Abstract—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 a best material distribution into variable domains. In order to perform this, we minimize the quadratic error between the prescribed magnetic field and the one computed by a finite element method. A dedicated software was developed in MatLab using fmincon routine and FEMM software. In order 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 SIMP method was used to converge to discrete solutions. Some numerical experiments with 40 and 800 variables concerning a circuit design, validated our approach. This represents a first study to design a Hall effect thruster
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