Title page for etd-0720109-211230


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URN etd-0720109-211230
Author Hong-da Yen
Author's Email Address No Public.
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Department Applied Mathematics
Year 2008
Semester 2
Degree Master
Type of Document
Language English
Title On the Increasingly Flat RBFs Based Solution Methods for Elliptic PDEs and Interpolations
Date of Defense 2009-06-04
Page Count 70
Keyword
  • multiquadric collocation method
  • meshless method
  • error estimate
  • arbitrary precision computation
  • RBF Limit
  • Spectral Collocation Method using Polynomial
  • Abstract Many types of radial basis functions, such as multiquadrics, contain a free parameter called shape factor, which controls the flatness of RBFs. In the 1-D problems, Fornberg et al. [2] proved that with simple conditions on the increasingly flat radial basis function, the solutions converge to the Lagrange interpolating. In this report, we study and extend it to the 1-D Poisson equation RBFs direct solver, and observed that the interpolants converge to the Spectral Collocation Method using Polynomial. In 2-D, however, Fornberg et al. [2] observed that limit of interpolants fails to exist in cases of highly regular grid layouts. We also test this in the PDEs solver and found the error behavior is different from interpolating problem.
    Advisory Committee
  • Zi-Cai Li - chair
  • Tzon-Tzer Lu - co-chair
  • Lih-jier Young - co-chair
  • Hung-Tsai Huang - co-chair
  • Chien-Sen Huang - advisor
  • Files
  • etd-0720109-211230.pdf
  • indicate access worldwide
    Date of Submission 2009-07-20

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