Title page for ETD etd-09252011-085711


Type of Document Dissertation
Author Yu, Haofeng
URN etd-09252011-085711
Title A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Iliescu, Traian Committee Chair
Borggaard, Jeffrey T. Committee Member
Burns, John A. Committee Member
De Vita, Raffaella Committee Member
Keywords
  • Ericksen’s Bar
  • Semi-linear Equations
  • Global Optimization
  • Canonical Duality Theory
  • Canonical Dual Finite Element Method
  • Landau-Ginzburg Problem.
  • Duality
  • Non-convex Variational Problems
Date of Defense 2011-09-19
Availability unrestricted
Abstract
This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and direct methods for non-convex variational problems. These non-convex variational problems arise in a wide range of scientific and engineering applications, such as phase transitions, post-buckling of large deformed beam models, nonlinear field theory, and superconductivity. The numerical discretization of these non-convex variational problems leads to global minimization problems in a finite dimensional space.

The primary goal of this thesis is to apply the newly developed canonical duality theory to two

non-convex variational problems: a modified version of Ericksen’s bar and a problem of Landau-

Ginzburg type. The canonical duality theory is investigated numerically and compared with classic

methods of numerical nature. Both advantages and shortcomings of the canonical duality theory

are discussed. A major component of this critical numerical investigation is a careful sensitivity

study of the various approaches with respect to changes in parameters, boundary conditions and

initial conditions.

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