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We propose a simple, but efficient method for design problems. Instead of using directly, a heavy numerical code in an optimization process, we successively define some approximated subproblems because of an appropriate analytical model. These subproblems can then be solved exactly by a deterministic global optimization solver and the procedure is updated until the approximation matches a 3-D FEM computation. The method is applied to an axial magnetic coupling. Comparative results show the effectiveness of this approach, and real design cases are studied because of this method. [ABSTRACT FROM PUBLISHER]

In this paper, we present a method to solve inverse problems of electromagnetic circuit design, which are formulated as a topology optimization problem. Indeed, by imposing the magnetic field inside a region, we search the best material distribution into variable domains. To perform this, we minimize the quadratic error between the prescribed magnetic field and the one computed by a finite element method (FEM). A dedicated software was developed in MATLAB using fmincon routine and FEM Magnetics (FEMM) software; this code is named ATOP^TO for algorithm to optimization propulsion using topology optimization. To perform the first derivative of the objective function, we implemented an adjoint variable method. Indeed, this approach makes it possible to provide the derivative by only two uses of the finite element tool. Nevertheless, the problem is discrete because we take only two possibilities: with or without material. Thus, the solid isotropic material with penalization method was used to penalize intermediate values to have discrete solutions. Some numerical experiments with 40 and 800 variables concerning circuit designs validated our approach. This represents a first study to design a Hall effect thruster. [ABSTRACT FROM AUTHOR]