Purpose: In this work, the authors deal with topology optimization in electromagnetism using solid isotropic material with penalization (SIMP) method associated with a gradient-based algorithm. The purpose of this study is to propose and investigate the impact of new generalized material interpolation scheme (MIS) used in SIMP approaches. Design/methodology/approach: The variable domains of this kind of electromagnetism design problem are decomposed into small squares which represent a material point (iron here) or void. A least square function where the magnetic field in a target zone has to be as close as possible to a fixed one is minimized. Then the binary optimization problem is relaxed to a continuous one. By using the adjoint variable method, the gradient is provided. By penalizing the objective function using MIS, gradient-based algorithms can then be directly applied to provide efficient solutions close to the binary ones. Findings: In this work, new general MISs are proposed. It is shown on numerous numerical instances that the so-obtained design solutions are more precise to define the zones with or without materials. Research limitations/implications: Only the linearity of the materials is addressed because the associated adjoint method needs this assumption. However, the new penalization approaches are not dependent directly on this assumption. Originality/value: The new MISs are efficiently applied to design of a hall effect thruster (HET) magnetic circuits. Furthermore, these schemes are generic and can then be applied to other topology optimization applications in electromagnetism as well as and in mechanism.

What is new in this work is the generic capabilities of the proposed analytical model of permanent magnet machines associated with a novel deterministic global optimization method. That allows to solve some more general inverse problem of designing. The analytical approach is powerful to take into account various kinds of constraints (electromagnetical, thermal, etc.). The inverse problem associated with the optimal design of actuators could then be formulated as a mixed‐constrained optimization problem. In order to solve these problems, interval Branch and Bound algorithms which have already proved their efficiency, have made it possible to determine some optimized rotating machines.