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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. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present a new numerical technique, called adaptive level set method, for use with the finite element method. Design/methodology/approach – A conventional level set method using the smeared Heaviside function has been employed for shape and topology optimizations. The smeared Heaviside function yields an indistinct interface boundary, and so can increase computational time and cause numerical errors. The adaptive level set method does not use the smeared Heaviside function. To coincide with the material interface, it processes the zero level as the boundary data of element meshing. Findings – Usefulness and accuracy of shape optimization using the adaptive level set method are shown by comparison to the conventional level set method. A shape optimization procedure using the adaptive level set method is introduced. Numerical examples are employed to explain how the adaptive level set method is applied. Originality/value – The adaptive level set method is proposed to relieve the interface problem of the conventional level set method. Shape variation in the optimization is calculated from the continuum sensitivity analysis. [ABSTRACT FROM AUTHOR]