<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> / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/12974 |
| Date | January 2013 |
| Creators | Niakhai, Katsiaryna |
| Contributors | Protas, Bartosz, Mathematics and Statistics |
| Source Sets | McMaster University |
| Detected Language | English |
| Type | thesis |
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