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dc.contributor.authorShenoy, Ajit R.en_US
dc.date.accessioned2014-03-14T20:21:54Z
dc.date.available2014-03-14T20:21:54Z
dc.date.issued1997-04-11en_US
dc.identifier.otheretd-402101939761081en_US
dc.identifier.urihttp://hdl.handle.net/10919/30505
dc.description.abstractThe research presented in this dissertation investigates the use of all-at-once methods applied to aerodynamic design. All-at-once schemes are usually based on the assumption of sufficient continuity in the constraints and objectives, and this assumption can be troublesome in the presence of shock discontinuities. Special treatment has to be considered for such problems and we study several approaches. Our all-at-once methods are based on the Sequential Quadratic Programming method, and are designed to exploit the structure inherent in a given problem. The first method is a Reduced Hessian formulation which projects the optimization problem to a lower dimension design space. The second method exploits the sparse structure in a given problem which can yield significant savings in terms of computational effort as well as storage requirements. An underlying theme in all our applications is that careful analysis of the given problem can often lead to an efficient implementation of these all-at-once methods. Chapter 2 describes a nozzle design problem involving one-dimensional transonic flow. An initial formulation as an optimal control problem allows us to solve the problem as as two-point boundary problem which provides useful insight into the nature of the problem. Using the Reduced Hessian formulation for this problem, we find that a conventional CFD method based on shock capturing produces poor performance. The numerical difficulties caused by the presence of the shock can be alleviated by reformulating the constraints so that the shock can be treated explicitly. This amounts to using a shock fitting technique. In Chapter 3, we study variants of a simplified temperature control problem. The control problem is solved using a sparse SQP scheme. We show that for problems where the underlying infinite-dimensional problem is well-posed, the optimizer performs well, whereas it fails to produce good results for problems where the underlying infinite-dimensional problem is ill-posed. A transonic airfoil design problem is studied in Chapter 4, using the Reduced SQP formulation. We propose a scheme for performing the optimization subtasks that is based on an Euler Implicit time integration scheme. The motivation is to preserve the solution-finding structure used in the analysis algorithm. Preliminary results obtained using this method are promising. Numerical results have been presented for all the problems described.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartetd.pdfen_US
dc.relation.haspartajit.pdfen_US
dc.rightsI hereby grant to Virginia Tech or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University Libraries in all forms of media, now or hereafter known. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.en_US
dc.subjectSequential Quadratic Programmingen_US
dc.subjectReduced Hessianen_US
dc.subjectTrust Regionen_US
dc.subjectSparse Optimizationen_US
dc.subjectAirfoil Designen_US
dc.titleOptimization Techniques Exploiting Problem Structure: Applications to Aerodynamic Designen_US
dc.typeDissertationen_US
dc.contributor.departmentAerospace and Ocean Engineeringen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineAerospace and Ocean Engineeringen_US
dc.contributor.committeechairCliff, Eugene M.en_US
dc.contributor.committeememberHerdman, Terry L.en_US
dc.contributor.committeememberKapania, Rakesh K.en_US
dc.contributor.committeememberLutze, Frederick H. Jr.en_US
dc.contributor.committeememberGrossman, Bernard M.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-402101939761081/en_US
dc.date.sdate1998-07-18en_US
dc.date.rdate1997-04-11
dc.date.adate1997-04-11en_US


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