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Chebyshev spectral method for superconductivity problems
Superconductor Science and Technology ( IF 3.6 ) Pub Date : 2020-07-01 , DOI: 10.1088/1361-6668/ab9800 Vladimir Sokolovsky 1 , Leonid Prigozhin 2 , Andrey B Kozyrev 3
Superconductor Science and Technology ( IF 3.6 ) Pub Date : 2020-07-01 , DOI: 10.1088/1361-6668/ab9800 Vladimir Sokolovsky 1 , Leonid Prigozhin 2 , Andrey B Kozyrev 3
Affiliation
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。
更新日期:2020-07-01
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。