{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T07:03:54Z","timestamp":1768028634793,"version":"3.49.0"},"reference-count":40,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2005,7,8]],"date-time":"2005-07-08T00:00:00Z","timestamp":1120780800000},"content-version":"vor","delay-in-days":3963,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[1994,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In recent years, competitive domain\u2010decomposed preconditioned iterative techniques of Krylov\u2010Schwarz type have been developed for nonsymmetric linear elliptic systems. Such systems arise when convection\u2010diffusion\u2010reaction problems from computational fluid dynamics or heat and mass transfer are linearized for iterative solution. Through domain decomposition, a large problem is divided into many smaller problems whose requirements for coordination can be controlled to allow effective solution on parallel machines. A central question is how to choose these small problems and how to arrange the order of their solution. Different specifications of decomposition and solution order lead to a plethora of algorithms possessing complementary advantages and disadvantages. In this report we compare several methods, including the additive Schwarz algorithm, the classical multiplicative Schwarz algorithm, an accelerated multiplicative Schwarz algorithm, the tile algorithm, the CGK algorithm, the CSPD algorithm, and also the popular global ILU\u2010family of preconditioners, on some nonsymmetric or indefinite elliptic model problems discretized by finite difference methods. The preconditioned problems are solved by the unrestarted GMRES method. A version of the accelerated multiplicative Schwarz method is a consistently good performer.<\/jats:p>","DOI":"10.1002\/nla.1680010504","type":"journal-article","created":{"date-parts":[[2005,10,14]],"date-time":"2005-10-14T19:52:07Z","timestamp":1129319527000},"page":"477-504","source":"Crossref","is-referenced-by-count":31,"title":["A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems"],"prefix":"10.1002","volume":"1","author":[{"given":"Xiao\u2010Chuan","family":"Cai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William D.","family":"Gropp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David E.","family":"Keyes","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385618"},{"key":"e_1_2_1_3_2","volume-title":"Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations","author":"Bj\u00f8rstad P. 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Ph.D. thesis Courant Institute 1989."},{"key":"e_1_2_1_9_2","volume-title":"Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations","author":"Cai X.\u2010C.","year":"1992"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385503"},{"key":"e_1_2_1_11_2","volume-title":"Proceedings of the International Workshop on Numerical Methods for the Navier\u2010Stokes Equations","author":"Cai X.\u2010C.","year":"1994"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0913013"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/0730049"},{"key":"e_1_2_1_14_2","volume-title":"Third International Symposium on Domain Decomposition Methods for Partial Differential Equations","author":"Chan T. F.","year":"1990"},{"key":"e_1_2_1_15_2","volume-title":"Domain Decomposition Methods for Partial Differential Equations II","author":"Dryja M.","year":"1989"},{"key":"e_1_2_1_16_2","unstructured":"M.DryjaandO. B.Widlund.An additive variant of the alternating method for the case of many subregions TR 339 Dept. of Comp. Sci. Courant Institute 1987."},{"key":"e_1_2_1_17_2","volume-title":"Third International Symposium on Domain Decomposition Methods for Partial Differential Equations","author":"Dryja M.","year":"1990"},{"key":"e_1_2_1_18_2","volume-title":"Parallel Algorithms for Partial Differential Equations, Proceedings of the Sixth GAMM\u2010Seminar, Kiel, Jan. 19\u201321","author":"Dryja M.","year":"1991"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1137\/0720023"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.2307\/2008089"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385726"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(89)90167-7"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/0899-8248(89)90003-7"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1137\/0913057"},{"key":"e_1_2_1_25_2","doi-asserted-by":"publisher","DOI":"10.1137\/0913008"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(84)90158-0"},{"key":"e_1_2_1_27_2","doi-asserted-by":"publisher","DOI":"10.1137\/0908020"},{"key":"e_1_2_1_28_2","volume-title":"Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations","author":"Keyes D. 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