Mathematical Sciences: Computations of Optimal Boundary Controls and Designs for Distributed Systems in Optics and Elasticity

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The project focuses on a computational study of problems related to boundary control and designs arising from engineering. These problems deal with optimal designs of boundary impedance for acoustic and optical scatterers, and boundary control of the plate equation in adaptive optics. The method of boundary integral equations and boundary elements will be used, and some recent global optimization techniques will be applied. Proper modelling will also be addressed to reflect the physics of the distributed systems. Substantial efforts will be directed toward calculations on a supercomputer fully utilizing its parallelism and speed. This research is part of control theory and is aimed at improving computational design methods for optimal design of structures and systems.