{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:37Z","timestamp":1787337217671,"version":"build-2736575974"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>\\noindent A reduced-order modeling methodology based on centroidal Voronoi tessellations (CVTs) is introduced. CVTs are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. For discrete data sets, CVTs are closely related to the h-means and k-means clustering techniques. A discussion of reduced-order modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed from snapshot sets and how they can be applied to the low-cost simulation of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples.<\/jats:p>","DOI":"10.1137\/5106482750342221x","type":"journal-article","created":{"date-parts":[[2006,4,3]],"date-time":"2006-04-03T21:00:16Z","timestamp":1144098016000},"page":"459-484","source":"Crossref","is-referenced-by-count":69,"title":["Centroidal Voronoi Tessellation-Based Reduced-Order Modeling of Complex Systems"],"prefix":"10.1137","volume":"28","author":[{"given":"John","family":"Burkardt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Max","family":"Gunzburger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyung-Chun","family":"Lee","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":"10.1137\/0914030"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Gal Berkooz, Philip Holmes, John Lumley, The proper orthogonal decomposition in the analysis of turbulent flows, Annual Reviews, Palo Alto, CA, 1993, 539\u201357594d:76040","DOI":"10.1146\/annurev.fl.25.010193.002543"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(93)90549-F"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598333181"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1063\/1.857881"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144599352836"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Q. 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Sp\u00e4th,\n                      Cluster Dissection and Analysis, Theory, FORTRAN Programs, Examples\n                      , Ellis Horwood, Chichester, 1985."},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.2307\/2346321"},{"key":"R41","doi-asserted-by":"publisher","DOI":"10.1002\/1521-4001(200102)81:2<83::AID-ZAMM83>3.0.CO;2-R"},{"key":"R42","unstructured":"S. Volkwein,\n                      Proper orthogonal decomposition and singular value decomposition\n                      , Spezialforschungsbereich F003 Optimierung und Kontrolle, Projektbereich Kontinuierliche Optimierung und Kontrolle, Bericht Nr. 153, Graz, 1999."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/5106482750342221x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:05Z","timestamp":1787334605000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/5106482750342221x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/5106482750342221x"],"URL":"https:\/\/doi.org\/10.1137\/5106482750342221x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}