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Topology optimization is a state-of-the-art technique for the innovative design of electromagnetic devices. The ON/OFF method is a typical approach for this purpose. However, the drawbacks of long iteration time and poor ability to express curved surfaces make the industry not shown their due interest so far in the ON/OFF method. The purpose of this paper is to study a novel ON/OFF method for topology optimization, which can bring feasible optimized shapes that are more friendly for industrial realization in a shorter time.

The proposed improved ON/OFF method uses structured triangular elements for finite element modeling because the triangular elements can more freely express shape features. Every four triangular elements are pieced together to form a square cell, each quadrilateral cell is associated with a binary value indicating the material state of the four triangular elements. The binary metaheuristic algorithms are used to optimize the material distribution. After the material filling for the elements based on the output of the metaheuristic algorithm, a two-step surface smoother will be performed as the postprocess to make the shapes more friendly for manufacturing.

The comparative numerical results on a benchmark topology optimization problem show that the proposed method can bring feasible optimized shapes that are more friendly for industrial realization in a shorter time. In addition, the speed and robustness of convergence, especially in the case of multiobjective topology optimization problem, are significantly improved.

A novel ON/OFF method for topology optimization is proposed. Compared with the traditional ON/OFF method, the proposed method is better in terms of searching efficiency and robustness. Moreover, the proposed method can provide feasible optimized shapes that are more friendly for industrial realization.

There are few reports that evolutional topology optimization methods are applied to the conductor geometry design problems. This paper aims to propose an evolutional topology optimization method is applied to the conductor design problems of an on-chip inductor model.

This paper presents a topology optimization method for conductor shape designs. This method is based on the normalized Gaussian network-based evolutional on/off topology optimization method and the covariance matrix adaptation evolution strategy. As a target device, an on-chip planer inductor is used, and single- and multi-objective optimization problems are defined. These optimization problems are solved by the proposed method.

Through the single- and multi-objective optimizations of the on-chip inductor, it is shown that the conductor shapes of the inductor can be optimized based on the proposed methods.

The proposed topology optimization method is applicable to the conductor design problems in that the connectivity of the shapes is strongly required.

Topology optimization (TO) methods have shown their unique advantage in the innovative design of electric machines. However, when introducing the TO method to the rotor design of interior permanent magnet (PM) synchronous machines (IPMSMs), the layout parameters of the magnet cannot be synchronously optimized with the topology of the air barrier; the full design potential, thus, cannot be unlocked. The purpose of this paper is to develop a novel method in which the layout parameters PMs and the topology of air barriers can be optimized simultaneously for aiding the innovative design of IPMSMs.

This paper presents a simultaneous TO and parameter optimization (PO) method that is applicable to the innovative design of IPMSMs. In this method, the mesh deformation technique is introduced to make it possible to make a connection between the TO and PO, and the multimodal optimization problem can thereby be solved more efficiently because good topological features are inherited during iterative optimization.

The numerical results of two case studies show that the proposed method can find better Pareto fronts than the traditional TO method within comparable time-consuming. As the optimal design result, novel rotor structures with better torque profiles and higher reluctance torque are respectively found.

A method that can simultaneously optimize the topology and parameter variables for the design of IPMSMs is proposed. The numerical results show that the proposed method is useful and practical for the conceptual and innovative design of IPMSMs because it can automatically explore optimal rotor structures from the full design space without relying on the experience and knowledge of the engineer.

In the development of electromagnetic devices, multiobjective topology optimisation is effective to obtain diverse design candidates for production models. However, multiobjective topology optimisation has not widely been performed because it is difficult to obtain resultant shapes for engineering realisation due to large search spaces. The purpose of this paper is to present a new multiobjective topology optimisation method.

This paper presents a new multiobjective topology optimisation method in which the Immune Algorithm is modified for multiobjecrive optimisation and a shape modification process based on spatial filtering is employed.

The present method shows that better Pareto solutions can be found in comparison with the conventional methods.

