Dissertation/Thesis Abstract

On Identification of Nonlinear Parameters in PDEs
by Kahler, Raphael, M.S., Rochester Institute of Technology, 2016, 80; 10117725
Abstract (Summary)

Inverse problems have been studied in great detail and optimization methods using objective functionals such as output least-squares (OLS) and modified output least-squares (MOLS) are well understood. However, the existing literature has only dealt with identifying parameters that appear linearly in systems of partial differential equations. We investigate the changes that occur in the identification process if the parameter appears nonlinearly. We extend the OLS and MOLS functionals to this nonlinear case and give first and second derivative formulas. We further show that the typical convexity of the MOLS functional can not be guaranteed when identifying nonlinear parameters. To numerically verify our findings we employ a C++ based computational framework. Discretization is done via the finite element method, and details are given for the new results of the functionals and their derivatives. Since we consider nonlinear parameters, gradient methods such as adjoint stiffness are not applicable to the OLS functional and we instead show computation methods using the adjoint approach.

Indexing (document details)
Advisor: Jadamba, Baasansuren, Khan, Akhtar A.
Commitee: Clark, Patricia, Faber, Joshua
School: Rochester Institute of Technology
Department: Applied Mathematics
School Location: United States -- New York
Source: MAI 55/05M(E), Masters Abstracts International
Subjects: Applied Mathematics
Keywords: Adjoint method, Elastography, Inverse problem, Modified output least-squares, Output least-squares, Parameter identification
Publication Number: 10117725
ISBN: 978-1-339-79098-5
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