{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T08:04:08Z","timestamp":1768723448971,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T00:00:00Z","timestamp":1580774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Multigrid methods (MGMs) are used for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier\u2013Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAEs) with a strongly non-Hermitian matrix appear. Hermitian\/skew-Hermitian splitting (HSS) and skew-Hermitian triangular splitting (STS) methods are considered as smoothers in the MGM for solving the SLAE. Numerical results for an algebraic multigrid (AMG) method with HSS-based smoothers are presented.<\/jats:p>","DOI":"10.3390\/sym12020233","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"233","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Numerical Solution of the Navier\u2013Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9816-6759","authenticated-orcid":false,"given":"Galina","family":"Muratova","sequence":"first","affiliation":[{"name":"Mechanics and Computer Science, Vorovich Institute of Mathematics, Southern Federal University, Rostov-on-Don 344000, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7073-1162","authenticated-orcid":false,"given":"Tatiana","family":"Martynova","sequence":"additional","affiliation":[{"name":"Mechanics and Computer Science, Vorovich Institute of Mathematics, Southern Federal University, Rostov-on-Don 344000, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Evgeniya","family":"Andreeva","sequence":"additional","affiliation":[{"name":"Mechanics and Computer Science, Vorovich Institute of Mathematics, Southern Federal University, Rostov-on-Don 344000, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vadim","family":"Bavin","sequence":"additional","affiliation":[{"name":"Mechanics and Computer Science, Vorovich Institute of Mathematics, Southern Federal University, Rostov-on-Don 344000, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeng-Qi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1137\/S0895479801395458","article-title":"Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems","volume":"24","author":"Bai","year":"2003","journal-title":"SIAM J. 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