{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T20:55:11Z","timestamp":1760820911055,"version":"3.41.0"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2017,7,24]],"date-time":"2017-07-24T00:00:00Z","timestamp":1500854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["OCI-1148116"],"award-info":[{"award-number":["OCI-1148116"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Computational Infrastructure in Geodynamics initiative (CIG) through the National Science Foundation","award":["EAR-0949446"],"award-info":[{"award-number":["EAR-0949446"]}]},{"DOI":"10.13039\/100007707","name":"University of California at Davis","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100007707","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2018,3,31]]},"abstract":"<jats:p>Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each edge relates to that of neighboring cells. However, we can simplify data structures and algorithms if we can a priori orient coordinate systems in such a way that the coordinate systems on the edges follow uniquely from those on the cells by rule.<\/jats:p>\n          <jats:p>\n            Such rules require that every unstructured mesh allow the assignment of directions to edges that satisfy the convention in adjacent cells. We show that the convention chosen for unstructured quadrilateral meshes in the\n            <jats:sc>deal.II<\/jats:sc>\n            library always allows to orient meshes. It can therefore be used to make codes simpler, faster, and less bug prone. We present an algorithm that orients meshes in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>N<\/jats:italic>\n            ) operations. We then show that consistent orientations are not always possible for 3D hexahedral meshes. Thus, cells generally need to store the direction of adjacent edges, but our approach also allows the characterization of cases where this is not necessary. The 3D extension of our algorithm either orients edges consistently, or aborts, both within\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>N<\/jats:italic>\n            ) steps.\n          <\/jats:p>","DOI":"10.1145\/3061708","type":"journal-article","created":{"date-parts":[[2017,7,24]],"date-time":"2017-07-24T12:52:34Z","timestamp":1500900754000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["On Orienting Edges of Unstructured Two- and Three-Dimensional Meshes"],"prefix":"10.1145","volume":"44","author":[{"given":"Rainer","family":"Agelek","sequence":"first","affiliation":[{"name":"Heidelberg, Germany"}]},{"given":"Michael","family":"Anderson","sequence":"additional","affiliation":[{"name":"DownUnder GeoSolutions, Perth, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2311-9402","authenticated-orcid":false,"given":"Wolfgang","family":"Bangerth","sequence":"additional","affiliation":[{"name":"Colorado State University, Fort Collins, CO"}]},{"given":"William L.","family":"Barth","sequence":"additional","affiliation":[{"name":"University of Texas at Austin, Austin, TX"}]}],"member":"320","published-online":{"date-parts":[[2017,7,24]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.847"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1268776.1268779"},{"key":"e_1_2_1_3_1","unstructured":"W. Bangerth T. Heister L. Heltai G. Kanschat M. Kronbichler M. Maier B. Turcksin and T. D. Young. 2015. The deal.II library version 8.2. Archive of Numerical Software 3 100 1--8.  W. Bangerth T. Heister L. Heltai G. Kanschat M. Kronbichler M. Maier B. Turcksin and T. D. Young. 2015. The deal.II library version 8.2. Archive of Numerical Software 3 100 1--8."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-008-0004-9"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/513001.513007"},{"volume-title":"Graduate Texts in Mathematics","author":"Bredon E.","key":"e_1_2_1_6_1"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2015.02.008"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2579"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-007-0629-4"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02570709"},{"key":"e_1_2_1_11_1","unstructured":"M. Homolya and D. A. Ham. 2015. A parallel edge orientation algorithm for quadrilateral meshes. arXiv:1505.03357. http:\/\/arxiv.org\/abs\/1505.03357  M. Homolya and D. A. Ham. 2015. A parallel edge orientation algorithm for quadrilateral meshes. arXiv:1505.03357. http:\/\/arxiv.org\/abs\/1505.03357"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-006-0049-3"},{"volume-title":"Lectures on General Algebra","author":"Kurosh A. G.","key":"e_1_2_1_13_1"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-7940-7"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2941-2"},{"volume-title":"Elements of Algebraic Topology","author":"Munkres J.","key":"e_1_2_1_16_1","doi-asserted-by":"crossref","DOI":"10.1201\/9780429493911"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/08073901X"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2004.10504548"},{"volume-title":"Calculus on Manifolds","author":"Spivak M.","key":"e_1_2_1_19_1","doi-asserted-by":"crossref","DOI":"10.1201\/9780429501906"},{"key":"e_1_2_1_20_1","unstructured":"D. Teleaga and J. Lang. 2008. Numerically Solving Maxwell\u2019s Equations: Implementation Issues for Magnetoquasistatics in KARDOS. Technical Report. TU Darmstadt.  D. Teleaga and J. Lang. 2008. Numerically Solving Maxwell\u2019s Equations: Implementation Issues for Magnetoquasistatics in KARDOS. Technical Report. TU Darmstadt."}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3061708","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3061708","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3061708","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:03:27Z","timestamp":1750215807000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3061708"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,24]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,3,31]]}},"alternative-id":["10.1145\/3061708"],"URL":"https:\/\/doi.org\/10.1145\/3061708","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"type":"print","value":"0098-3500"},{"type":"electronic","value":"1557-7295"}],"subject":[],"published":{"date-parts":[[2017,7,24]]},"assertion":[{"value":"2015-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-03-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-07-24","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}