Numerical effects in the simulation of Ginzburg-Landau models for superconductivity

Inadequate spatial mesh resolution for simulation of the time-dependent Ginzburg–Landau equations is shown to give rise to spurious solutions. Phenomenological studies to examine the effect of the physical parameters and boundary conditions in 2D and 3D are presented to illustrate the solution structure and to highlight non-linear effects related to evolving vortex patterns. We illustrate and explore this issue further by considering a related simplified model in which the number of vortices is equal to the ‘winding number’ that is associated with the applied boundary conditions. Using this model we demonstrate that the solution structure is non-unique for several values of winding number