This paper presents a topology optimization method for multimaterial models based on the normalized Gaussian network (NGnet). In this method, one can determine optimal shapes of machines which are composed of various materials such as iron, magnet and nonmagnetic material. The present method is applied to the optimization of interior permanent magnet motor to determine the distributions of magnetic core and flux barrier as well as magnets. The optimization results show that average torque can be improved using as small amount of magnet as possible. In addition, characteristic of the present method is discussed in detail.Index Terms-interior permanent magnet motor, topology optimization.

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Abstract-This paper discusses properties of the curl-curl matrix in the finite element formulation with edge elements. Moreover the observed deceleration in convergence of the CG and ICCG methods applied to magnetostatic problems through the tree-cotree gauging is explained on the basis of the eigenvalue separation property. From the eigenvalue separation property it follows that neither minimum nonzero eigenvalue of the curl-curl matrix nor maximum one increase through the tree-cotree gauging. Hence it is concluded that the condition number of the curl-curl matrix tends to grow by its definition. Moreover the maximum eigenvalue tends to keep constant whereas the minimum nonzero eigenvalue reduces. This property also makes the condition number worse.

The model reduction based on the method of snapshots is applied to the finite element analysis of three dimensional transient eddy current problems. It is known that accuracy of the reduced model highly depends on the number of snapshots. In this paper, we introduce a novel method which determines the adequate number of snapshots automatically. It is shown that the computational time can be reduced when using the model reduction based on the present method.Index Terms-Model order reduction, method of snapshots, proper orthogonal decomposition, finite element method, eddy current problem.