Chebyshev spectral method for superconductivity problems

Abstract

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, assuming the Bean critical-state model, we apply this method to two-dimensional problems for stacks and pancake coils made of coated conductors. 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.