Title page for etd-0603106-210320


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URN etd-0603106-210320
Author Heng-Shuing Tsai
Author's Email Address h04s04@yahoo.com.tw
Statistics This thesis had been viewed 5066 times. Download 2083 times.
Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title The Trefftz Method for Solving Eigenvalue Problems
Date of Defense 2006-05-25
Page Count 48
Keyword
  • nonlinear solutions
  • the cracked beam
  • interfaces
  • Helmholtz equation
  • eigenvalue problems
  • the Trefftz method
  • Abstract For Laplace's eigenvalue problems, this thesis presents new algorithms of the Trefftz method (i.e. the boundary approximation method), which solve the Helmholtz equation and then use a iteration process to yield approximate eigenvalues and eigenfunctions. The new iteration method has superlinear convergence rates and gives a better performance in numerical testing, compared with the other popular methods of rootfinding. Moreover, piecewise particular solutions are used for a basic model of eigenvalue problems on the unit square with the Dirichlet condition. Numerical experiments are also conducted for the eigenvalue problems with singularities. Our new algorithms using piecewise particular solutions are well suited to seek very accurate solutions of eigenvalue problems, in particular those with multiple singularities, interfaces and those on unbounded domains. Using piecewise particular solutions has also the advantage to solve complicated problems because uniform particular solutions may not always exist for the entire solution domain.
    Advisory Committee
  • Cheng-Sheng Chien - chair
  • Tzon-Tzer Lu - co-chair
  • Hung-Tsai Huang - co-chair
  • Chieh-Sen Huang - co-chair
  • Zi-Cai Li - advisor
  • Files
  • etd-0603106-210320.pdf
  • indicate access worldwide
    Date of Submission 2006-06-03

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