The sensitivity equation method for optimal design

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dc.contributor.authorBorggaard, Jeffrey T.en
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberGunzburger, Max D.en
dc.contributor.committeememberHannsgen, Kenneth B.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:14:53Zen
dc.date.adate2006-06-07en
dc.date.available2014-03-14T21:14:53Zen
dc.date.issued1994-12-02en
dc.date.rdate2006-06-07en
dc.date.sdate2006-06-07en
dc.description.abstractIn this work, we introduce the Sensitivity Equation Method (SEM) as a method for approximately solving infinite dimensional optimal design problems. The SEM couples a trust-region/quasi-Newton optimization algorithm with gradient information provided by apprOXimately solving the sensitivity equation for (design) sensitivities. The sensitivity equation is (in the problems considered here) a partial differential equation (POE) which describes the influence of a design parameter on the state of the system. It is shown that obtaining design sensitivities from the sensitivity equation has advantages over finite difference and semi-analytical methods in that there is no need to remesh or compute mesh sensitivities (even if the domain is parameter dependent), the sensitivity equation is a linear POE for the sensitivities and can be approximated in an efficient manner using the same approximation scheme used to approximate the states. The applicability of the SEM to shape optimization problems, where the state is described by the Euler equations, is studied in detail. In particular, we prove convergence of the method for a one dimensional test problem. These results are used to speculate on the applicability of the method for more complex problems. Finally. we solve a two dimensional forebody simulator design problem (for use in wind tunnel experiments) using the SEM, which is shown to be a very efficient method for this problem.en
dc.description.degreePh. D.en
dc.format.extentvii, 91 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06072006-124214en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06072006-124214/en
dc.identifier.urihttp://hdl.handle.net/10919/38563en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1994.B673.pdfen
dc.relation.isformatofOCLC# 32749841en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1994.B673en
dc.subject.lcshMathematical optimizationen
dc.subject.lcshOptimal designs (Statistics)en
dc.titleThe sensitivity equation method for optimal designen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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