Title page for etd-0722104-210155


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URN etd-0722104-210155
Author Tung-Yen Wu
Author's Email Address No Public.
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Department Applied Mathematics
Year 2003
Semester 2
Degree Master
Type of Document
Language English
Title Fast Symbolic Boundary Approximation Method
Date of Defense 2004-05-28
Page Count 68
Keyword
  • Schiff's model
  • Symbolic boundary approximation method
  • Boundary approximation method
  • Motz problem
  • BAM
  • SBAM
  • Numerical boundary approximation method
  • NBAM
  • preconditioner
  • Abstract Boundary Approximation Method (BAM), or the Collocation Trefftz Method called in the literature, is the most efficient method to solve elliptic boundary value problems with singularities. There are several versions of BAM in practical computation, including the Numerical BAM, Symbolic BAM and their variants. It is known that the Symbolic BAM is much slower than Numerical counterpart. In this thesis, we improve the Symbolic BAM to become the fastest method among all versions of BAM. We prove several important lemmas to reduce the computing time, and a recursive procedure is found to expedite the evaluation of major integrals. Another drawback of the Symbolic BAM is its large condition number. We find a good and easy preconditioner to significantly reduce the condition number. The numerical experiments and comparison are also provided for the Motz problem, a prototype of Laplace boundary value problem with singularity, and the Schiff's Model, a prototype of biharmonic boundary value problem with singularity.
    Advisory Committee
  • Zi-Cai Li - chair
  • Shih-Yu Shen - co-chair
  • T. L. HORNG - co-chair
  • Chien-Sen Huang - co-chair
  • Tzon-Tzer Lu - advisor
  • Files
  • etd-0722104-210155.pdf
  • indicate access worldwide
    Date of Submission 2004-07-22

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