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

Numerical simulation of superconducting devices is a powerful tool for understanding the principles of their work and improving their design. Usually, such 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 one-dimensional integro-differential equations or a system of such equations. Here we propose a new pseudospectral method for two-dimensional 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 the bivariate expansions in Chebyshev polynomials and Hermite functions. It can be used for numerical modeling magnetic flux pumps of different types and investigating AC losses in coated conductors with local defects. Using a realistic two-dimensional version of the superconducting dynamo benchmark problem as an example, we showed that our new method is a competitive alternative to finite element methods.