Accuracy control in the optimization of microwave devices by finite element methods

Computational optimization methods have long been used to aid the design of microwave devices. Cost functions are commonly defined to be functions of S-parameters that are often unavailable analytically. With the ever-increasing speed of computer processors, it is becoming standard practice for designers to use field-based computer-aided design tools as "black boxes" to calculate as accurately as possible the cost functions for such devices. However, demanding high accuracy from every cost function evaluation (CFE) of the optimization can lead to excessive computational costs. These costs can be reduced by two means: use a black box that calculates the gradient of the cost function very cheaply and vary the accuracy of CFEs throughout the optimization.This thesis presents a system for automatically controlling the accuracy throughout an optimization. A gradient-based, constrained optimizer is combined with a 2-D finite element p-adaptive scheme that calculates the gradient at a low cost. The accuracy of a CFE is controlled through a link from the optimization to adaption. The accuracy link is based on the last computed gradient of the cost function and serves as an error tolerance used to terminate the adaption. A new error estimator is developed to assess accurately the error in the gradient, used for the termination.Three H-plane, rectangular waveguide test cases are used for validation: a waveguide T-junction with inductive post; a miter bend with dielectric column; a two-cavity, iris coupled filter. Numerical tests show that the system is very effective in reducing the computational costs of an optimization without sacrificing the accuracy of the final answer. Compared to an optimization system with no link to the adaption, there is a speed-up in computation by at least an order of magnitude for each problem