Convexity-Oriented Mapping Method for the Topology Optimization of Electromagnetic Devices Composed of Iron and Coils

In order to perform parameter or shape optimizations, an initial topology is required which affects the final solution. This constraint is released in topology optimization methods. They are based on a splitting of the design space into cells, in which they attempt to distribute optimally predefined materials. In topology optimization, a lack of convexity has already been observed by several authors. Final results are often affected by the initial material distribution. This paper aims at improving the convexity in static electromagnetic problems where both ferromagnetic materials and coils are distributed in the design domain. The paper focuses on the mapping function used to derive the permeability of a cell from its composition. In addition to convexity issues, sensitivity concerns arise when the relative permeability of iron is large. Several methods based on a sensitivity-oriented mapping are suggested in the literature, such as the solid isotropic material with penalization (SIMP) method or the homogenization theory method (HDM). This paper shows that a geometric mapping is effective in combination with the convexity-oriented mapping to tackle both problems. This paper suggests computing the cell permeabilities by two successive mapping functions and illustrates the effectiveness of this method on the design of a switched reluctant actuator.