乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T18:16:26Z","timestamp":1719598586732},"reference-count":48,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2021,5,11]],"date-time":"2021-05-11T00:00:00Z","timestamp":1620691200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701133","11726636"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,12]]},"abstract":"Abstract<\/jats:title>Space\u2010time methods are able to solve time\u2010dependent problems faster by exploiting the full power of high\u2010performance computer. In this article, a multilevel space\u2010time multiplicative Schwarz method is presented for solving parabolic equations in parallel on both spatial and temporal directions. In the implementation, the proposed Schwarz method is treated as preconditioner for GMRES, that is, a coupled system arising from the discretization of the parabolic equation is solved by using a multiplicative Schwarz preconditioned GMRES algorithm. We develop an optimal convergence theory to show that the convergence rate is bounded and independent of the spatial mesh sizes, the time step size, the number of subdomains, the number of levels, and the window size. Some numerical results obtained on a parallel computer with thousands of processors are presented to confirm the theory in terms of optimality and scalability. Moreover, numerical comparisons with traditional time\u2010stepping algorithms show that the proposed space\u2010time method earns lots of benefits when the number of processor cores is large.<\/jats:p>","DOI":"10.1002\/nla.2390","type":"journal-article","created":{"date-parts":[[2021,5,12]],"date-time":"2021-05-12T07:09:35Z","timestamp":1620803375000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multilevel space\u2010time multiplicative Schwarz preconditioner for parabolic equations"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-2163-9949","authenticated-orcid":false,"given":"Shishun","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science Henan Polytechnic University Jiaozuo P.R. China"}]},{"given":"Xinping","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Science Hangzhou Dianzi University Hangzhou P.R. China"}]},{"given":"Rongliang","family":"Chen","sequence":"additional","affiliation":[{"name":"Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen P.R. China"}]}],"member":"311","published-online":{"date-parts":[[2021,5,11]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.1982.1270004"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199903)6:2<125::AID-NLA152>3.0.CO;2-4"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35275-1_53"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596305337"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/0916004"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/110854187"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-08-02145-5"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/050642137"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1072620"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/0916034"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/0733024"},{"key":"e_1_2_10_13_1","first-page":"189","article-title":"Parabolic multigrid methods","volume":"7","author":"Hackbusch W","year":"1984","journal-title":"Comput Methods Appl Sci Eng"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1137\/15M1046605"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.1630080906"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/0916050"},{"key":"e_1_2_10_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01934186"},{"key":"e_1_2_10_18_1","doi-asserted-by":"publisher","DOI":"10.4208\/nmtma.m12si07"},{"key":"e_1_2_10_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(00)01793-6"},{"key":"e_1_2_10_20_1","first-page":"189","volume-title":"Recent developments in domain decomposition methods. Lecture Notes in Computational Science and Engineering","author":"Bal G","year":"2001"},{"key":"e_1_2_10_21_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.860"},{"key":"e_1_2_10_22_1","doi-asserted-by":"publisher","DOI":"10.1137\/05064607X"},{"key":"e_1_2_10_23_1","doi-asserted-by":"publisher","DOI":"10.1137\/050647086"},{"key":"e_1_2_10_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/140970756"},{"key":"e_1_2_10_25_1","doi-asserted-by":"publisher","DOI":"10.1137\/130944230"},{"key":"e_1_2_10_26_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1082330"},{"key":"e_1_2_10_27_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1144982"},{"key":"e_1_2_10_28_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2155"},{"key":"e_1_2_10_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2110"},{"key":"e_1_2_10_30_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1074266"},{"key":"e_1_2_10_31_1","doi-asserted-by":"publisher","DOI":"10.1137\/110843484"},{"key":"e_1_2_10_32_1","doi-asserted-by":"publisher","DOI":"10.1137\/14097536X"},{"key":"e_1_2_10_33_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500315360"},{"key":"e_1_2_10_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-23321-5_3"},{"key":"e_1_2_10_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s42514-019-00003-x"},{"key":"e_1_2_10_36_1","doi-asserted-by":"publisher","DOI":"10.1137\/12090410X"},{"key":"e_1_2_10_37_1","doi-asserted-by":"publisher","DOI":"10.1137\/140993776"},{"key":"e_1_2_10_38_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M113808X"},{"key":"e_1_2_10_39_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1991-1090464-8"},{"key":"e_1_2_10_40_1","doi-asserted-by":"publisher","DOI":"10.1137\/0915039"},{"key":"e_1_2_10_41_1","doi-asserted-by":"publisher","DOI":"10.1137\/0730049"},{"key":"e_1_2_10_42_1","doi-asserted-by":"publisher","DOI":"10.1137\/090755849"},{"key":"e_1_2_10_43_1","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/S0096-3003(02)00085-1","article-title":"Multiplicative Schwarz methods for parabolic problems","volume":"136","author":"Rui H","year":"2003","journal-title":"Appl Math Comput"},{"key":"e_1_2_10_44_1","doi-asserted-by":"publisher","DOI":"10.1137\/0730013"},{"key":"e_1_2_10_45_1","doi-asserted-by":"publisher","DOI":"10.1137\/1034116"},{"key":"e_1_2_10_46_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01385873"},{"key":"e_1_2_10_47_1","doi-asserted-by":"publisher","DOI":"10.1137\/0720023"},{"key":"e_1_2_10_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.03.027"},{"key":"e_1_2_10_49_1","doi-asserted-by":"publisher","DOI":"10.2172\/1483828"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2390","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/nla.2390","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2390","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T16:34:44Z","timestamp":1699029284000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.2390"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,11]]},"references-count":48,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["10.1002\/nla.2390"],"URL":"https:\/\/doi.org\/10.1002\/nla.2390","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,11]]},"assertion":[{"value":"2020-02-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-26","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}