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High-Order Solution of Elliptic Partial Differential Equations in Domains Containing Conical Singularities


Li, Zhiyi (2009) High-Order Solution of Elliptic Partial Differential Equations in Domains Containing Conical Singularities. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VEEB-AV75.


In this thesis we introduce an algorithm, based on the boundary integral equation method, for the numerical evaluation of singular solutions of the Laplace equation in three dimensional space, with singularities induced by a conical point on an otherwise smooth boundary surface. This is a model version of a fundamental problem in science and engineering: accurate evaluation of solutions of Partial Differential Equations in domains whose boundaries contain geometric singularities. For simplicity we assume a small region near the conical point coincides with a straight cone of given cross section; otherwise the boundary surface is not restricted in any way. Our numerical results demonstrate excellent convergence as discretizations are refined, even at the singular point where the solutions tend to infinity.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Conical point; Integral equation; Partial Differential Equation; Singularity
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bruno, Oscar P.
Thesis Committee:
  • Bruno, Oscar P. (chair)
  • Shepherd, Joseph E.
  • Schroeder, Peter
  • Hou, Thomas Y.
Defense Date:28 July 2008
Record Number:CaltechETD:etd-08042008-005339
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3013
Deposited By: Imported from ETD-db
Deposited On:12 Aug 2008
Last Modified:26 Nov 2019 19:14

Thesis Files

PDF (Zhiyi_Thesis.pdf) - Final Version
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