Hermite-Chebyshev pseudospectral method for inhomogeneous superconducting strip problems and magnetic flux pump modeling

The numerical simulation of superconducting devices is a powerful tool for understanding the principles of how they work and improving their design. Usually, these simulations are based on a finite element method but, recently, a different approach, based on the spectral technique, has been presented for very efficient solution of several applied superconductivity problems described by 1D integro-differential equations or a system of such equations. Here, we propose a new pseudospectral method for 2D magnetization and transport current superconducting strip problems with an arbitrary current-voltage relation, spatially inhomogeneous strips and strips in a nonuniform applied field. The method is based on bivariate expansions in Chebyshev polynomials and Hermite functions. It can be used for numerical modeling of magnetic flux pumps of different types and investigating AC losses in coated conductors with local defects. Using a realistic 2D version of the superconducting dynamo benchmark problem as an example, we show that our new method is a competitive alternative to finite element methods.