Title page for etd-0620108-143445


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URN etd-0620108-143445
Author Wei-ling Lin
Author's Email Address No Public.
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Department Applied Mathematics
Year 2007
Semester 2
Degree Master
Type of Document
Language English
Title The Trefftz Method using Fundamental Solutions and Particular Solutions for Exterior and Annular Problems of Laplace's Equation
Date of Defense 2008-05-22
Page Count 59
Keyword
  • error analysis
  • annular problems
  • Method of fundamental solutions
  • fundamental solutions
  • exterior problems
  • particular solutions
  • Method of particular solutions
  • Abstract Most of reports deal with bounded simply-connected domains; only a few involve in exterior and annular problems (Chen et al. [3], Katsuroda[10] and Ushijima and Chibu [30]). For exterior problems of Laplace's equations, there exist two kinds of infinity conditions, (1) |u|≤C and (2) u=O( ln r), which must be complied with by the fundamental solutions chosen. For u=O(ln r), the traditional fundamental solutions can be used. However, for |u|≤C, new fundamental solutions are explored, with a brief error analysis. Numerical experiments are carried out to verify the theoretical analysis made. Numerical experiments are also provided for annular domains, to show that the method of fundamental solutions (MFS) is inferior to the method of particular solutions (MPS), in both accuracy and stability. MFS and MPS are classified into the Trefftz method (TM) using fundamental solutions (FS) and particular solutions (PS), respectively. The remarkable advantage of MFS over MPS is the uniform $ln|overline{PQ_i}|$, to lead to simple algorithms and programming, thus to save a great deal of human power. Hence, we may reach the engineering requirements by much less efforts and a little payment. Besides, the crack singularity in unbounded domain is also studied. A combination of both PS and FS is also employed, called combination of MFS. The numerical results of MPS and combination of MFS are coincident with each other. The study in this thesis may greatly extend the application of MFS from bounded simply-connected domains to other more complicated domains.
    Advisory Committee
  • Zi-Cai Li - chair
  • Der-Liang Young - co-chair
  • Jeng-Tzong Chen - co-chair
  • Chien-Sen Huang - co-chair
  • Tzon-Tzer Lu - advisor
  • Files
  • etd-0620108-143445.pdf
  • indicate in-campus access immediately and off_campus access in a year
    Date of Submission 2008-06-20

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