{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/28510"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/28510","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Stanley, Lisa Gayle"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Burns, John A."],"committee_members":["King, Belinda B.","Herdman, Terry L.","Cliff, Eugene M.","Borggaard, Jeffrey T."],"year":1999,"date_issued":"1999-07-08","date_published":"1999-07-08","updated_at":"2026-07-22T22:19:51Z","subjects":["Elliptic Differential Operators","Finite Element Methods","Sensitivity Equations","Sobolev Spaces"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-080399-111602"],"render_values":[{"text":"etd-080399-111602","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/28510","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Burns, John A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["King, Belinda B.","Herdman, Terry L.","Cliff, Eugene M.","Borggaard, Jeffrey T."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Stanley, Lisa Gayle"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:14:43Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:14:43Z","2000-08-26"]},{"key":"dc:date.issued","label":"Date","values":["1999-07-08"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Elliptic Differential Operators","Finite Element Methods","Sensitivity Equations","Sobolev Spaces"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-080399-111602"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/28510"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Burns, John A."],"dc:contributor.committeemember":["King, Belinda B.","Herdman, Terry L.","Cliff, Eugene M.","Borggaard, Jeffrey T."],"dc:contributor.department":["Mathematics"],"dc:creator":["Stanley, Lisa Gayle"],"dc:date.accessioned":["2014-03-14T20:14:43Z"],"dc:date.available":["2014-03-14T20:14:43Z","2000-08-26"],"dc:date.issued":["1999-07-08"],"dc:description.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."],"dc:description.degree":["Ph. D."],"dc:identifier.other":["etd-080399-111602"],"dc:identifier.uri":["http://hdl.handle.net/10919/28510"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Elliptic Differential Operators","Finite Element Methods","Sensitivity Equations","Sobolev Spaces"],"dc:title":["Computational Methods for Sensitivity Analysis with Applications to Elliptic Boundary Value Problems"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:51Z"}