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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