Two-phase optimization for the design of multiple coils

A novel two-phase design method based on the topology optimization formulation is proposed in order to configure not only the optimal coil shape, but also the optimal number of coils without using any initial layout. The specific design objective is to find an optimal coil configuration maximizing the Lorentz force in the desired direction and minimizing the force in other directions under a given magnetic field. The problem complexity comes from the fact that the location and the number of coils should be determined during the optimization process. To overcome this difficulty, a two-phase topology optimization method is developed where the location and number of coils are determined in the first phase, and the detailed coil shape in the second phase.