Parametric Model-Order Reduction for Accelerating the Gradient-Based Optimization of Microwave Structures Using Finite-Elements

Abstract A numerical method for optimizing the frequency response of linear time-invariant microwave structures at the fields level is presented. It is based on the finite-element method in the frequency-domain, a quasi-Newton optimizer, and the reduced-basis method. The reduced-order model is constructed adaptively, in the course of the optimization process, and its validity is restricted to some neighborhood of the trajectory drawn by the optimizer in parameter space. The computational complexity of the method is independent of the number of design variables. The present study is restricted to material parameters which lead to affine parameterization. Numerical results demonstrate that the number of finite-element evaluations, which are computationally expensive, is greatly reduced, even in the pre-asymptotic region of the optimization process. Moreover, it is shown that computing the gradient of the cost function analytically provides significant savings in computer runtime over finite-difference approximations.