A new effective multiobjective topology optimisation is presented. This method enables to diverse design candidates for production models.

The paper introduces an evolutionary algorithm based on the artificial immune systems paradigm for topology optimization (TO) in 3D.

The 3D TO algorithm is described, and experimentally validated on an electromagnetic design problem.

The proposed method is capable of finding an optimal configuration for the validation problem used.

More tests are needed in order to fully assert the capabilities of the algorithm. Moreover, further improvements are needed in order to obtain smoother topologies at the end of the optimization procedure.

The paper presents a novel tool for the design of electromagnetic devices, using a TO approach.

So far most of the TO algorithms did not tackle true 3D problems, and the ones capable of 3D optimization do it at high computational costs. The algorithm presented here is capable of true 3D design at a reasonable computational budget.

Three-dimensional (3D) mesh generation for shape optimizations needs long computational time. This makes it difficult to perform 3D shape optimizations. The purpose of this paper is to present a new meshing method with light computational cost for 3D shape optimizations.

This paper presents a new meshing method on the basis of nonconforming voxel finite element method. The 3D mesh generation is performed with light computational cost keeping the computational accuracy.

It is shown that the computational cost for 3D mesh generation can be reduced without deteriorating numerical accuracy in the FE analysis. It is reported the performance of the present method.

The validity of the nonconforming voxel elements is tested to apply it to the optimization of 3D optimizations.

This paper discusses the robustness of the algebraic multigrid (AMG) method as well as geometric multigrid (GMG) method against mesh distortion in edge‐based finite element analysis.

Analyzes a simple magnetostatic problem, in which the model consists of a cubic iron and the surrounding air region. Prepares three meshes which have same number of elements to evaluate the robustness of multigrid against the distortion of mesh.

The AMG method is shown to be more robust against mesh distortion than the GMG method.

Shows that the AMG is more robust than the GMG. This result is of practical interest to the researchers in this field.

Conventional level-set method tends to fall into local optima because optimization is conducted based on gradient method. The purpose of this paper is to develop a novel topology optimization in which simulated annealing (SA) is introduced to overcome the difficulties in level-set method.

Level-set based topology optimization for two-dimensional optimization problem.

It is shown in the numerical examples, where conventional and present methods are applied to shape optimization of ferrite inductor and Interior Permanent Magnetic (IPM)-motor, the present method can find solutions with better performance than those obtained by the conventional method.

SA is introduced to improve the search performances of level-set method.

It is important to investigate large‐scale numerical analyses of electromagnetic fields in design processes of electromagnetic machines. Thus, faster solvers for eddy current analyses are necessary. Parallel computation methods for linear solvers in electromagnetic field analyses have been investigated. These methods have gained importance due to the diffusion of PC clusters and multi‐core CPUs in recent years.

This paper discuses linear solvers for the finite element method in eddy current analyses on parallel computers. The preconditioned conjugate gradient method with overlapping domain decomposition is treated. Some techniques treated to improve the convergence was investigated.

The numerical results show that the overlapping effect results in good convergence in eddy current analyses.

The preconditioned conjugate gradient method with overlapping domain decomposition has been treated. The numerical results show that the overlapping method works more efficiently for eddy current analyses. Moreover, this method enables large‐scale analyses on popular computers such as PC clusters.

The purpose of this paper is to present a new method to obtain robust solutions to electromagnetic optimization problems, solved with evolutional algorithms, which are insensitive to changes in design parameters such as spatial size, positioning and material constant.

Adjoint variable method is employed to evaluate the sensitivity of individuals in evolutional processes.

It is shown in the numerical examples, where the present method is applied to optimization of a superconducting energy storage system and C‐shape magnet, that robust solutions are actually obtained which are insensitive to deviations in spatial sizes.

Unlike usual optimization methods, the present method takes into account deviation in the design parameters due to production errors and long‐term changes. Moreover, the present method is limited to about twice the computational cost of non‐robust optimization methods.