Higher finite element derivatives for the quick synthesis of electromagnetic devices

A fast, robust scheme for synthesizing electromagnetic devices from the higher derivatives of object functions is presented. A method of computing derivatives of any given order from a finite element solution employing trial functions of any order is presented. These derivatives are used in expanding the object function in device optimization as a Taylor series. The series truncates after the eighth term or before because of subsequent Taylor terms being vanishingly small in the vicinity of the minimum. This series is used to predict the optimum of the device by solving the single polynomial equation by Newton´s scheme. The procedure is shown to result in much faster convergence towards the optimum