{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:31Z","timestamp":1787337031372,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>In this paper, Fourier analysis is used for finding efficient multigrid components. The individual multigrid components for several discrete partial differential operators are chosen automatically by a genetic optimization method. From a set of multigrid components, such as different smoothers, coarse grid correction components, cycle types, number of smoothing iterations, and relaxation parameters, an optimal three-grid Fourier convergence factor corrected for computational complexity is obtained by the genetic search. The resulting methods can be tuned for optimal efficiency or toward robustness. The analysis results are verified by numerical experiments.<\/jats:p>","DOI":"10.1137\/s1064827501397950","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"924-944","source":"Crossref","is-referenced-by-count":11,"title":["A Genetic Search for Optimal Multigrid Components Within a Fourier Analysis Setting"],"prefix":"10.1137","volume":"24","author":[{"given":"C. W.","family":"Oosterlee","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Wienands","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":"10.1007\/BF02238488"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1977-0431719-X"},{"key":"R3","first-page":"162","volume":"6","author":"Brandt A.","year":"1997","journal-title":"Electron. Trans. Numer. Anal."},{"key":"R4","unstructured":"A. Brandt and S. Ta\u2019asan,\n                      Multigrid method for nearly singular and slightly indefinite problems\n                      , in Proc. EMG\u201985 (Cologne), Multigrid Methods II, W. Hackbusch and U. Trottenberg, eds., Springer, Berlin, 1986, pp. 99\u2013121."},{"key":"R5","unstructured":"D. L. Carroll,\n                      Genetic algorithms and optimizing chemical oxygen\u2010iodine lasers\n                      , in Developments in Theoretical and Applied Mechanics, Vol. XVIII, H. B. Wilson, R. C. Batra, C. W. Bert, A. M. J. Davis, R. A. Schapery, D. S. Stewart, and F. F. Swinson, eds., School of Engineering, University of Alabama, Tuscaloosa, AL, 1996, pp. 411\u2013424."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(83)90016-4"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501357190"},{"key":"R8","unstructured":"D. E. Goldberg,\n                      Genetic Algorithms in Search, Optimization, and Machine Learning\n                      , Addison\u2010Wesley, Reading, MA, 1989."},{"key":"R9","volume-title":"Adaptation in natural and artificial systems","author":"Holland John","year":"1975"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(90)90094-P"},{"key":"R11","unstructured":"K. Krishnakumar,\n                      Microgenetic algorithms for stationary and nonstationary function optimization\n                      , in SPIE Proc. Vol. 1196:"},{"key":"R11","unstructured":"Intelligent Control and Adaptive Systems, G. Rodriguez, ed., International Society for Optical Engineering, Bellingham, WA, 1990, pp. 289\u2013296."},{"key":"R12","unstructured":"M. Mitchell,\n                      An Introduction to Genetic Algorithms\n                      , MIT Press, Cambridge, MA, 1996."},{"key":"R13","unstructured":"J. Ruge, K. St\u00fcben, Algebraic multigrid, Frontiers Appl. Math., Vol. 3, SIAM, Philadelphia, PA, 1987, 73\u2013130972756"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(98)00023-1"},{"key":"R16","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"},{"key":"R17","volume-title":"Multigrid","author":"Trottenberg U.","year":"2001"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021191719400"},{"key":"R19","first-page":"271","volume":"6","author":"Washio T.","year":"1997","journal-title":"Electron. Trans. Numer. Anal."},{"key":"R20","volume-title":"An introduction to multigrid methods","author":"Wesseling Pieter","year":"1992"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599353014"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750037367X"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/0917013"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(90)90252-U"},{"key":"R25","volume-title":"El m\u00e9todo de los elementos finitos. Vol. 1","author":"Zienkiewicz O.","year":"1994"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827501397950","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:41:45Z","timestamp":1787334105000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827501397950"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":26,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S1064827501397950"],"URL":"https:\/\/doi.org\/10.1137\/s1064827501397950","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}