Asger Limkilde -- Shape Optimization using Isogeometric Analysis
10 April 2019 –
Shape Optimization with Isogeometric Analysis (IGA) has gained popularity in recent years, due to the prospect of seamless integration of such optimization strategies into already existing CAD software. In this talk I will consider the model problem of optimizing a metallic nano-antenna using IGA. The goal is to concentrate electrical energy in a small target region, by optimization of the shape of the metallic antenna.
One of the challenges when using IGA for shape optimization is that the shape of an object only depends on its boundary, but to perform the (Isogeometric) analysis we need a parametrization of the interior of the domain. This is of special importance when performing shape optimization, since we need not only to find a good parametrization once, but to maintain it every time we update the design variables during the shape optimization algorithm. In this work we compute the parametrization by solving a constraint optimization problem, which is linearized at a reference parametrization, to be applicable in the optimization algorithm.
I will present some preliminary results from the optimization, with a special focus on the parametrization strategy used, as well as some ideas for future work on how to use residual estimates and adaptivity to increase the efficiency of the method. The method is implemented in the IGA library G+Smo using the IpOpt extension for the optimization.
Mr. Limkilde (Department of Applied Mathematics and Computer Science, Technical University of Denmark) is a PhD student at DTU, supervised by Jens Grevesen. He is visiting Inria until end of April.