Development of Methods for Analyzing Eddy Currents in Moving Conductors and Verification

发展了运动导体中三维涡流的分析方法，并对各种方法进行了比较。文中还研究了ICCG方法作为大型线性方程组的解算器的加速性能。1.运动导体中涡流分析方法的发展对运动导体磁路的分析方法进行了系统的分类，并指出了每种分析方法的优劣。研究了用移动坐标系和固定坐标系处理涡流项的方法，并开发了相应的软件。2.各种方法的比较通过一个验证模型，从精度、内存需求和CPU时间的角度对移动坐标系和固定坐标系的方法进行了比较。结果表明：(1)在暂态分析中，移动坐标系在精度、计算机内存和计算时间等方面都是优越的。(2)在大Peclet数的直流和交流稳态分析中，用普通Galerkin有限元方法在固定坐标系下会出现虚假振荡。然而，使用移动坐标系的解可以得到可靠性很高的解。3.加速求解大型线性方程组为了提高计算速度，对ICCG方法中计算非零点分布的算法进行了改进。结果表明，通过引入电标量势，ICCG方法的收敛特性得到了很大的改善。

The methods for analyzing 3-D eddy currents in moving conductors are developed and the various methods are compared with each other. The acceleration of the ICCG method which is used as solver for large linear equation systems is also investigated. The results obtained can be summarized as follows :1.Development of Methods for Analyzing Eddy Currents in Moving ConductorsThe methods for analyzing magnetic circuits with moving conductors are systematically classified and the preferable method for each circuit is shown. The treatment of eddy current term using moving and fixed coordinate systems are investigated and the software is developed.2.Comparison of Various MethodsThe methods using moving and fixed coordinate systems are compared with each other from the standpoints of accuracy, memory requirement and CPU time by using a verification model. The results obtained can be described as follows :(1) In the transient analysis, the moving coordinate system is superior from the standpoints of accuracy, computer storage and CPU time.(2) In the dc and ac steady state analysis for large Peclet numbers, spurious oscillations occur when using a fixed coordinate system with ordinary Galerkin finite element method. The solution using a moving coordinate system, however, can be obtained with a high reliability. The optimal value of the time step for the moving coordinate system is also clarified.3.Acceleration of Solving Large Linear Equation SystemsThe algorithm for the calculation of the distribution of non-zero entries in ICCG method is improved in order to accelerate the computation. It is shown that the convergence characteristics of the ICCG method for the analysis using magnetic vector potential and edge elements can be considerably massively improved by introducing the electric scalar potential.