乐胖代购免代理版

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The Schur complement for the generalized saddle\u2010point system is very difficult or even impossible to approximate, which prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle\u2010point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simplified wind farm control example to illustrate the performance of the MSSS preconditioner. We also compare the performance of the MSSS preconditioner with the performance of the state\u2010of\u2010the\u2010art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for the control of the Navier\u2013Stokes equation.<\/jats:p>","DOI":"10.1002\/nla.2349","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T04:09:55Z","timestamp":1605240595000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Preconditioning Navier\u2013Stokes control using multilevel sequentially semiseparable matrix computations"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-0360-0442","authenticated-orcid":false,"given":"Yue","family":"Qiu","sequence":"first","affiliation":[{"name":"School of Information Science and Technology ShanghaiTech University Shanghai China"}]},{"given":"Martin B.","family":"van Gijzen","sequence":"additional","affiliation":[{"name":"Delft Institute of Applied Mathematics Delft University of Technology Delft The Netherlands"}]},{"given":"Jan\u2010Willem","family":"van Wingerden","sequence":"additional","affiliation":[{"name":"Delft Center for Systems and Control Delft University of Technology Delft The Netherlands"}]},{"given":"Michel","family":"Verhaegen","sequence":"additional","affiliation":[{"name":"Delft Center for Systems and Control Delft University of Technology Delft The Netherlands"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-5988-9153","authenticated-orcid":false,"given":"Cornelis","family":"Vuik","sequence":"additional","affiliation":[{"name":"Delft Institute of Applied Mathematics Delft University of Technology Delft The Netherlands"}]}],"member":"311","published-online":{"date-parts":[[2020,11,12]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_8_2_1","DOI":"10.1016\/S0098-1354(02)00158-8"},{"doi-asserted-by":"publisher","key":"e_1_2_8_3_1","DOI":"10.1137\/060671590"},{"doi-asserted-by":"publisher","key":"e_1_2_8_4_1","DOI":"10.1007\/978-3-642-55508-4_1"},{"doi-asserted-by":"publisher","key":"e_1_2_8_5_1","DOI":"10.1137\/0613022"},{"doi-asserted-by":"publisher","key":"e_1_2_8_6_1","DOI":"10.1137\/060660977"},{"doi-asserted-by":"publisher","key":"e_1_2_8_7_1","DOI":"10.1016\/j.jcp.2013.08.044"},{"doi-asserted-by":"publisher","key":"e_1_2_8_8_1","DOI":"10.1137\/S0363012999361810"},{"doi-asserted-by":"publisher","key":"e_1_2_8_9_1","DOI":"10.1137\/S1052623496302877"},{"doi-asserted-by":"publisher","key":"e_1_2_8_10_1","DOI":"10.1137\/S1064827595294678"},{"doi-asserted-by":"publisher","key":"e_1_2_8_11_1","DOI":"10.1137\/S0363012994273374"},{"doi-asserted-by":"publisher","key":"e_1_2_8_12_1","DOI":"10.1017\/jfm.2015.70"},{"doi-asserted-by":"publisher","key":"e_1_2_8_13_1","DOI":"10.1137\/070687426"},{"doi-asserted-by":"publisher","key":"e_1_2_8_14_1","DOI":"10.1002\/nla.310"},{"doi-asserted-by":"publisher","key":"e_1_2_8_15_1","DOI":"10.1007\/s11075-016-0111-1"},{"doi-asserted-by":"publisher","key":"e_1_2_8_16_1","DOI":"10.1007\/s11075-016-0136-5"},{"doi-asserted-by":"publisher","key":"e_1_2_8_17_1","DOI":"10.1016\/j.laa.2008.01.018"},{"doi-asserted-by":"publisher","key":"e_1_2_8_18_1","DOI":"10.1007\/s00211-017-0892-8"},{"doi-asserted-by":"publisher","key":"e_1_2_8_19_1","DOI":"10.1007\/s00211-017-0908-4"},{"doi-asserted-by":"publisher","key":"e_1_2_8_20_1","DOI":"10.1137\/100807776"},{"doi-asserted-by":"publisher","key":"e_1_2_8_21_1","DOI":"10.1137\/100798491"},{"doi-asserted-by":"publisher","key":"e_1_2_8_22_1","DOI":"10.1137\/130926365"},{"doi-asserted-by":"publisher","key":"e_1_2_8_23_1","DOI":"10.1137\/140980016"},{"doi-asserted-by":"publisher","key":"e_1_2_8_24_1","DOI":"10.1007\/s10543-016-0635-8"},{"doi-asserted-by":"publisher","key":"e_1_2_8_25_1","DOI":"10.1002\/nla.2218"},{"doi-asserted-by":"publisher","key":"e_1_2_8_26_1","DOI":"10.1016\/j.jcp.2015.03.029"},{"doi-asserted-by":"publisher","key":"e_1_2_8_27_1","DOI":"10.1002\/we.469"},{"key":"e_1_2_8_28_1","first-page":"367","article-title":"Efficient preconditioners for PDE\u2010constrained optimization problems with a multilevel sequentially semiseparable matrix structure","volume":"44","author":"Qiu Y","year":"2015","journal-title":"Electr Trans Numer Anal"},{"doi-asserted-by":"publisher","key":"e_1_2_8_29_1","DOI":"10.1002\/mma.3416"},{"doi-asserted-by":"publisher","key":"e_1_2_8_30_1","DOI":"10.1137\/120891393"},{"unstructured":"SilvesterDJ ElmanHC RamageA. 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