Thesis Title: A Parallel Branch-and-Bound Algorithm for Thin-Film Optical Systems, with Application to Realizing a Broadband Omnidirectional Antireflection Coating for Silicon Solar Cells, and a Mathematical Framework for Bounding Semilinear Parabolic PDEs
Speaker: Paul Azunre

Tuesday, May 20, 2014 / 10:30am / Haus Room (36–428)

Thesis advisors:
Prof. Marc Baldo and Prof. George Verghese

For the class of multilayer thin-film optical systems, this thesis develops a parallel branch-and-bound computational system on Amazon’s EC2 platform, using the Taylor model mathematical framework of Berz and Makino to construct the required bounds on the merit function on subsets of the search space. The resulting deterministic global optimization algorithm for this important class of problems produces solutions with guaranteed optimality bounds. To the best of our knowledge, this is the first algorithm to achieve this.

Applying the algorithm to the particular problem of reducing reflection using multilayer systems, it is shown that a gradient index constraint on the solution can be exploited to significantly reduce the search space and thereby make the algorithm more practical. The optimization system is used to design a broadband omnidirectional antireflection coating for silicon solar cells. The design is experimentally validated using RF sputtering, and shows performance that is competitive with existing solutions that are based on impractical and more elaborate nano-deposition techniques.

Finally, motivated by design problems for bulk heterojunction organic solar cells, the thesis also develops a mathematical framework for effectively bounding solutions to parametric weakly-coupled semilinear parabolic (reaction-diffusion) partial differential equation systems. A serial branch-and-bound algorithm implementation illustrates the applicability of the bounds on simple examples.

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