We solve several applied superconductivity problems using the series in Chebyshev polynomials. ‎Although this method may be less general than the usually employed finite element methods, ‎accuracy of the obtained solutions is often much higher due to the very fast convergence of the ‎Chebyshev expansions. First, as an introduction, we consider the thin strip magnetization and ‎transport current problems for which the analytical solutions are known. Then we apply this method ‎to two-dimensional problems for stacks and pancake coils made of coated conductors assuming the ‎Bean critical-state model. Finally, we extend this approach to evolutionary stack problems with an ‎arbitrary current-voltage relation. Simulation of coils with a large number of turns is also discussed.‎

中文翻译：

---

超导问题的切比雪夫谱法

我们使用 Chebyshev 多项式中的级数解决了几个应用的超导问题。尽管这种方法可能不如通常采用的有限元方法通用，但由于 Chebyshev 展开式的收敛速度非常快，因此获得的解的精度通常要高得多。首先，作为介绍，我们考虑已知解析解的薄带磁化和传输电流问题。然后我们将这种方法应用到二维问题中，假设 Bean 临界状态模型由涂层导体制成的堆栈和薄饼线圈。最后，我们将此方法扩展到具有任意电流-电压关系的演化堆栈问题。还讨论了具有大量匝数的线圈的模拟。