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An immersive real-time visualization system of 3-D magnetic field for educational purposes is presented. This immersive visualization system is based on augmented reality technology. The proposed system provides observation of a magnetic field distribution and its stereoscopic vision in 3-D space using head mounted display. To improve the visualization capabilities, a new real-time method for drawing magnetic flux lines in 3-D space is developed and presented in this paper. It enables a user to easily observe and grasp a magnetic field generated by multiple sources (e.g., magnets and/or multiple coils) in an augmented 3-D space. Additionally, it permits a user to freely and interactively move the magnetic sources within the visualization space and to observe the magnetic fields interference in real-time. As a result, one can intuitively and easy visualize, observe and grasp the magnetic field even in 3-D space.

Mesh quality strongly affects the solution accuracy in electromagnetic finite-element analysis. Hence, the realization of adequate mesh generation becomes a very important task. Several adaptive meshing methods for automatic adjustments of the mesh density in accordance with the shape and complexity of the analyzed problem have been proposed. However, the most of them are not enough robust, some are quite laborious and could not be universally used for adaptive meshing of complex analysis models. In this paper, a new adaptive mesh refinement method based on magnetic field conservation at the border between finite elements is proposed. The proposed error estimation method provides easy mesh refinements, and generates smaller element within regions with large curvature of the magnetic flux lines. The proposed adaptive mesh refinement method based on non-conforming edge finite elements, which could avoid generation of flat or ill-shaped elements, was applied to a simple magnetostatic permanent magnet model. To confirm the validity and accuracy, the obtained results were compared with those obtained by means of the Zienkiewicz-Zhu (ZZ) error estimator. The results show that the computational error using the proposed method was reduced down to 1% compared with that of the ZZ method, which yields error of 8.6%, for the same model.

Mesh quality strongly affects the solution accuracy in electromagnetic finite-element analysis. Hence, the realization of adequate mesh generation becomes a very important task. Several adaptive meshing methods for automatic adjustments of the mesh density in accordance with the shape and complexity of the analyzed problem have been proposed. However, the most of them are not enough robust, some are quite laborious and could not be universally used for adaptive meshing of complex analysis models. In this paper, a new adaptive mesh refinement method based on magnetic field conservation at the border between finite elements is proposed. The proposed error estimation method provides easy mesh refinements, and generates smaller element within regions with large curvature of the magnetic flux lines. The proposed adaptive mesh refinement method based on non-conforming edge finite elements, which could avoid generation of flat or ill-shaped elements, was applied to a simple magnetostatic permanent magnet model. To confirm the validity and accuracy, the obtained results were compared with those obtained by means of the Zienkiewicz-Zhu (ZZ) error estimator. The results show that the computational error using the proposed method was reduced down to 1% compared with that of the ZZ method, which yields error of 8.6%, for the same model.

In this paper, we propose an economically efficient optimal design method of different-size interior permanent magnet (IPM) motors to maximize their efficiency. Since the homothetic shape is used, the optimization design is, at once, performed. The use of the commonalized design can reduce the productive costs. Game theory is employed as an optimization method. The game theory can simultaneously increase the efficiency of all the IPM motors with the common and homothetic shape. So far, there are no previous reports considering both the economical efficiency and the motor performance simultaneously. Therefore, the proposed optimal design method of the commonalized different-size IPM motors using the game theory method achieves a high electrical efficiency in addition to the economical efficiency due to design optimization.

In this paper, we propose an economically efficient optimal design method of different-size interior permanent magnet (IPM) motors to maximize their efficiency. Since the homothetic shape is used, the optimization design is, at once, performed. The use of the commonalized design can reduce the productive costs. Game theory is employed as an optimization method. The game theory can simultaneously increase the efficiency of all the IPM motors with the common and homothetic shape. So far, there are no previous reports considering both the economical efficiency and the motor performance simultaneously. Therefore, the proposed optimal design method of the commonalized different-size IPM motors using the game theory method achieves a high electrical efficiency in addition to the economical efficiency due to design optimization.

The optimization method is often used for designing the configuration of electromagnetic apparatuses in order to enhance performance. Many optimal design methods have been developed and popularized. However, most of the optimal design methods can only take into account a single objective function. Therefore, when the problem has a few purposes, a weighted summed objective function is usually employed. Recently, we have proposed a new method, taking into account the multiple purposes simultaneously and individually. The proposed method can select one rational solution from among the Pareto optima, based on the game theory. However, the meaning of the selected rational solution is unclear. Therefore, the meaning is investigated by calculating the weight parameters of the weighted summed objective function so that the optimal solution of the weighted summed objective function is identical to the rational solution of the game theory. We can intuit the meaning of the rational solution by comparing the weight parameters.

The optimization method is often used for designing the configuration of electromagnetic apparatuses in order to enhance performance. Many optimal design methods have been developed and popularized. However, most of the optimal design methods can only take into account a single objective function. Therefore, when the problem has a few purposes, a weighted summed objective function is usually employed. Recently, we have proposed a new method, taking into account the multiple purposes simultaneously and individually. The proposed method can select one rational solution from among the Pareto optima, based on the game theory. However, the meaning of the selected rational solution is unclear. Therefore, the meaning is investigated by calculating the weight parameters of the weighted summed objective function so that the optimal solution of the weighted summed objective function is identical to the rational solution of the game theory. We can intuit the meaning of the rational solution by comparing the weight parameters.

In this paper, we propose a real-time visualization system utilizing Augmented Reality Technology for electromagnetics education. It gives an image of magnetic field generated by a bar magnet with a piece of iron in real-time, however the bar magnet and the piece of iron are represented by mock ones. In the newly proposed visualization system, these mocks are captured by a web camera, and mesh needed in the calculation of magnetic field is deformed. Subsequently, a finite element analysis is carried out in very short time and then the magnetic field is immediately visualized. Thereby, it is, in real-time, observable that magnetic flux lines generated by the bar magnet are attracted to a piece of iron. Moreover, when a user moves the mocks, the magnetic flux lines are immediately depicted according to the position of the mocks.