Critical points of the Ginzburg-Landau functional on multiply-connected domains

Abstract

We give a numerical method for approximating critical points of the Ginzburg-Landau functional, and present test results in the form of plots of the corresponding electron densities, magnetic fields, and currents. Our domains include a rectangle, a rectangle with a rectangular hole in the center, and a rectangle with two rectangular holes. In each case, we found several critical points. The plots reveal interesting patterns, including the existence of counter-currents (adjacent currents in opposite directions).