{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,30]],"date-time":"2025-08-30T16:35:08Z","timestamp":1756571708842,"version":"3.37.3"},"reference-count":112,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T00:00:00Z","timestamp":1738108800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T00:00:00Z","timestamp":1738108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s10915-024-02779-9","type":"journal-article","created":{"date-parts":[[2025,1,29]],"date-time":"2025-01-29T09:22:19Z","timestamp":1738142539000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Body-Fitted Tracking Within a Surface via a Level Set Based Mesh Evolution Method"],"prefix":"10.1007","volume":"102","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5913-2847","authenticated-orcid":false,"given":"C.","family":"Brito-Pacheco","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Dapogny","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,1,29]]},"reference":[{"key":"2779_CR1","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1002\/(SICI)1097-0312(199612)49:12<1339::AID-CPA5>3.0.CO;2-B","volume":"49","author":"R Abgrall","year":"1996","unstructured":"Abgrall, R.: Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes. Commun. Pure Appl. Math. 49, 1339\u20131373 (1996)","journal-title":"Commun. Pure Appl. Math."},{"key":"2779_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9286-6","volume-title":"Shape Optimization by the Homogenization Method","author":"G Allaire","year":"2002","unstructured":"Allaire, G.: Shape Optimization by the Homogenization Method, vol. 146. Springer, New York (2002)"},{"key":"2779_CR3","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1051\/cocv\/2013076","volume":"20","author":"G Allaire","year":"2014","unstructured":"Allaire, G., Dapogny, C., Delgado, G., Michailidis, G.: Multi-phase structural optimization via a level set method. ESAIM Control Optim. Calc. Var. 20, 576\u2013611 (2014)","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"2779_CR4","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1016\/j.crma.2011.08.012","volume":"349","author":"G Allaire","year":"2011","unstructured":"Allaire, G., Dapogny, C., Frey, P.: Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. C.R. Math. 349, 999\u20131003 (2011)","journal-title":"C.R. Math."},{"key":"2779_CR5","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1007\/s00158-013-0929-2","volume":"48","author":"G Allaire","year":"2013","unstructured":"Allaire, G., Dapogny, C., Frey, P.: A mesh evolution algorithm based on the level set method for geometry and topology optimization. Struct. Multidiscip. Optim. 48, 711\u2013715 (2013)","journal-title":"Struct. Multidiscip. Optim."},{"key":"2779_CR6","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.cma.2014.08.028","volume":"282","author":"G Allaire","year":"2014","unstructured":"Allaire, G., Dapogny, C., Frey, P.: Shape optimization with a level set based mesh evolution method. Comput. Methods Appl. Mech. Eng. 282, 22\u201353 (2014)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2779_CR7","doi-asserted-by":"crossref","unstructured":"Allaire, G., Dapogny, C., Jouve, F.: Shape and topology optimization. In: Bonito, A., Nochetto, R. (eds.) Geometric partial differential equations, part II. Handbook of Numerical Analysis, vol. 22, pp.\u00a01\u2013132 (2021)","DOI":"10.1016\/bs.hna.2020.10.004"},{"key":"2779_CR8","volume-title":"Conception Optimale de Structures","author":"G Allaire","year":"2007","unstructured":"Allaire, G., Schoenauer, M.: Conception Optimale de Structures, vol. 58. Springer, Berlin (2007)"},{"key":"2779_CR9","volume-title":"Geometric Evolution Problems, Distance Function and Viscosity Solutions","author":"L Ambrosio","year":"2000","unstructured":"Ambrosio, L., Dancer, N., Ambrosio, L.: Geometric Evolution Problems, Distance Function and Viscosity Solutions. Springer, Berlin (2000)"},{"key":"2779_CR10","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1007\/s10444-018-9650-4","volume":"45","author":"M Ambroz","year":"2019","unstructured":"Ambroz, M., Bala\u017eovjech, M., Medl\u2019a, M., Mikula, K.: Numerical modeling of wildland surface fire propagation by evolving surface curves. Adv. Comput. Math. 45, 1067\u20131103 (2019)","journal-title":"Adv. Comput. Math."