{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:31:31Z","timestamp":1787337091926,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>A multilevel nonlinear method (MNM) for the numerical solution of nonlinear partial differential equations is developed. The MNM algorithm is motivated and analyzed using a simplified model which retains the essential features of the new approach. It is thereby shown to combine the advantages of the two classical multigrid approaches to nonlinear problems. The analysis is supported by numerical tests for nonlinear differential equations in one and two dimensions.<\/jats:p>","DOI":"10.1137\/040613809","type":"journal-article","created":{"date-parts":[[2006,3,15]],"date-time":"2006-03-15T21:00:21Z","timestamp":1142456421000},"page":"24-46","source":"Crossref","is-referenced-by-count":18,"title":["A Multilevel Nonlinear Method"],"prefix":"10.1137","volume":"28","author":[{"given":"Irad","family":"Yavneh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gregory","family":"Dardyk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431719-X"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Achi Brandt, Guide to multigrid development, Lecture Notes in Math., Vol. 960, Springer, Berlin, 1982, 220\u201331284k:65124","DOI":"10.1007\/BFb0069930"},{"key":"R3","unstructured":"A. Brandt, S. McCormick, J. Ruge, Algebraic multigrid (AMG) for sparse matrix equations, Cambridge Univ. Press, Cambridge, 1985, 257\u201328486m:65038"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(92)90049-5"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719505"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/nla.380"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0913028"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(82)90057-2"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(83)90016-4"},{"key":"R10","volume-title":"Numerical methods for unconstrained optimization and nonlinear equations","author":"Dennis John","year":"1983"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6067"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6698"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6671"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02427-0"},{"key":"R15","unstructured":", Multigrid methods, Proceedings of the Conference held in Cologne, November 23\u201327, 1981, Lecture Notes in Mathematics, Vol. 960, Springer\u2010Verlag, 1982, 0\u20130, vii+65284b:65007"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/prot.340180304"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.540160308"},{"key":"R18","first-page":"56","volume":"10","author":"Korsawe Johannes","year":"2000","journal-title":"Electron. Trans. Numer. Anal."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0914058"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(94)00061-K"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595284841"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"J. Ruge, K. St\u00fcben, Algebraic multigrid, Frontiers Appl. Math., Vol. 3, SIAM, Philadelphia, PA, 1987, 73\u2013130972756","DOI":"10.1137\/1.9781611971057.ch4"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/s006070070028"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598339384"},{"key":"R25","volume-title":"Multigrid","author":"Trottenberg U.","year":"2001"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.2136\/sssaj1980.03615995004400050002x"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/0917016"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/0731090"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/040613809","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:44:22Z","timestamp":1787334262000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/040613809"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":28,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/040613809"],"URL":"https:\/\/doi.org\/10.1137\/040613809","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}