A LINEARIZED CRANK-NICOLSON-GALERKIN METHOD FOR THE GINZBURG-LANDAU MODEL

The time-dependent Ginzburg-Landau model is used extensively in studyi ng the nonequilibrium state of superconductivity. The computer simulat ion of this model requires highperformance computing power and reliabl e and efficient numerical methods to solve the Ginzburg-Landau equatio ns. In this paper, a linearized Crank-Nicolson-Galerkin method is prop osed for solving these nonlinear and coupled partial differential equa tions. The method uses the Galerkin finite element approximation in sp atial discretization and the Crank-Nicolson implicit scheme in time di scretization, together with certain techniques which linearize and dec ouple the Ginzburg-Landau equations. While retaining the stability and accuracy of the Crank-Nicolson scheme, the proposed approach results in symmetric and positive definite matrix problems, thus substantially improving the computational efficiency. Furthermore, and even more im portant, the proposed approach is suitable for large-scale parallel co mputation. Numerical results from simulating the vortex dynamics of su perconductivity by using the linearized Crank-Nicolson-Galerkin method are presented.