Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems

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.

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

1999

Author dc:creator

• Stanley, Lisa Gayle

Chair dc:contributor.committeechair

• Burns, John A.

Committee members dc:contributor.committeemember

• King, Belinda B.
• Herdman, Terry L.
• Cliff, Eugene M.
• Borggaard, Jeffrey T.

• Elliptic Differential Operators
• Finite Element Methods
• Sensitivity Equations
• Sobolev Spaces

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-080399-111602

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28510