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

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dc.contributor.authorStanley, Lisa Gayleen
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberKing, Belinda B.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:14:43Zen
dc.date.adate1999-08-26en
dc.date.available2014-03-14T20:14:43Zen
dc.date.issued1999-07-08en
dc.date.rdate2000-08-26en
dc.date.sdate1999-08-03en
dc.description.abstractSensitivity 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-080399-111602en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-080399-111602/en
dc.identifier.urihttp://hdl.handle.net/10919/28510en
dc.publisherVirginia Techen
dc.relation.haspartetd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectElliptic Differential Operatorsen
dc.subjectFinite Element Methodsen
dc.subjectSensitivity Equationsen
dc.subjectSobolev Spacesen
dc.titleComputational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problemsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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