{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T17:19:21Z","timestamp":1700587161758},"reference-count":13,"publisher":"ASME International","issue":"4","content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2005,12,1]]},"abstract":"<jats:p>The formulation of a local cell quality metric [Branets, L., and Carey, G. F., 2003, Proceedings of the 12th International Meshing Roundtable, Santa Fe, NM, pp. 371\u2013378;Engineering with Computers (in press)] for standard elements defined by affine maps is extended here to the case of elements with quadratically curved boundaries. We show for two-dimensional and three-dimensional simplex elements with quadratically curved boundaries that all cases of map degeneracy can be identified by the metric. Moreover, we establish a \u201cmaximum principle\u201d which allows estimating the bounds on the quality metric. The nondegeneracy conditions for biquadratic quadrilaterals with one curved edge are also determined. The metric is implemented in an untangling\/smoothing algorithm for improving unstructured meshes including simplex elements that have curved boundary segments. The behavior and efficiency of this algorithm is illustrated for numerical test problems in two and three dimensions.<\/jats:p>","DOI":"10.1115\/1.2052827","type":"journal-article","created":{"date-parts":[[2005,11,4]],"date-time":"2005-11-04T18:14:06Z","timestamp":1131128046000},"page":"302-308","update-policy":"http:\/\/dx.doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":10,"title":["Extension of a Mesh Quality Metric for Elements With a Curved Boundary Edge or Surface"],"prefix":"10.1115","volume":"5","author":[{"given":"Larisa","family":"Branets","sequence":"first","affiliation":[{"name":"Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 E. 24th St., ACES 6.430, 1 University Station C0200, Austin, TX 78712-0227"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Graham F.","family":"Carey","sequence":"additional","affiliation":[{"name":"Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 201 E. 24th St., ACES 6.430, 1 University Station C0200, Austin, TX 78712-0227"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2004,6,15]]},"reference":[{"key":"2019100319290170200_c1","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1002\/nme.1620370510","article-title":"Inverse Mapping and Distortion Measures for Quadrilaterals with Curved Boundaries","volume":"37","author":"Yuan","journal-title":"Int. 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Appl.","ISSN":"http:\/\/id.crossref.org\/issn\/0020-2932","issn-type":"print"},{"key":"2019100319290170200_c5","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1002\/nme.1620190602","article-title":"Algorithms for Determining Invertible Two- and Three-Dimensional Quadratic Isoparametric Finite Element Transformations","volume":"19","author":"Field","journal-title":"Int. J. Numer. Methods Eng.","ISSN":"http:\/\/id.crossref.org\/issn\/0029-5981","issn-type":"print"},{"key":"2019100319290170200_c6","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1002\/cnm.1630030614","article-title":"A Note on Invertible Two-Dimensional Quadratic Finite Element Transformations","volume":"3","author":"Baart","journal-title":"Commun. Appl. Numer. Methods","ISSN":"http:\/\/id.crossref.org\/issn\/0748-8025","issn-type":"print"},{"key":"2019100319290170200_c7","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1090\/S0025-5718-1978-0474877-4","article-title":"Some Results on the Global Inversion of Bilinear and Quadratic Isoparametric Finite Element Transformations","volume":"32","author":"Frey","journal-title":"Math. Comput.","ISSN":"http:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"2019100319290170200_c8","first-page":"371","article-title":"A Local Cell Quality Metric and Variational Grid Smoothing Algorithm","volume-title":"Proceedings of the 12th International Meshing Roundtable","author":"Branets"},{"key":"2019100319290170200_c9","unstructured":"Branets, L., and Carey, G. F., \u201cA Local Cell Quality Metric and Variational Grid Smoothing Algorithm,\u201d Engineering with Computers (in press)."},{"key":"2019100319290170200_c10","first-page":"45","article-title":"Global Condition Number of Trilinear Mapping. Application to 3D Grid Generation","volume-title":"Proceedings of the Minisymposium in the International Conference, \u201cOptimization of finite-element approximations, splines and wavelets,\u201d","author":"Branets"},{"key":"2019100319290170200_c11","first-page":"1617","article-title":"Barrier Variational Generation of Quasi-Isometric Grids","volume":"40","author":"Garanzha","journal-title":"Computational Mathematics and Mathematical Physics"},{"key":"2019100319290170200_c12","doi-asserted-by":"crossref","volume-title":"Analysis of Finite Element Method","author":"Strang","DOI":"10.1115\/1.3423272"},{"key":"2019100319290170200_c13","first-page":"333","article-title":"Smoothing and Adaptive Redistribution for Grids with Irregular Valence and Hanging Nodes","volume-title":"Proceedings of the 13th International Meshing Roundtable","author":"Branets"}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/5\/4\/302\/5774428\/302_1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/5\/4\/302\/5774428\/302_1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T19:29:14Z","timestamp":1570130954000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/5\/4\/302\/474327\/Extension-of-a-Mesh-Quality-Metric-for-Elements"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,6,15]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,12,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.2052827","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,6,15]]}}}