Problems on Annular Domains. [Thesis]. University of North Texas; 1998. Available from: https://digital.library.unt.edu/ark:/67531/metadc278251/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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