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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