Numerical algorithms of the Lawrence-Doniach model for layered superconductors and their parallel implementation

The Lawrence-Doniach model is often used for studying vortex dynamics in su perconductors which exhibit a layered structure. In solving these model equ ations numerically, the added degrees of complexity due to the coupling and nonlinearity of the model often warrant the extensive use of high-performa nce computers for their solution. Approaches for reducing the complexity of the Lawrence-Doniach model and for simplifying the calculation of the nume rical solution are presented in this work. Numerical results and benchmarks are included for models involving the motion of vortices due to an applied current and the pinning of vortices due to nonuniform pinning sites (norma l inclusions) placed within the material.