{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:52:15Z","timestamp":1777675935456,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[1993,6,1]],"date-time":"1993-06-01T00:00:00Z","timestamp":738892800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Supercomputing Applications"],"published-print":{"date-parts":[[1993,6]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1177\/109434209300700204","type":"journal-article","created":{"date-parts":[[2007,3,4]],"date-time":"2007-03-04T20:17:47Z","timestamp":1173039467000},"page":"129-143","source":"Crossref","is-referenced-by-count":2,"title":["Computation of Equilibrium Vortex Structures for Type-II Superconductors"],"prefix":"10.1177","volume":"7","author":[{"given":"Mark T.","family":"Jones","sequence":"first","affiliation":[{"name":"MATHEMATICS AND COMPUTER SCIENCE DIVISION ARGONNE NATIONAL\rLABORATORY 9700 SOUTH CASS AVENUE ARGONNE, ILLINOIS 60439"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul E.","family":"Plassmann","sequence":"additional","affiliation":[{"name":"MATHEMATICS AND COMPUTER SCIENCE DIVISION ARGONNE NATIONAL\rLABORATORY 9700 SOUTH CASS AVENUE ARGONNE, ILLINOIS 60439"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[1993,6,1]]},"reference":[{"key":"atypb1","volume-title":"Fundamentals of the theory of metals","author":"Abrikosov, A.","year":"1988"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01303701"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/0720013"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.41.6335"},{"key":"atypb5","volume-title":"Unpublished information. 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