{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T20:09:13Z","timestamp":1759176553863},"reference-count":27,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,24]],"date-time":"2006-10-24T00:00:00Z","timestamp":1161648000000},"content-version":"vor","delay-in-days":5166,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Concurrency: Pract. Exper."],"published-print":{"date-parts":[[1992,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The parallelization of sophisticated applications has dramatically increased in recent years. As machine capabilities rise, greater emphasis on modeling complex phenomena can be expected. Many of these applications require the solution of large sparse matrix equations which approximate systems of partial differential equations (PDEs). Therefore we consider parallel iterative solvers for large sparse non\u2010symmetric systems and issues related to parallel sparse matrix software. We describe a collection of parallel iterative solvers which use a distributed sparse matrix format that facilitates the interface between specific applications and a variety of Krylov subspace techniques and multigrid methods. These methods have been used to solve a number of linear and non\u2010linear PDE problems on a 1024\u2010processor NCUBE 2 hypercube. Over 1 Gflop sustained computation rates are achieved with many of these solvers, demonstrating that high performance can be attained even when using sparse matrix data structures.<\/jats:p>","DOI":"10.1002\/cpe.4330040605","type":"journal-article","created":{"date-parts":[[2006,11,17]],"date-time":"2006-11-17T16:23:44Z","timestamp":1163780624000},"page":"481-497","source":"Crossref","is-referenced-by-count":12,"title":["Sparse iterative algorithm software for large\u2010scale MIMD machines: An initial discussion and implementation"],"prefix":"10.1002","volume":"4","author":[{"given":"John N.","family":"Shadid","sequence":"first","affiliation":[]},{"given":"Ray S.","family":"Tuminaro","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,24]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"I. S.DuffandJ. K.Reid MA27\u2010a Set of Fortran Subroutines for Solving Sparse Symmetric Sets of Linear Equations Tech. 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Research Institute for Advanced Computer Science NASA Ames Research Center Moffett Field CA Apr.1990."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/63047"},{"key":"e_1_2_1_10_2","unstructured":"R.Williams Optimization by a Computational Neural Net Tech. Rep. C3P371 Caltech Concurrent Computing Project Pasadena CA Nov.1986."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1970.tb01770.x"},{"key":"e_1_2_1_12_2","unstructured":"R.MorrisonandS.Otto The Scattered Decomposition for Finite Elements Tech. Rep. Memo 286 Caltech Concurrent Computing Project Pasadena CA May1985."},{"key":"e_1_2_1_13_2","first-page":"570","article-title":"A partitioning strategy for non\u2010uniform problems on multiprocessors","volume":"36","author":"Berger M.","year":"1987","journal-title":"IEEE Trans."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0611030"},{"key":"e_1_2_1_15_2","volume-title":"Solving Problems on Concurrent Processors","author":"Fox G.","year":"1988"},{"key":"e_1_2_1_16_2","unstructured":"S. A.Hutchinson J. N.ShadidandK. T.Ng A Comparison of Sparse Matrix Methods on Distributed Memory SIMD and MIMD machines Tech. Rep. to be published Sandia National Laboratories Albuquerque NM 1991."},{"key":"e_1_2_1_17_2","first-page":"409","article-title":"Methods of conjugate gradients for solving linear systems","volume":"49","author":"Hestenes M.","year":"1952","journal-title":"J. Res. 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January1990."},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(81)90034-6"},{"key":"e_1_2_1_26_2","unstructured":"J. N.Shadid Experimental and Computational Study of the Stability of Natural Convection Flow in an Inclined Enclosure Ph.D. thesis University of Minnesota 1989."},{"key":"e_1_2_1_27_2","doi-asserted-by":"publisher","DOI":"10.1137\/0909041"},{"key":"e_1_2_1_28_2","unstructured":"J. N.ShadidandR. S.Tuminaro \u2018Iterative methods for nonsymmetric systems on mimd machines\u2019 to be published inProceedings of Fifth SIAM Conference on Parallel Processing for Scientific Applications SIAM 1991."}],"container-title":["Concurrency: Practice and Experience"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcpe.4330040605","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cpe.4330040605","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T14:28:24Z","timestamp":1698071304000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cpe.4330040605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,9]]},"references-count":27,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1992,9]]}},"alternative-id":["10.1002\/cpe.4330040605"],"URL":"https:\/\/doi.org\/10.1002\/cpe.4330040605","archive":["Portico"],"relation":{},"ISSN":["1040-3108","1096-9128"],"issn-type":[{"value":"1040-3108","type":"print"},{"value":"1096-9128","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,9]]}}}