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"A Rapid and Efficient Design Space Exploration Framework for Isogeometric Analysis"

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The allure of computer-aided engineering is that after a suitable system model is constructed, the design can be optimized via iteration for performance by constraints such as cost, efficiency, structural loading, etc. Unfortunately, this vision has still largely not been realized due to the ever-increasing complexity of engineering systems and the apparent disconnect between design and analysis. Currently, engineering designs are optimized by iterating on models with highly simplified physics and geometry. The resulting designs are then physically prototyped and undergo extensive testing. Consequently, the lack of high-fidelity models in the design iterations commonly results in an over-designed, sub-optimal final product. Isogeometric analysis is a recently developed computational approach that offers the possibility of integrating finite element analysis into conventional computer aided design tools. Moreover, this approach introduces a familial relationship between the set of possible designs on which a partial differential equation is posed. In this talk, I will discuss a problem-independent methodology to exploring solutions to a family of domains for parametric partial differential equations, accomplished through the use of sparse collocation at intelligently-chosen sample points, pseudospectral expansions, and compressed sensing. The primary focus of the method in this presentation is on its application to thin shells, which are curved, load-bearing members such as aircraft skin panels. Results from both structural shell simulations and tokamak reactor designs will be presented.