Dot sensitivity analysis of ferromagnetic materials for topology optimization in an axi-symmetric magnetostatic system

Purpose The purpose of this paper is to propose dot sensitivity analysis of ferromagnetic materials for topology optimization in an axi-symmetric magnetostatic system. Design/methodology/approach The dot sensitivity formula for the axi-symmetric system is derived as a closed form using the continuum shape sensitivity formula. The dot sensitivity method is combined with the level set method to perform topology optimization. Findings Derived dot sensitivity analysis can generate a ferromagnetic ring torus in a vacant region. Thus, an initial design is not needed for the design material. Two design problems are tested to demonstrate the usefulness of dot sensitivity. Originality/value By simultaneously using the shape sensitivity and dot sensitivity, in axi-symmetric magnetic system, the design space is expanded and it includes the interface and the inside of the vacant region. This property can reduce the possibility of local optimum convergence.