Fast Large-Scale Electromagnetic Field Analysis Using PC Cluster for Optimal Design of Electric Machines

对复杂现象的精确分析和对电气电子设备的详细设计优化需要进行大规模的电磁场分析，这需要花费大量的计算时间。然而，近年来包括并行计算在内的高性能计算技术在大规模电磁场分析中的应用还不够充分，本研究的目的是在并行计算环境下实现电机优化设计中快速、精确的大规模电磁场分析。为此，本研究旨在发展(1)快速电磁场分析的有效算法和(2)包括精确铁损计算在内的电机优化设计方法。所获得的结果可归结为以下四个方面。(1-a)用于电磁场分析的代数多重网格(AMG)算法发展了包含实对称H-矩阵的线性方程组的AMG求解器。提出了一种用于电磁有限边元分析的新的AMG技术。(1-b)用于线性方程组的并行求解器提出了一种新的并行排序--块红黑排序，用于同步点较少、收敛速度较快的并行ICCG求解器。(2-a)用于电机优化设计的并行遗传算法(GA)在分布式并行计算系统上高效地实现了电机的优化设计。(2-b)用于高级电磁场分析的磁特性建模和非协调网格有限元分析。建立了高效、准确的电工钢板直流磁滞模型。其基于停止和/或播放模型。用直流滞环模型进行涡流分析，以准确表示交流B-H回路。研究了在旋转机械磁场分析中应用的Mortar有限元方法。

Precise analysis of complex phenomena and detailed design optimization of electric and electronic devices require a large-scale electromagnetic field analysis, which costs a large amount of computation time. However, the recent development of high performance computing techniques including parallel computation has not yet been applied sufficiently to the large-scale electromagnetic field analysis.The purpose of this research is to achieve the fast and precise large-scale electromagnetic field analysis for optimal design of electric machines under parallel computing environment. For this purpose this research aims to develop (1) efficient algorithms for fast electromagnetic field analyses, and (2) advanced optimal design methods for electric machines including accurate iron-loss evaluation.The obtained results are categorized into the four elements below.(1-a)Algebraic Multigrid (AMG) Algorithm for Electromagnetic Field AnalysesAn AMG solver for linear systems of equations involving real symmetric H-matrices is developed. A new AMG technique for electromagnetic finite edge-element analysis is proposed.(1-b).Parallel Solvers for Linear Systems of EquationsA new parallel ordering, "block red-black ordering," is proposed for a parallelized ICCG solver with fewer synchronization points and a high convergence rate.(2-a)Parallel Genetic Algorithm (GA) for Optimal Design of Electric MachinesThe island parallel GA efficiently achieves an optimum design of electric machinery on a distributed parallel computing system.(2-b)Magnetic Property Modeling and Nonconforming Mesh FEM for Advanced Electromagnetic Field AnalysisEfficient arid accurate DC hysteresis models for electrical steel sheets are developed, which are based on the stop and/or play models. The DC hysteresis models are used for eddy-current analyses to represent AC B-H loops accurately. The mortar finite element method is studied, which is applied to a magnetic-field analysis of rotating machinery.