Large-scale electromagnetic field analyses of coils wound with coated conductors using a current-vector-potential formulation with a thin-strip approximation
Large-scale electromagnetic field analyses of coils wound with coated conductors using a current-vector-potential formulation with a thin-strip approximation
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DOI：
10.1088/1361-6668/ab1d35
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发表时间：
2019-07
影响因子：
3.6
通讯作者：
T. Mifune;Naoki Tominaga;Y. Sogabe;Y. Mizobata;Masahiro Yasunaga;Akihiro Ida;T. Iwashita;N. Amemiya
中科院分区：
文献类型：
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作者：
T. Mifune;Naoki Tominaga;Y. Sogabe;Y. Mizobata;Masahiro Yasunaga;Akihiro Ida;T. Iwashita;N. Amemiya
基于电流矢势公式和薄条近似，我们开发了一种新的软件，用于大规模分析有涂层导体的线圈的电磁场。虽然该公式对于获得电磁场的精确解是有效的，但超导材料的强非线性特性经常导致线性方程组的高度病态，难以有效地求解。此外，由于密集的矩阵运算，分析所需的内存消耗和计算时间随着分析的规模而迅速增加。在我们的软件中，第一个困难是通过一种基于代数多重网格法的新的预处理技术来解决的。代数多重网格预处理使我们能够高效而稳定地求解分析中遇到的病态线性方程组。它还提高了含有复丝涂层导体的分析的稳健性。对于第二个困难，分层矩阵表示大大减少了与稠密矩阵相关的内存消耗以及计算时间。同时，我们的分层矩阵表示的实现与分布式存储计算机上的并行计算非常兼容。最后，我们给出了一些使用新软件进行大规模分析的实际例子。例如，对自由度超过150万的余弦-西塔偶极子磁体的分析，通过56个并行处理，在78小时内成功完成，总内存消耗为177 GB。
We developed a novel software for large-scale electromagnetic field analyses of coils wound with coated conductors based on current-vector-potential formulation with thin-strip approximation. Although this formulation was effective for obtaining the precise solutions of the electromagnetic field, the strong nonlinear property of superconducting materials frequently led to highly ill-conditioned linear systems of equations, which were difficult to solve efficiently. Moreover, the memory consumption and computation time required for the analyses rapidly increased with the size of the analysis due to dense matrix operations. In our software, the first difficulty was addressed by a novel preconditioning technique based on the algebraic multigrid method. Algebraic multigrid preconditioning enabled us to efficiently and stably solve the ill-conditioned linear systems of equations encountered in our analyses. It also improved the robustness of the analyses containing multifilament-coated conductors. As regards the second difficulty, the hierarchical matrices representation drastically reduced the memory consumption related to the dense matrices, as well as computation time. Meanwhile, our implementation of the hierarchical matrices representation was quite compatible with parallel computations on distributed memory computers. Finally, we presented some practical examples of large-scale analyses, which became possible by using the new software. For instance, the analysis of a cosine-theta dipole magnet whose number of degrees of freedom was more than 1.5 million was successfully completed in 78 h by 56 parallel processes and with a total memory consumption of 177 GB.