A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems

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dc.contributor.authorYu, Haofengen
dc.contributor.committeechairIliescu, Traianen
dc.contributor.committeememberBurns, John A.en
dc.contributor.committeememberDe Vita, Raffaellaen
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:16:46Zen
dc.date.adate2011-10-07en
dc.date.available2014-03-14T20:16:46Zen
dc.date.issued2011-09-19en
dc.date.rdate2011-10-07en
dc.date.sdate2011-09-25en
dc.description.abstractThis 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-09252011-085711en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-09252011-085711/en
dc.identifier.urihttp://hdl.handle.net/10919/29095en
dc.publisherVirginia Techen
dc.relation.haspartYu_H_D_2011.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectEricksen's Baren
dc.subjectSemi-linear Equationsen
dc.subjectGlobal Optimizationen
dc.subjectCanonical Duality Theoryen
dc.subjectCanonical Dual Finite Element Methoden
dc.subjectLandau-Ginzburg Problemen
dc.subjectDualityen
dc.subjectNon-convex Variational Problemsen
dc.titleA Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problemsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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