{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:18:46Z","timestamp":1787383126971,"version":"build-2736575974"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>The Monge\u2013Kantorovich grid generation and adaptation scheme of [Delzanno et al., J. Comput. Phys., 227 (2008), pp. 9841\u20139864] is generalized from a variational principle based on $L_{2}$ to a variational principle based on $L_{p}$. A generalized Monge\u2013Amp\u00e8re (MA) equation is derived and its properties are discussed. Results for $p&gt;1$ are obtained and compared in terms of the quality of the resulting grid and a measure of computational performance. We conclude that for the grid generation application, the formulation based on $L_{p}$ for p close to unity can lead to serious problems associated with the boundary. On the other hand, $p\\gg2$ also leads to worse quality grids and performance. Thus, it is concluded that $p=2$ produces the best quality grids, particularly in terms of mean grid cell distortion. Furthermore, the Newton\u2013Krylov methods used to solve the generalized MA equation perform best for $p=2$.<\/jats:p>","DOI":"10.1137\/090749785","type":"journal-article","created":{"date-parts":[[2010,12,2]],"date-time":"2010-12-02T18:09:05Z","timestamp":1291313345000},"page":"3524-3547","source":"Crossref","is-referenced-by-count":4,"title":["Generalized Monge\u2013Kantorovich Optimization for Grid Generation and Adaptation in $L_{p}$"],"prefix":"10.1137","volume":"32","author":[{"given":"G. L.","family":"Delzanno","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. M.","family":"Finn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,12,2]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.07.020"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"J. M. Finn, G. L. Delzanno, and L. Chac\u00f3n,\n                      Grid generation and adaptation by Monge-Kantorovich optimization in two and three dimensions\n                      , in Proceedings of the 17th International Meshing Roundtable, Pittsburgh, PA, 2008, p. 551.","DOI":"10.1007\/978-3-540-87921-3_33"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/39\/19\/S06"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.09.013"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.08.004"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160370306"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598332709"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6395"},{"key":"R9","unstructured":"G. Monge,\n                      M\u00e9moire sur la th\u00e9orie des d\u00e9blais at des remblais\n                      , Histoire de l'Acad\u00e9mie Royale des Sciences de Paris, (1781), pp. 666\u2013704."},{"key":"R10","doi-asserted-by":"crossref","unstructured":"L. C. Evans,\n                      Partial differential equations and Monge-Kantorovich mass transfer\n                      , in Current Developments in Mathematics, R. Bott, A. Jaffe, D. Jerison, G. Lusztig, I. Singer, and S. T. Yau, eds., International Press Incorporated Boston, Cambridge, MA, 1997.","DOI":"10.4310\/CDM.1997.v1997.n1.a2"},{"key":"R11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/memo\/0653","volume":"137","author":"Evans L. C.","year":"1999","journal-title":"Mem. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0065-9266","issn-type":"print"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141002410927"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1023\/B:VISI.0000036836.66311.97"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.896637"},{"key":"R15","unstructured":"L. C. Evans,\n                      Partial Differential Equations\n                      , American Mathematical Society, Providence, RI, 1999."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"C. T. Kelley,\n                      Iterative Methods for Linear and Nonlinear Equations\n                      , SIAM, Philadelphia, 1995.","DOI":"10.1137\/1.9781611970944"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(86)90211-1"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(91)90270-U"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(91)90240-L"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1080\/00036819208840084"},{"key":"R21","unstructured":"G. L.  Delzanno and J. M. Finn,\n                      The fluid dynamic approach to equidistribution methods for grid adaptation\n                      , Comput. Phys., to appear."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090749785","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:35:25Z","timestamp":1787330125000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090749785"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090749785"],"URL":"https:\/\/doi.org\/10.1137\/090749785","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}