Title page for etd-0717106-100501


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URN etd-0717106-100501
Author Jau-Ren Wang
Author's Email Address No Public.
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Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title Convergence Analysis of BAM on Laplace BVP with Singularities
Date of Defense 2006-06-07
Page Count 67
Keyword
  • Laplace equation
  • convergence
  • singularity
  • BAM
  • Abstract The particular solutions of the Laplace equations and their singularities are fundamental
    to numerical partial di erential equations in both algorithms and error analysis. We
    first review the explicit solutions of Laplace’s equations on sectors with the Dirichlet
    and the Neumann boundary conditions. These harmonic functions clearly expose the
    solution’s regularity/singularity at the vertex. So we can analyze the singularity of
    the Laplace’s solutions on polygons at di erent domain corners and for various boundary
    conditions. By using this knowledge we can designed many new testing models
    with di erent kind of singularities, like discontinuous and mild singularities, beside the
    popular singularity models, Motz’s and the cracked beam problems,
    We use the boundary approximation method, i.e. the collocation Tre tz method
    in engineering literatures, to solve the above testing models of Laplace boundary value
    problems on polygons. Suppose the uniform particular solutions are chosen in the entire
    domain. When there is no singularity on all corners, this method has the exponential
    convergence. However, its rate of convergence will deteriorate to polynomial if there
    exist some corner singularities. From experimental data, we even have three type of
    convergence, i.e. exponential, polynomial or their mixed types. We will study these
    convergent behaviors and their causes. Finally, we will uncover the relation between
    the order of convergence and the intensity of corner singularities.
    Advisory Committee
  • Zi-Cai Li - chair
  • Leevan Ling - co-chair
  • none - co-chair
  • Chien-Sen Huang - co-chair
  • Tzon-Tzer Lu - advisor
  • Files
  • etd-0717106-100501.pdf
  • indicate accessible in a year
    Date of Submission 2006-07-17

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