Comparison of vector potential and flux density based object functions in magnetic shape optimization

One classical example of electromagnetic device often used to demonstrate and validate electromagnetic optimization methods, is the pole face of a magnetic circuit. In many shape optimization problems, the performance measure is defined in terms of an object function. The object function in turn involves the magnetic flux density B. In a large subclass of these problems, the flux density may be defined in terms of derivatives of the magnetic vector potential A along a line or, by suitable inspection, simply by the vector potential itself along the line. The two cases are studied in the shape optimization of a pole face. The displacements of the nodes along the pole face are selected as the geometric design parameters. It is shown that where the object function is simply definable in terms of nodal potentials, a very powerful and efficient gradients-based optimization scheme results. Where derivatives of the potential are avoided, it is shown that the object function has a simpler dependence on the geometric parameters of the design because derivatives are strongly influenced by changes in shape. Using a simple nodal potential based object function, smooth geometric contours are obtained without the expense of more elaborate methods of ensuring the smoothness of the optimized geometry.