An Integration of Optimal Topology and Shape Design for Magnetostatics

Topology optimization searches for an optimal distribution of material and void without any restrictions on the structure of the design geometry. Shape optimization tunes the shape of the geometry, while the topology is fixed. In this paper we proceed sequentially with the optimal topology and shape design so that a coarsely optimized topology is the initial guess for the following shape optimization. In between we identify the topology by hand and approximate it by piecewise Bézier shapes by means of the least square method. For the topology optimization we use the steepest descent method, while a quasi–Newton method and multilevel techniques are used for the shape optimization. We apply the machinery to optimal design of a direct electric current electromagnet. The resulting optimal design corresponds to physical experiments.