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dc.contributor.authorLetona Bolivar, Cristina Felicitasen_US
dc.date.accessioned2016-10-20T08:00:41Z
dc.date.available2016-10-20T08:00:41Z
dc.date.issued2016-10-19en_US
dc.identifier.othervt_gsexam:9076en_US
dc.identifier.urihttp://hdl.handle.net/10919/73308
dc.description.abstractThe methods for solving domain optimization problems depends on the case of study. There are methods that have been developed for the discretized problem, but not much is done in the infinite dimensional case. We analyze the theoretical aspects of the infinite dimensional case for a particular domain optimization problem where a portion of the boundary is parametrized, these results involve the existence of the solution to our problem and the calculation of the derivative of the shape functional. Shape optimization problems have a long history of mathematical study and a wide range of applications. In recent decades there has been an interest in solving these problems with partial differential equation (PDE) constraints. We consider a special class of PDE-constrained shape optimization problems where different boundary condition types (Dirichlet and Neumann) are imposed on the same boundary segment. We also consider the case where the interface between these different boundary condition types may also be parameter dependent. This study also includes special cases where the shape of the region where the PDE is imposed does not change, but the domain of the partial differential operator is parameter dependent, due to the change in boundary condition type. Our treatment centers on the infinite dimensional formulation of the optimization problem. We consider existence of solutions as well as the calculation of derivatives of the associated shape functionals via adjoint solutions. These derivative formulations serve as a starting point for practical numerical approximations.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectDomain Optimizationen_US
dc.subjectShape Derivativesen_US
dc.subjectPDE Constraintsen_US
dc.subjectMixed Boundary Conditions.en_US
dc.titleOn a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Typesen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_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.disciplineMathematicsen_US
dc.contributor.committeechairBorggaard, Jeffrey T.en_US
dc.contributor.committeememberZietsman, Lizetteen_US
dc.contributor.committeememberIliescu, Traianen_US
dc.contributor.committeememberLin, Taoen_US


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