Virginia Tech
A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems
Abstract
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.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Yu, Haofeng
- Chair dc:contributor.committeechair
-
- Iliescu, Traian
- Committee members dc:contributor.committeemember
-
- Burns, John A.
- De Vita, Raffaella
- Borggaard, Jeffrey T.
Subjects
dc:subject × 8Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-09252011-085711
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/29095