{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T19:50:43Z","timestamp":1760644243793},"reference-count":10,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2001,11,5]],"date-time":"2001-11-05T00:00:00Z","timestamp":1004918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2001,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The efficiency of three multigrid methods for solving highly non\u2010linear diffusion problems on two\u2010dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the non\u2010linearities of the governing equations are handled. These comprise a non\u2010linear full approximation storage (FAS) multigrid method which is used to solve the non\u2010linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non\u2010linear system, and a hybrid scheme which is based on a non\u2010linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that, in the asymptotic convergence region, all methods are equally effective at converging the non\u2010linear residual in a given number of multigrid cycles, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non\u2010linear grid sweeps. Copyright \u00a9 2001 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.262","type":"journal-article","created":{"date-parts":[[2002,8,25]],"date-time":"2002-08-25T16:20:51Z","timestamp":1030292451000},"page":"499-512","source":"Crossref","is-referenced-by-count":24,"title":["Multigrid approaches to non\u2010linear diffusion problems on unstructured meshes"],"prefix":"10.1002","volume":"8","author":[{"given":"Dimitri J.","family":"Mavriplis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2001,11,5]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"BrandtA.Multigrid techniques with applications to fluid dynamics: 1984 guide. 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(Journal of Quantitative Spectroscopy & Radiative Transfer submitted)."}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.262","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.262","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T19:10:11Z","timestamp":1694545811000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.262"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,11,5]]},"references-count":10,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2001,12]]}},"alternative-id":["10.1002\/nla.262"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1002\/nla.262","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,11,5]]}}}