Type of Document	Thesis
Author	Steward, Jeffrey L.
Author's Email Address	jeffsteward@gmail.com
URN	etd-07062009-230217
Title	The Solution Of A Burgers' Equation Inverse Problem With Reduced-Order Modeling Proper Orthogonal Decomposition
Degree	Master of Science
Department	Scientific Computing, Department of
Advisory Committee	Advisor Name Title Ionel Michael Navon Committee Chair Gordon Erlebacher Committee Member Max Gunzburger Committee Member
Keywords	Reduced Order Modeling Proper Orthogonal Decomposition Inverse Problem Partial Differential Equations pde Optimization Optimal Control Fluid Dynamics Finite Difference Finite Element
Date of Defense	2009-05-20
Availability	unrestricted
Abstract This thesis presents and evaluates methods for solving the 1D viscous Burgers’ partial differential equation with finite difference, finite element, and proper orthogonal decomposition (POD) methods in the context of an optimal control inverse problem. Based on downstream observations, the initial conditions that optimize a lack-of-fit cost functional are reconstructed for a variety of different Reynolds numbers. For moderate Reynolds numbers, our POD method proves to be not only fast and accurate, it also demonstrates a regularizing effect on the inverse problem.
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