Optimal Design of Materials, Structures, and Devices

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This project addresses a suite of structural optimization problems unified by their mathematical formulation. The problems treated in this project come from several application areas including the design of gradient coils used in magnetic resonance imaging, catalysis design, the design of damage tolerant bridges, and nonlinear optics. Presently there is no systematic design methodology that addresses these problems. The first goal of this project is to extend the mathematical theory of homogenization so that one can systematically describe minimizing sequences of designs. The second goal is to use the homogenization theory to develop numerical methods for the systematic solution of these design problems.This research project focuses on areas of technological interest that require new mathematical and computational techniques for the simultaneous optimization of material properties and structural form. The problems treated in this project come from several application areas including the design of gradient coils used in magnetic resonance imaging, catalysis design, the design of damage tolerant bridges, and nonlinear optics. These problems, although diverse in nature, can be formulated along similar mathematical lines. The goal of this project is to develop a mathematical and computational tool box for the systematic solution of problems requiring the simultaneous design of material and structure.