{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:28:41Z","timestamp":1787336921934,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:p>An efficient multigrid approach for solving a discretized elliptic equation whose boundary values are determined in part by integral relations is developed, analyzed, and tested. The algorithm is motivated by a problem that is solved during integration of the 3D quasigeostrophic (QG) equations, which model large-scale rotating stratifiedflows, where the integral constraints represent mass conservation.<\/jats:p>","DOI":"10.1137\/s1064827597331813","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1357-1369","source":"Crossref","is-referenced-by-count":3,"title":["Multigrid Solution of an Elliptic Boundary-Value Problem with Integral Constraints"],"prefix":"10.1137","volume":"21","author":[{"given":"Achi","family":"Brandt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Moshe","family":"Israeli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Irad","family":"Yavneh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew","family":"Siegel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"A. Brandt,\n                      Multigrid Techniques: 1984 with Applications to Fluid Dynamics\n                      , GMD\u2010Studien 85, Gesellschaft f\u00fcr Mathematik and Datenverarbeitung m. b. H., Bonn, St. Augustin, West Germany, 1984."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0731087"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139168489"},{"key":"R4","unstructured":"E. Hairer, S. P. N\u00f8rsett, and G. Wanner,\n                      Solving Ordinary Differential Equations I. Nonstiff Problems\n                      , 2nd ed., Springer\u2010Verlag, Berlin, Heidelberg, 1993."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(90)90047-4"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0485(1990)020<1349:ALBMOW>2.0.CO;2"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780195108088.001.0001"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"Klaus St\u00fcben, Ulrich Trottenberg, Multigrid methods: fundamental algorithms, model problem analysis and applications, Lecture Notes in Math., Vol. 960, Springer, Berlin, 1982, 1\u201317684m:65129","DOI":"10.1007\/BFb0069928"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/0732051"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/0917013"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596310998"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827597331813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:36:43Z","timestamp":1787333803000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827597331813"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1137\/S1064827597331813"],"URL":"https:\/\/doi.org\/10.1137\/s1064827597331813","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}