{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,29]],"date-time":"2023-11-29T11:53:10Z","timestamp":1701258790418},"reference-count":22,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T00:00:00Z","timestamp":1620259200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["BO 3405\/2"],"id":[{"id":"10.13039\/501100001659","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>Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development and analysis of new block smoothers for the Stokes equations that are discretized on staggered grids. These smoothers are nonoverlapping and therefore desirable due to reduced computational costs. Traditional geometric multigrid methods are based on simple pointwise smoothers. However, using multigrid methods to efficiently solve more difficult problems such as the Stokes equations leads to computationally more expensive smoothers, for example, overlapping block smoothers. Nonoverlapping smoothers are less expensive, but have been considered less efficient in the literature. In this paper, we develop new nonoverlapping smoothers, the so\u2010called triad\u2010wise smoothers, and show their efficiency within multigrid methods to solve the Stokes equations. In addition, we compare overlapping and nonoverlapping smoothers by measuring their computational costs and analyzing their behavior by the use of local Fourier analysis.<\/jats:p>","DOI":"10.1002\/nla.2389","type":"journal-article","created":{"date-parts":[[2021,5,7]],"date-time":"2021-05-07T02:35:38Z","timestamp":1620354938000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Nonoverlapping block smoothers for the Stokes equations"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-5854-157X","authenticated-orcid":false,"given":"Lisa","family":"Claus","sequence":"first","affiliation":[{"name":"Computational Research Division Lawrence Berkeley National Laboratory Berkeley California USA"},{"name":"University of Wuppertal Wuppertal Germany"}]},{"given":"Matthias","family":"Bolten","sequence":"additional","affiliation":[{"name":"University of Wuppertal Wuppertal Germany"}]}],"member":"311","published-online":{"date-parts":[[2021,5,6]]},"reference":[{"key":"e_1_2_11_2_1","volume-title":"Numerical mathematics and scientific computation","author":"Elman HC","year":"2005"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-40528-5_10"},{"key":"e_1_2_11_4_1","volume-title":"Multigrid","author":"Trottenberg U","year":"2001"},{"key":"e_1_2_11_5_1","series-title":"Notes Numerical\u2009Fluid Mechanics","first-page":"269","volume-title":"Large\u2010scale scientific computations of engineering and environmental problems (Varna, 1997)","author":"John V","year":"1998"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1194407"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2016.06.006"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/130941353"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/16M1106304"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-002-0448-3"},{"key":"e_1_2_11_11_1","doi-asserted-by":"crossref","unstructured":"FarrellPE HeY andMacLachlanSP. A local Fourier analysis of additive Vanka relaxation for the Stokes equations;2020.","DOI":"10.1002\/nla.2306"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(86)90008-2"},{"key":"e_1_2_11_13_1","volume-title":"Multigrid smoothers for saddle point systems","author":"Claus L","year":"2019"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431719-X"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/0731087"},{"key":"e_1_2_11_16_1","volume-title":"Practical Fourier analysis for multigrid methods. vol. 4 of Numerical Insights","author":"Wienands R","year":"2005"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(90)90048-8"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2147"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.01.029"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2016.02.006"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(91)90178-N"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.762"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2285"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2389","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/nla.2389","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2389","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T12:08:34Z","timestamp":1693224514000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.2389"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,6]]},"references-count":22,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["10.1002\/nla.2389"],"URL":"https:\/\/doi.org\/10.1002\/nla.2389","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,6]]},"assertion":[{"value":"2020-07-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-20","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-06","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}