Topology Optimization of Eddy Current Systems by Level-Set and Primal-Dual Methods

The paper deals with a topology optimization of electromagnetic media described by the eddy current equations. This problem finds many applications in the design of modern high power electronic devices. The construction of a subtle layout of the devices requires to avoid significant losses in the power transmission due to parasitic inductivities. We consider a minimization problem with an objective function related to the energy dissipation given by the Joule-Lenz law. Our purpose is to find the optimal material distribution in the conductive medium with a prescribed fluxes through the ports. The structural boundary of the design domain changes during the optimization process. A level-set method is proposed for an implicit representation of this boundary. The description includes the evolution of the scalar level-set function and thus, the optimal propagation of the design boundary by solving the Hamilton-Jacobi equation. Another approach to find the optimal material design is to consider the electromagnetic potentials as state variables and the conductivity as a design variable. This formulation gives rise to a nonlinear minimization problem which we solve by the primal-dual approach. Some numerical experiments by using the second approach applied to a two-dimensional isotropic electromagnetic model are presented.