{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T18:44:48Z","timestamp":1768589088035,"version":"3.49.0"},"reference-count":0,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":18,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["VLSI Design"],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>We derive the constant\u2010<jats:italic>j<\/jats:italic> box method discretization for the convection\u2010diffusion\nequation, \u2207<jats:italic>j<\/jats:italic> = <jats:italic>f<\/jats:italic>, with <jats:italic>j<\/jats:italic> = \u2212<jats:italic>\u03b1<\/jats:italic>\u2207<jats:italic>u<\/jats:italic> + <jats:italic>\u03b2<\/jats:italic><jats:italic>u<\/jats:italic>\n. In two dimensions, <jats:italic>\u03b1<\/jats:italic> is a 2 \u00d7 2 symmetric, positive\ndefinite tensor field and <jats:italic>\u03b2<\/jats:italic> is a two\u2010dimensional vector field. This derivation generalizes\nthe well\u2010known Scharfetter\u2010Gummel discretization of the continuity equations in\nsemiconductor device simulation. We define the anisotropic Delaunay condition and\nshow that under this condition and appropriate evaluations of <jats:italic>\u03b1<\/jats:italic> and <jats:italic>\u03b2<\/jats:italic>, the stiffness\nmatrix, <jats:italic>M<\/jats:italic>, of the discretization is a convective <jats:italic>M<\/jats:italic>\u2010matrix. We then examine classical\niterative splittings of <jats:italic>M<\/jats:italic> and show that convection (even convection dominance) does\nnot degrade the rate of convergence of such iterations relative to the purely diffusive (<jats:italic>\u03b2<\/jats:italic>=0) problem under certain conditions.<\/jats:p>","DOI":"10.1155\/2000\/98424","type":"journal-article","created":{"date-parts":[[2007,9,18]],"date-time":"2007-09-18T12:58:37Z","timestamp":1190120317000},"page":"485-529","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Discretization of Anisotropic Convection\u2010diffusionEquations, Convective M\u2010matrices and their IterativeSolution"],"prefix":"10.1155","volume":"10","author":[{"given":"Donald J.","family":"Rose","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hai","family":"Shao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Craig S.","family":"Henriquez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[1999,12,14]]},"container-title":["VLSI Design"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2000\/098424.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/vlsi\/2000\/098424.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2000\/98424","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T13:21:24Z","timestamp":1723123284000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2000\/98424"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,12,14]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1155\/2000\/98424"],"URL":"https:\/\/doi.org\/10.1155\/2000\/98424","archive":["Portico"],"relation":{},"ISSN":["1065-514X","1563-5171"],"issn-type":[{"value":"1065-514X","type":"print"},{"value":"1563-5171","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,12,14]]},"assertion":[{"value":"1998-12-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"1999-12-14","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"1999-12-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}