Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/12974
Title: | SHAPE OPTIMIZATION OF ELLIPTIC PDE PROBLEMS ON COMPLEX DOMAINS |
Authors: | Niakhai, Katsiaryna |
Advisor: | Protas, Bartosz |
Department: | Mathematics and Statistics |
Keywords: | shape calculus;optimization;elliptic PDEs;boundary integral equations;spectral methods;heat transfer;Applied Mathematics;Applied Mathematics |
Publication Date: | 2013 |
Abstract: | <p>This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady state heat conduction described by elliptic partial differential equations (PDEs) and involving a one dimensional cooling element represented by an open contour. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least square sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using the conjugate gradient algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus combined with adjoint analysis. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary integral formulation. A number of computational aspects of the proposed approach is discussed and optimization results obtained in several test problems are presented.</p> |
URI: | http://hdl.handle.net/11375/12974 |
Identifier: | opendissertations/7813 8895 4161049 |
Appears in Collections: | Open Access Dissertations and Theses |
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fulltext.pdf | 823.36 kB | Adobe PDF | View/Open |
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