Fast solution of the superconducting dynamo benchmark problem

A model of high temperature superconducting dynamo, a promising type of flux pumps 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.