Abstract
dc:description.abstractWhen applying optimization techniques to complex physical systems, using very large numerical models for the solution of a system of parameter dependent partial differential equations (PDEs) is usually intractable. Surrogate models are used to provide an approximation to the high fidelity models while being computationally cheaper to evaluate. Typically, for time dependent nonlinear problems a reduced order model is built using a basis obtained through proper orthogonal decomposition (POD) and Galerkin projection of the system dynamics. In this thesis we present theoretical and numerical results for parameter dependent model reduction techniques. The methods are motivated by the need for surrogate models specifically designed for nonlinear parameter dependent systems. We focus on methods in which the projection basis also depends on the parameter through extrapolation and interpolation. Numerical examples involving 1D Burgers' equation, 2D Navier-Stokes equations and 2D Boussinesq equations are presented. For each model problem comparison to traditional POD reduced order models will also be presented.
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
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Jarvis, Christopher Hunter
- Chair dc:contributor.committeechair
-
- Burns, John A.
- Committee members dc:contributor.committeemember
-
- Zietsman, Lizette
- Borggaard, Jeffrey T.
- Cliff, Eugene M.
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:2360
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/47357