Optimizing Shape Design of Magnetic Pole Contour using a Special Mesh Generator

Abstract

First order optimization methods, while being powerful and rapidly convergent, suffer from the fact that as the descriptive geometric parameters change from iteration to iteration, corresponding to these new geometries, new meshes need to be implemented. Correspondingly the new topologies of the meshes introduce non-physical jumps in the object function. These jumps are seen as physical minima by the optimization algorithm and slow down and even prevent the identification of the true global minimum. Different starting points have been used with some amelioration but there has been no satisfactory solution to this problem. To overcome this problem, a special mesh generator has been introduced earlier. This generator allows us to move a node which is tied directly to a parameter without changing connectivity of nodes in the mesh topology. This procedure yields C1 continuity of the object functions. Thus, gradient optimization methods can be efficiently used for shape optimization problems. In this paper, the scheme is implemented optimizing the shape of magnetic pole contour with important implications for the problem and the accuracy of its solutions.