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This paper proposes dot sensitivity analysis of a current region for topology optimization. A continuum shape sensitivity formula is employed to derive a dot sensitivity formula in a simple closed form. The derived dot sensitivity formula provides the information on where the current dots should be created for topology optimization. This is necessary to generate the current dots in a vacant region of the design domain. Because this dot sensitivity analysis can obtain various topologies of material distribution, the possibility of local optimum convergence is reduced. Furthermore, because this dot sensitivity analysis does not require a specific initial design, its numerical implementation is simple. This dot sensitivity method is combined with the level set method to perform topology optimization. To demonstrate the usefulness of the proposed method, it is applied to two optimization problems of magnetic resonance imaging. [ABSTRACT FROM AUTHOR]

In this paper, a dot sensitivity analysis is proposed for the topology optimization of dielectric materials in an electrostatic system. Dot sensitivity formula is analytically derived in closed form using the continuum shape sensitivity formula. The level set method is used for evolving the geometry in the topology optimization. As the dot sensitivity analysis can generate new material in a vacant region, it does not require an initial design for the dielectric material and widens the design space. Two numerical examples are tested to show the usefulness of dot sensitivity analysis. [ABSTRACT FROM AUTHOR]

In this paper, the hole sensitivity analysis is proposed for topology optimization in the electrostatic system. The hole sensitivity formula is derived using the virtual hole concept and the continuum shape sensitivity. Since the derived formula is expressed as a closed form, it is simple and easy to implement and apply to real problems. The hole sensitivity analysis provides information for topology variation. The geometrical expression of the topology variation is obtained using the level set method. Two numerical examples are tested to show the usefulness of the hole sensitivity analysis. [ABSTRACT FROM AUTHOR]