{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T19:21:53Z","timestamp":1790882513361,"version":"4.1.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:00:00Z","timestamp":1689120000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:00:00Z","timestamp":1689120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100006227","name":"Lawrence Livermore National Laboratory","doi-asserted-by":"publisher","award":["B648806"],"award-info":[{"award-number":["B648806"]}],"id":[{"id":"10.13039\/100006227","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s00366-023-01869-w","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T19:01:55Z","timestamp":1689188515000},"page":"1375-1396","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Seventeen criteria for evaluating Jacobian-based optimization metrics"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4217-6787","authenticated-orcid":false,"given":"Patrick","family":"Knupp","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,12]]},"reference":[{"key":"1869_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0378-4754(98)00074-3","volume":"46","author":"P Barrera-Sanchez","year":"1998","unstructured":"Barrera-Sanchez P, Tinoco-Ruiz J (1998) Smooth and convex grid generation over general plane regions. Math Comput Simul 46:87\u2013102","journal-title":"Math Comput Simul"},{"key":"1869_CR2","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1016\/0021-9991(82)90020-1","volume":"46","author":"J Brackbill","year":"1981","unstructured":"Brackbill J, Saltzman J (1981) Adaptive zoning for singular problems in two dimensions. J Comput Phys 46:342\u2013368","journal-title":"J Comput Phys"},{"key":"1869_CR3","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1137\/0912025","volume":"12","author":"J Castillo","year":"1991","unstructured":"Castillo J (1991) A discrete variational grid generation method. SIAM J Sci Comput 12:454\u2013468","journal-title":"SIAM J Sci Comput"},{"issue":"4","key":"1869_CR4","doi-asserted-by":"publisher","first-page":"1252","DOI":"10.1137\/S1064827594274760","volume":"20","author":"V de Almeida","year":"1999","unstructured":"de Almeida V (1999) Domain deformation mapping: application to variational mesh generation. SIAM J Sci Comput 20(4):1252\u20131275","journal-title":"SIAM J Sci Comput"},{"issue":"1","key":"1869_CR5","doi-asserted-by":"publisher","first-page":"B50","DOI":"10.1137\/18M1167206","volume":"41","author":"V Dobrev","year":"2019","unstructured":"Dobrev V, Knupp P, Kolev T, Mittal K, Tomov V (2019) The target-matrix optimization paradigm for high-order meshes. SIAM J Sci Comput 41(1):B50\u2013B68","journal-title":"SIAM J Sci Comput"},{"key":"1869_CR6","doi-asserted-by":"crossref","unstructured":"Dobrev V, Knupp P, Kolev T, Tomov V (2019) Towards simulation-driven optimization of high-order meshes by the target-matrix optimization paradigm. In: International meshing roundtable. Springer Intl. Pub., p 285\u2013302","DOI":"10.1007\/978-3-030-13992-6_16"},{"key":"1869_CR7","doi-asserted-by":"publisher","first-page":"104602","DOI":"10.1016\/j.compfluid.2020.104602","volume":"208","author":"V Dobrev","year":"2020","unstructured":"Dobrev V, Knupp P, Kolev T, Rieben R, Tomov V (2020) Simulation-driven optimization of high-order meshes in ALE hydrodynamics. Comput Fluids 208:104602","journal-title":"Comput Fluids"},{"issue":"4","key":"1869_CR8","doi-asserted-by":"publisher","first-page":"3721","DOI":"10.1007\/s00366-021-01407-6","volume":"38","author":"V Dobrev","year":"2022","unstructured":"Dobrev V, Knupp P, Kolev TZ, Mittal K, Tomov V (2022) hr-adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm. Eng Comput 38(4):3721\u20133737","journal-title":"Eng Comput"},{"issue":"2","key":"1869_CR9","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1016\/0021-9991(91)90285-S","volume":"95","author":"A Dvinsky","year":"1991","unstructured":"Dvinsky A (1991) Adaptive grid generation from harmonic maps on Riemannian manifolds. J Comput Phys 95(2):450\u2013476","journal-title":"J Comput Phys"},{"key":"1869_CR10","doi-asserted-by":"publisher","first-page":"1377","DOI":"10.1002\/nme.341","volume":"53","author":"L Freitag","year":"2002","unstructured":"Freitag L, Knupp P (2002) Tetrahedral mesh improvement via optimization of the element condition number. Int J Numer Methods Eng 53:1377\u20131391","journal-title":"Int J Numer Methods Eng"},{"issue":"9","key":"1869_CR11","doi-asserted-by":"publisher","first-page":"1561","DOI":"10.1134\/S0965542510090095","volume":"50","author":"V