三维非线性eddy currents的计算：变分法和超导立方体
3D computation of non-linear eddy currents: variational method and superconducting cubic bulk
摘要：
计算非线性材料（如超导体）中的电涡流是\E{not straightforward}。超导磁体和电力应用的设计需要电磁计算机建模，在许多情况下是三维（3D）问题。由于3D问题需要高计算时间，因此非常需要新颖的时间有效的建模工具。提出了一种基于变分原理的计算建模方法。自编程实现使用原始的最小化方法，该方法将样本划分为扇区。这在不损失准确性的情况下加快了计算速度，同时实现了高效的并行化。该方法也可用于线性材料或非线性电气元件网络中的瞬态模型。作为例子，我们分析了立方超导体的磁化电流。尽管在材料表征和批量应用中经常遇到这种情况，但这种3D情况仍然未知。我们发现，低于渗透场和样品的一部分，电流通量线不是矩形的，并显着弯曲的方向平行于所施加的磁场。总之，所提出的数值方法能够有效地解决完全3D的情况下，没有损失的准确性。
英文摘要：
Computing the electric eddy currents in non-linear materials, such as superconductors, is \E{not straightforward}. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a three-dimensional (3D) problem. Since 3D problems require high computing times, novel time-efficient modeling tools are highly desirable. This article presents a novel computing modeling method based on a variational principle. The self-programmed implementation uses an original minimization method, which divides the sample into sectors. This speeds-up the computations with no loss of accuracy, while enabling efficient parallelization. This method could also be applied to model transients in linear materials or networks of non-linear electrical elements. As example, we analyze the magnetization currents of a cubic superconductor. This 3D situation remains unknown, in spite of the fact that it is often met in material characterization and bulk applications. We found that below the penetration field and in part of the sample, current flux lines are not rectangular and significantly bend in the direction parallel to the applied field. In conclusion, the presented numerical method is able to time-efficiently solve fully 3D situations without loss of accuracy.
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