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The purpose of this paper is to present a new numerical technique, called adaptive level set method, for use with the finite element method.

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.

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.

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.

The purpose of this paper is to propose a level set method (LSM) for topology optimization of an electromagnetic system.

The classical shape optimization method has a meshing problem for shape changes and so the level set method is employed to overcome this difficulty, due to its efficient representation of evolving geometry. The velocity field is required to solve the level set equation of the Hamilton‐Jacobi equation. It is obtained using the continuum shape sensitivity in a closed form by the material derivative concept. The optimization problem is modeled as a coupled system of Poisson's equation and the level set equation. They are solved using a standard FEM in the time domain.

Numerical examples are shown to test an optimization problem in the electric and magnetic field system. The design goal is to obtain the maximum torque for an operating electrostatic actuator and synchronous reluctance motor (SynRM), respectively. The results of the optimal shape and topology for electromagnetic system are presented.

This paper presents a theoretical algorithm and numerical techniques for topology optimization of an electromagnetic system to generate the maximum torque using the level set method and design sensitivity analysis.

Product variant design can only be achieved after all its constituent parts have been implemented by variant design. It is necessary to plan the sequence of part variant design reasonably. The product variant design process involves a large amount of information transfer events at the dimensional level. A reasonable product variant design process needs to make full use of the information transfer characters of parts to decrease the uncertainty of product variant design process. The existing methods of researching the product variant design process mainly focus on resource constraint and activity logic. They are deficient, however, in information transfer resolution and uncertainty management. This paper aims to address these issues.

This paper identifies the number of dimension transfer paths and the position of dimension locating within a transfer path as being the key factors affecting the information transfer role of dimension. Information transfer utility is proposed to measure the information transfer capability of dimensions and parts. Based on these, a two-stage approach of generating the sequence of part variant design based on information transfer utility is proposed.

The uncertainty of dimension constraint network is minimal during the product variant design process when parts are implemented by variant design under the sequence generated through a two-stage method based on the information transfer utilities of parts, as does the times of parameter transferring and iteration in dimension constraint network.

Part variant design under the sequence of descending information transferring utilities can decrease the difficulty of implementing product variant design validly and also increase the efficiency. This suggests an innovative method to planning the product variant design process reasonably from the perspective of informatics.