Garanzha","year":"2010","unstructured":"Garanzha V (2010) Polyconvex potentials, invertible deformations, and thermodynamically consistent formulation of the non-linear elasticity equations. Comput Math Math Phys 50(9):1561\u20131587","journal-title":"Comput Math Math Phys"},{"key":"1869_CR12","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.cam.2014.03.006","volume":"269","author":"V Garanzha","year":"2014","unstructured":"Garanzha V, Kudryavtseva L, Utyuzhnikov S (2014) Variational method for untangling and optimization of spatial meshes. J Comput Appl Math 269:24\u201341","journal-title":"J Comput Appl Math"},{"key":"1869_CR13","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1016\/j.jcp.2004.10.024","volume":"204","author":"W Huang","year":"2005","unstructured":"Huang W (2005) Metric tensors for anisotropic mesh generation. J Comput Phys 204:663\u2013665","journal-title":"J Comput Phys"},{"key":"1869_CR14","doi-asserted-by":"crossref","unstructured":"Ivanenko S (1999) Harmonic mappings, handbook of grid generation. CRC Press","DOI":"10.1201\/9781420050349.ch8"},{"issue":"4","key":"1869_CR15","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s00366-011-0230-1","volume":"28","author":"P Knupp","year":"2012","unstructured":"Knupp P (2012) Introducing the target matrix paradigm for mesh optimization via node movement. Eng Comput 28(4):419\u2013429","journal-title":"Eng Comput"},{"key":"1869_CR16","doi-asserted-by":"publisher","unstructured":"Tomov VZ, Gu X, Verdicchio J (2021) Proceedings of the 29th International Meshing Roundtable. 28th International Meshing Roundtable (IMR), Virtual Conference, Zenodo. https:\/\/doi.org\/10.5281\/zenodo.5551173","DOI":"10.5281\/zenodo.5551173"},{"issue":"5","key":"1869_CR17","doi-asserted-by":"publisher","first-page":"4451","DOI":"10.1007\/s00366-022-01653-2","volume":"38","author":"P Knupp","year":"2022","unstructured":"Knupp P (2022) A target construction methodology for mesh quality improvement. Eng Comput 38(5):4451\u20134474","journal-title":"Eng Comput"},{"key":"1869_CR18","volume":"5","author":"P Knupp","year":"2022","unstructured":"Knupp P (2022) Geometric parameters in the target matrix mesh optimization paradigm. Part Differ Equ Appl Math 5:100390","journal-title":"Part Differ Equ Appl Math"},{"issue":"6","key":"1869_CR19","doi-asserted-by":"publisher","first-page":"5695","DOI":"10.1007\/s00366-022-01753-z","volume":"38","author":"P Knupp","year":"2022","unstructured":"Knupp P (2022) Worst case mesh quality in the target matrix optimization paradigm. Eng Comput 38(6):5695\u20135711","journal-title":"Eng Comput"},{"key":"1869_CR20","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1002\/nme.2347","volume":"76","author":"E Lopez","year":"2008","unstructured":"Lopez E, Nigro N, Storti M (2008) Simultaneous untangling and smoothing of moving grids. Int J Numer Methods Eng 76:994\u20131019","journal-title":"Int J Numer Methods Eng"},{"key":"1869_CR21","unstructured":"Shewchuk J (2002) What is a good Linear Finite Element? Unpublished, UC Berkeley. https:\/\/people.eecs.berkeley.edu\/~jrs\/papers\/elemj.pdf. Accessed Nov 2022"},{"issue":"1","key":"1869_CR22","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1002\/num.1690020107","volume":"2","author":"S Steinberg","year":"1986","unstructured":"Steinberg S, Roache P (1986) Variational grid generation. Numer Methods Part Differ Equ 2(1):71\u201396","journal-title":"Numer Methods Part Differ Equ"},{"issue":"1","key":"1869_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/cnm.1067","volume":"25","author":"Y Zhang","year":"2009","unstructured":"Zhang Y, Bajaj C, Xu G (2009) Surface smoothing and quality improvement of quadrilateral\/hexahedral meshes with geometric flow. J Commun Num Methods Eng 25(1):1\u201318","journal-title":"J Commun Num Methods Eng"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01869-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01869-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01869-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T09:06:30Z","timestamp":1719911190000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01869-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,12]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["1869"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01869-w","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,12]]},"assertion":[{"value":"9 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 July 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}