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Title On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types
URL
Publication Date
Date Accessioned
Degree PhD
Discipline/Department Mathematics
Degree Level doctoral
University/Publisher Virginia Tech
Abstract The 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.
Subjects/Keywords Domain Optimization; Shape Derivatives; PDE Constraints; Mixed Boundary Conditions.
Contributors Borggaard, Jeffrey T. (committeechair); Zietsman, Lizette (committee member); Iliescu, Traian (committee member); Lin, Tao (committee member)
Rights In Copyright
http://rightsstatements.org/vocab/InC/1.0/
Country of Publication us
Record ID handle:10919/73308
Repository vt
Date Retrieved
Date Indexed 2020-10-14
Grantor Virginia Polytechnic Institute and State University
Issued Date 2016-10-19 00:00:00
Note [degree] Ph. D.;

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