Iteration Schemes for Parallelizing Models of Superconductivity
                                       
                                 Paul A. Gray

                          Michigan State University
                               East Lansing, MI

                                   Abstract

The time dependent Lawrence-Doniach model, valid for high fields and high
values of the Ginzburg-Landau parameter, is often used for studying vortex
dynamics in layered high-T_c superconductors.  When solving these equations
numerically, the added degrees of complexity due to the coupling and
nonlinearity of the model often warrant the use of high-performance computers
for their solution.  However, the interdependence between the layers can be
manipulated so as to allow parallelization of the computations at an
individual layer level.  The reduced parallel tasks may then be solved
independently using a heterogeneous cluster of networked workstations
connected together with Parallel Virtual Machine (PVM) software.  Here, this
parallelization of the model is discussed and several computational
implementations of varying degrees of parallelism are presented.
Computational results are also given which contrast properties of convergence
speed, stability, and consistency of these implementations.  Included in these
results are models involving the motion of vortices due to an applied current.