{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T22:19:52Z","timestamp":1773785992895,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T00:00:00Z","timestamp":1640304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ERDF - European Regional Development Fund","award":["KK.01.2.1.01.0124"],"award-info":[{"award-number":["KK.01.2.1.01.0124"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper presents an algorithm for the fully automatic mesh generation for the finite element analysis of ships and offshore structures. The quality requirements on the mesh generator are imposed by the acceptance criteria of the classification societies as well as the need to avoid shear locking when using low degree shell elements. The meshing algorithm will be generating quadrilateral dominated meshes (consisting of quads and triangles) and the mesh quality requirements mandate that quadrilaterals with internal angles close to 90\u00b0 are to be preferred. The geometry is described by a dictionary containing points, rods, surfaces, and openings. The first part of the proposed method consists of an algorithm to automatically clean the geometry. The corrected geometry is then meshed by the frontal Delaunay mesh generator as implemented in the gmsh package. We present a heuristic method to precondition the cross field of the fronatal quadrilateral mesher. In addition, the influence of the order in which the plates are meshed will be explored as a preconditioning step.<\/jats:p>","DOI":"10.3390\/a15010002","type":"journal-article","created":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T08:38:46Z","timestamp":1640335126000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Preconditioning the Quad Dominant Mesh Generator for Ship Structural Analysis"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3370-9353","authenticated-orcid":false,"given":"Luka","family":"Grubi\u0161i\u0107","sequence":"first","affiliation":[{"name":"Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia"}]},{"given":"Domagoj","family":"Lacmanovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1792-6056","authenticated-orcid":false,"given":"Josip","family":"Tamba\u010da","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nersesian, R., and Mahmood, S. (2009). International Association of Classification Societies: Handbook of Transnational Economic Governance Regimes, Brill|Nijhoff.","DOI":"10.1163\/ej.9789004163300.i-1081.675"},{"key":"ref_2","unstructured":"Hughes, O., and Paik, J.K. (2010). Ship Structural Analysis and Design, The Society of Naval Architects and Marine Engineers."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1002\/nme.2579","article-title":"Gmsh: A 3D finite element mesh generator with built-in pre- and post-processing facilities","volume":"79","author":"Geuzaine","year":"2009","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_4","unstructured":"Grubi\u0161i\u0107, L., Lacmanovi\u0107, D., and Tamba\u010da, J. (2021, January 6\u20138). Automatic mesh generation for structural analysis in naval architecture. Proceedings of the International Conference on Ships and Offshore Structures ICSOS 2021, Hamburg, Germany. 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Methods Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1002\/nme.1620240603","article-title":"Robust, geometrically based, automatic two-dimensional mesh generation","volume":"24","author":"Baehmann","year":"1987","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.proeng.2014.10.395","article-title":"QMCF: QMorph Cross Field-driven Quad-dominant Meshing Algorithm","volume":"82","author":"Pellenard","year":"2014","journal-title":"Procedia Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1102","DOI":"10.1002\/nme.3279","article-title":"Blossom-Quad: A non-uniform quadrilateral mesh generator using a minimum-cost perfect-matching algorithm","volume":"89","author":"Remacle","year":"2012","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_11","first-page":"119","article-title":"Lp Centroidal Voronoi Tessellation and Its Applications","volume":"29","author":"Liu","year":"2010","journal-title":"ACM Trans. Graph."},{"key":"ref_12","first-page":"55","article-title":"Maximum matching and a polyhedron with 0,1-vertices","volume":"69","author":"Edmonds","year":"1965","journal-title":"J. Res. Natl. Bur. Stand. Sect. B Math. Math. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1002\/nme.4458","article-title":"A frontal Delaunay quad mesh generator using the L\u221e norm","volume":"94","author":"Remacle","year":"2013","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1186\/2213-7467-1-8","article-title":"A frontal approach to hex-dominant mesh generation","volume":"1","author":"Baudouin","year":"2014","journal-title":"Adv. Model. Simul. Eng. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1137\/S0036144599352836","article-title":"Centroidal Voronoi Tessellations: Applications and Algorithms","volume":"41","author":"Du","year":"1999","journal-title":"SIAM Rev."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/1\/2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:52:36Z","timestamp":1760169156000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/1\/2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,24]]},"references-count":15,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["a15010002"],"URL":"https:\/\/doi.org\/10.3390\/a15010002","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202112.0279.v1","asserted-by":"object"}]},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,24]]}}}