{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:42:20Z","timestamp":1760240540262,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T00:00:00Z","timestamp":1562630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We propose a novel deviation-based vertex reordering method for 2D mesh quality improvement. We reorder free vertices based on how likely this is to improve the quality of adjacent elements, based on the gradient of the element quality with respect to the vertex location. Specifically, we prioritize the free vertex with large differences between the best and the worst-quality element around the free vertex. Our method performs better than existing vertex reordering methods since it is based on the theory of non-smooth optimization. The downhill simplex method is employed to solve the mesh optimization problem for improving the worst element quality. Numerical results show that the proposed vertex reordering techniques improve both the worst and average element, compared to those with existing vertex reordering techniques.<\/jats:p>","DOI":"10.3390\/sym11070895","type":"journal-article","created":{"date-parts":[[2019,7,10]],"date-time":"2019-07-10T03:05:26Z","timestamp":1562727926000},"page":"895","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Deviation-Based Dynamic Vertex Reordering Technique for 2D Mesh Quality Improvement"],"prefix":"10.3390","volume":"11","author":[{"given":"Junhyeok","family":"Choi","sequence":"first","affiliation":[{"name":"SK Hynix, Icheon-si, Gyeonggi-do 28429, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harrim","family":"Kim","sequence":"additional","affiliation":[{"name":"Midas Information Technology, Seongnam-si, Gyeonggi-do 13487, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shankar Prasad","family":"Sastry","sequence":"additional","affiliation":[{"name":"C3, 1300 Seaport Boulevard Suite 500, Redwood City, CA 94025, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7172-5039","authenticated-orcid":false,"given":"Jibum","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Incheon National University, Incheon 22012, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,9]]},"reference":[{"key":"ref_1","unstructured":"Shewchuk, J. (2002, January 15\u201318). What is a good linear element? Interpolation, conditioning, and quality measures. Proceedings of the International Meshing Roundtable, Ithaca, NY, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s00366-011-0231-0","article-title":"A numerical investigation on the interplay amongst geometry, meshes, and linear algebra in the finite element solution of elliptic PDEs","volume":"28","author":"Kim","year":"2012","journal-title":"Eng. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1137\/S1064827500371499","article-title":"Algebraic mesh quality metrics","volume":"23","author":"Knupp","year":"2001","journal-title":"SIAM J. Sci. 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(2011, January 23\u201326). A log-barrier method for mesh quality improvement. Proceedings of the International Meshing Roundtable, Paris, France.","DOI":"10.1007\/978-3-642-24734-7_18"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1002\/1097-0207(20000910\/20)49:1\/2<109::AID-NME925>3.0.CO;2-U","article-title":"Local optimization-based simplicial mesh untangling and improvement","volume":"49","author":"Freitag","year":"2000","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_9","unstructured":"Sastry, S. (2015, January 10\u201312). Maximizing the minimum angle with the insertion of steiner vertices. Proceedings of the Canadian Conference on Computational Geometry, Kingston, ON, Canada."},{"key":"ref_10","unstructured":"Shontz, S., and Knupp, P. (2008, January 12\u201315). The effect of vertex ordering on 2D local mesh optimization efficiency. Proceedings of the International Meshing Roundtable, Pittsburgh, PA, USA."},{"key":"ref_11","unstructured":"Park, J., Knupp, P., and Shontz, S. (June, January 31). Static vertex reordering schemes for local mesh quality improvement. Proceedings of the CSRI Summer Proceedings, Albuquerque, NM, USA."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Strout, M., Osheim, N., and Rostron, D. (2009, January 25\u201327). Evaluation of hierarchical mesh reordering. Proceedings of the International Conference on Computational Science, Baton Rouge, LO, USA.","DOI":"10.1007\/978-3-642-01970-8_53"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Aupy, G., Park, J., and Raghavan, P. (2016, January 16\u201319). Locality-aware Laplacian mesh smoothing. Proceedings of the International Conference on Parallel Processing, Philadelphia, PA, USA.","DOI":"10.1109\/ICPP.2016.74"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1007\/s10107-006-0014-3","article-title":"Mesh shape-quality optimization using the inverse mean-ratio metric","volume":"110","author":"Munson","year":"2007","journal-title":"Math. Program."},{"key":"ref_15","first-page":"264741","article-title":"A derivative-free mesh optimization algorithm for mesh quality improvement and untangling","volume":"2015","author":"Kim","year":"2015","journal-title":"Math. Probl. Eng."},{"key":"ref_16","unstructured":"Nocedal, J., and Wright, S. (2006). Numerical Optimization, Springer. [2nd ed.]."},{"key":"ref_17","unstructured":"Brewer, M., Diachin, L., and Knupp, P. (2003, January 14\u201317). The mesquite mesh quality improvement toolkit. Proceedings of the International Meshing Roundtable, Santa Fe, NM, USA."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/7\/895\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:03:50Z","timestamp":1760187830000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/7\/895"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,9]]},"references-count":17,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["sym11070895"],"URL":"https:\/\/doi.org\/10.3390\/sym11070895","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,7,9]]}}}