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URN etd-0630109-020518
Author Guan-yu Lin
Author's Email Address m962040022@student.nsysu.edu.tw
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Department Applied Mathematics
Year 2008
Semester 2
Degree Master
Type of Document
Language English
Title Convergence Transition of BAM on Laplace BVP with Singularities
Date of Defense 2009-06-01
Page Count 57
Keyword
  • Boundary approximation method
  • Laplace equation
  • Transition of convergence
  • Order of convergence
  • Trefftz method
  • Singularity
  • Abstract Boundary approximation method, also known as the collocation Trefftz method in
    engineering, is used to solve Laplace boundary value problem on rectanglular domain.
    Suppose the particular solutions are chosen for the whole domain. If there is no singularity
    on other vertices, it should have exponential convergence. Otherwise, it will
    degenerate to polynomial convergence. In the latter case, the order of convergence has
    some relation with the intensity of singularity. So, it is easy to design models with
    desired convergent orders.
    On a sectorial domain, when one side of the boundary conditions is a transcendental
    function, it needs to be approximated by power series. The truncation of this power
    series will generate an artificial singularity when solving Laplace equation on polygon.
    So it will greatly slow down the expected order of convergence. This thesis study how
    the truncation error affects the convergent speed. Moreover, we focus on the transition
    behavior of the convergence from one order to another. In the end, we also apply our
    results to boundary approximation method with enriched basis.
    Advisory Committee
  • Zi-Cai Li - chair
  • none - co-chair
  • Hung-Tsai Huang - co-chair
  • Chien-Sen Huang - co-chair
  • Tzon-Tzer Lu - advisor
  • Files
  • etd-0630109-020518.pdf
  • indicate access worldwide
    Date of Submission 2009-06-30

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