{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T04:34:22Z","timestamp":1712464462513},"reference-count":18,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2008,4,28]],"date-time":"2008-04-28T00:00:00Z","timestamp":1209340800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2008,12]]},"abstract":"Abstract<\/jats:title>Meshfree methods are suitable for solving problems on irregular domains, avoiding the use of a mesh. To deal with the boundary conditions, we can use Lagrange multipliers and obtain a sparse, symmetric and indefinite system of saddle\u2010point type. Many methods have been developed to solve the indefinite system. Previously, we presented an algebraic method to construct an LU\u2010based preconditioner for the saddle\u2010point system obtained by meshfree methods, which combines the multilevel clustering method with the \u210b\ufe01\u2010matrix arithmetic. The corresponding preconditioner has both \u210b\ufe01\u2010matrix and sparse matrix subblocks. In this paper we refine the above method and propose a way to construct a pure \u210b\ufe01\u2010matrix preconditioner. We compare the new method with the old method, JOR and smoothed algebraic multigrid methods. The numerical results show that the new preconditioner outperforms the preconditioners based on the other methods. Copyright \u00a9 2008 John Wiley & Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.599","type":"journal-article","created":{"date-parts":[[2008,4,28]],"date-time":"2008-04-28T15:17:48Z","timestamp":1209395868000},"page":"911-924","source":"Crossref","is-referenced-by-count":2,"title":["\u210b\ufe01\u2010matrix preconditioners for symmetric saddle\u2010point systems from meshfree discretization"],"prefix":"10.1002","volume":"15","author":[{"given":"Sabine","family":"Le Borne","sequence":"first","affiliation":[]},{"given":"Suely","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"Fang","family":"Yang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,4,28]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(96)01083-3"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/nla.383"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s006070050015"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0955-7997(02)00152-2"},{"key":"e_1_2_1_6_2","unstructured":"B\u00f6rmS GrasedyckL HackbuschW. Hierarchical matrices. Technical Report Max\u2010Planck\u2010Institut f\u00fcr Mathematik in den Naturwissenschaften Leipzig Germany. 2003. Lecture Notes No. 21. Available from:www.mis.mpg.de\/preprints\/ln\/ revised2006."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1137\/040615845"},{"key":"e_1_2_1_8_2","series-title":"Lecture Notes in Computational Science and Engineering","first-page":"661","volume-title":"Domain Decomposition Methods in Science and Engineering XVI","author":"Le Borne S","year":"2006"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-003-0019-1"},{"key":"e_1_2_1_10_2","unstructured":"GrasedyckL KriemannR Le BorneS.Parallel black box domain decomposition based \u210b\ufe01\u2010LU preconditioning. Technical Report 115 Max\u2010Planck\u2010Institute for Mathematics in the Sciences 2005."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-007-0224-4"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO;2-9"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.05.194"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970937"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595287997"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1137\/040607964"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.2307\/2007773"},{"key":"e_1_2_1_18_2","unstructured":"StewartDE LeykZ.Meschach: matrix computations in C. 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