Title page for ETD etd-080399-111602


Type of Document Dissertation
Author Stanley, Lisa Gayle
Author's Email Address stanley@icam.vt.edu
URN etd-080399-111602
Title Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Borggaard, Jeffrey T. Committee Member
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
King, Belinda B. Committee Member
Keywords
  • Elliptic Differential Operators
  • Finite Element Methods
  • Sensitivity Equations
  • Sobolev Spaces
Date of Defense 1999-07-08
Availability unrestricted
Abstract
Sensitivity analysis is a useful mathematical tool for many designers,

engineers and mathematicians. This work presents a study of

sensitivity equation methods for elliptic boundary value problems

posed on parameter dependent domains.

The current focus of our efforts is the construction of a

rigorous mathematical framework for sensitivity analysis and the

subsequent development of efficient, accurate algorithms for

sensitivity computation.

In order to construct the framework, we use the classical

theory of partial differential equations along with the method of

mappings and the Implicit Function Theorem. Examples are given which

illustrate the use of the framework, and some of the shortcomings of

the theory are also identified. An overview of some computational

methods which make use of the method of mappings is also included.

Numerical results for a specific example show that convergence (energy norm)

of the sensitivity

approximations can be influenced by the specific structure of the

computational scheme.

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