A model of high-temperature superconducting dynamos, a promising type of flux pump capable of wireless injection of a large DC current into a superconducting circuit, has recently been chosen as an applied superconductivity benchmark problem and solved using ten different numerical methods (Ainslie et al 2020 Supercond. Sci. Technol. 33 105009). Using expansions in Chebyshev polynomials for approximation in space and the method of lines for integration in time we derive a simple and accurate numerical method which is much faster. The proposed numerical method was applied also to problems with transport current and a field-dependent sheet critical current density.

高温超导发电机模型是一种很有前途的磁通泵，能够将大直流电流无线注入超导电路，最近被选为应用超导基准问题，并使用十种不同的数值方法解决（Ainslie等人2020 Supercond. Sci. Technol. 33 105009)。使用切比雪夫多项式中的展开来逼近空间，并使用线的方法进行时间积分，我们推导出了一种简单而准确的数值方法，该方法要快得多。所提出的数值方法也适用于传输电流和依赖于场的片材临界电流密度的问题。