HIGHER FINITE-ELEMENT DERIVATIVES FOR THE QUICK SYNTHESIS OF ELECTROMAGNETIC DEVICES

The synthesis of electromagnetic devices from performance criteria is an attractive and increasingly robust art. Speeding up the solution time would increase its utility. This paper presents a method of computing derivatives of any given order from a finite element solution employing trial functions of any order. These derivatives are then used in expanding the object function in device optimization as a Taylor's series. The series truncates after the eight term or before because of subsequent Taylor terms being vanishingly small in the vicinity of the minimum. This series is then 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.