Reducing Bias and Optimising Execution Time in Iterative Solutions of the Time Dependent Ginzburg Landau Equations

Abstract

The importance of simulating pinning arrays in superconducting samples for the increase of critical currents has been increasing in the last few years. Since the Time Dependent Ginzburg Landau (TDGL) can be more accurate than alternative methodologies, the simulation procedures involving it are critical to design devices that can sustain higher critical currents and, therefore, to the field of applied superconductivity. In this article, a simple novel algorithm is presented for the reduction of bias and optimisation of execution time in iterative time dependent simulations, applied to TDGL solutions of superconducting samples. Taking a time series approach to the magnetic response of the sample, stationary solutions are found for each step in the evolution of the applied external field, leading to bias reduction and minimisation of iterations needed to be spent at each step in the applied field. The results are presented for a pure superconductor, in a framework of simulations via link variable technique, with simple Euler algorithm for the solution in time, but the implementation can be adapted easily to deal with adaptive step size solutions or semi-implicit methods, which are not exempt from the bias and iterations tradeoff.