Computation of Equilibrium Vortex Structures for Type-II Superconductors

Abstract

A model of the vortex structure and configuration for homogeneous type-II superconductors can be deter mined by minimization of the Ginzburg-Landau free energy functional. A generalization of this formulation, the Lawrence-Doniach model, can be used for layered systems. A finite-dimensional approximation of this functional leads to a very large, sparse optimization problem. A number of algorithms have been used to attempt to solve this problem. The most successful of these is a damped, inexact Newton algorithm. Its com putational kernel is the iterative solution of a large, sparse, linear system that is nearly singular. We present computational results for solving these three- dimensional problems on the Intel DELTA. Using a general-purpose, scalable, iterative solver based on the preconditioned conjugate gradient method, we ob tained sustained computational rates of up to 4.26 GFLOPS on 512 processors. We find improvements of over a factor of 100 in the total execution time when compared with the same problem run on the CRAY-2. This computational tool has given us the first compu tational view of three-dimensional vortex phenomena such as vortex locking.

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