},{"key":"2779_CR11","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1088\/0266-5611\/20\/3\/003","volume":"20","author":"HB Ameur","year":"2004","unstructured":"Ameur, H.B., Burger, M., Hackl, B.: Level set methods for geometric inverse problems in linear elasticity. Inverse Prob. 20, 673 (2004)","journal-title":"Inverse Prob."},{"key":"2779_CR12","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.camwa.2020.06.009","volume":"81","author":"R Anderson","year":"2021","unstructured":"Anderson, R., Andrej, J., Barker, A., Bramwell, J., Camier, J.-S., Cerveny, J., Dobrev, V., Dudouit, Y., Fisher, A., Kolev, T., et al.: MFEM: A modular finite element methods library. Comput. Math. Appl. 81, 42\u201374 (2021)","journal-title":"Comput. Math. Appl."},{"key":"2779_CR13","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1137\/080719583","volume":"47","author":"B Ayuso","year":"2009","unstructured":"Ayuso, B., Marini, L.D.: Discontinuous Galerkin methods for advection\u2013diffusion\u2013reaction problems. SIAM J. Numer. Anal. 47, 1391\u20131420 (2009)","journal-title":"SIAM J. Numer. Anal."},{"key":"2779_CR14","unstructured":"Baggag, A., Atkins, H., Keyes, D.: Parallel implementation of the discontinuous Galerkin method, tech. rep. (1999)"},{"key":"2779_CR15","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/s003660200017","volume":"18","author":"TJ Baker","year":"2002","unstructured":"Baker, T.J.: Mesh movement and metamorphosis. Eng. Comput. 18, 188\u2013198 (2002)","journal-title":"Eng. Comput."},{"key":"2779_CR16","doi-asserted-by":"crossref","unstructured":"Balarac, G., Basile, F., B\u00e9nard, P., Bordeu, F., Chapelier, J.-B., Cirrottola, L., Caumon, G., Dapogny, C., Frey, P., Froehly, A. et\u00a0al.: Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing. Maths in Action (2021, to appear)","DOI":"10.5802\/msia.22"},{"key":"2779_CR17","doi-asserted-by":"crossref","first-page":"2217","DOI":"10.1016\/j.combustflame.2009.07.010","volume":"156","author":"JH Balbi","year":"2009","unstructured":"Balbi, J.H., Morandini, F., Silvani, X., Filippi, J.B., Rinieri, F.: A physical model for wildland fires. Combust. Flame 156, 2217\u20132230 (2009)","journal-title":"Combust. Flame"},{"key":"2779_CR18","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1080\/00102200701484449","volume":"179","author":"J-H Balbi","year":"2007","unstructured":"Balbi, J.-H., Rossi, J.-L., Marcelli, T., Santoni, P.-A.: A 3D physical real-time model of surface fires across fuel beds. Combust. Sci. Technol. 179, 2511\u20132537 (2007)","journal-title":"Combust. Sci. Technol."},{"key":"2779_CR19","doi-asserted-by":"crossref","unstructured":"Filippi, J.\u00a0Baptiste, Bosseur, F., Mari, C., Lac, C., Le\u00a0Moigne, P., Cuenot, B., Veynante, D., Cariolle, D., Balbi, J.-H.: Coupled atmosphere-wildland fire modelling. J. Adv. Model. Earth Syst. 1 (2009)","DOI":"10.3894\/JAMES.2009.1.11"},{"key":"2779_CR20","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s00366-018-0607-5","volume":"35","author":"N Barral","year":"2019","unstructured":"Barral, N., Alauzet, F.: Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach. Eng. Comput. 35, 397\u2013422 (2019)","journal-title":"Eng. Comput."},{"key":"2779_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jcph.1998.6007","volume":"145","author":"TJ Barth","year":"1998","unstructured":"Barth, T.J., Sethian, J.A.: Numerical schemes for the Hamilton\u2013Jacobi and level set equations on triangulated domains. J. Comput. Phys. 145, 1\u201340 (1998)","journal-title":"J. Comput. Phys."},{"key":"2779_CR22","volume-title":"Topology Optimization: Theory, Methods, and Applications","author":"MP Bendsoe","year":"2013","unstructured":"Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer, Berlin (2013)"},{"key":"2779_CR23","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1006\/jcph.2001.6937","volume":"174","author":"M Bertalm\u0131o","year":"2001","unstructured":"Bertalm\u0131o, M., Cheng, L.-T., Osher, S., Sapiro, G.: Variational problems and partial differential equations on implicit surfaces. J. Comput. Phys. 174, 759\u2013780 (2001)","journal-title":"J. Comput. Phys."},{"key":"2779_CR24","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1109\/42.774172","volume":"18","author":"M Bertalmio","year":"1999","unstructured":"Bertalmio, M., Sapiro, G., Randall, G.: Region tracking on level-sets methods. IEEE Trans. Med. Imaging 18, 448\u2013451 (1999)","journal-title":"IEEE Trans. Med. Imaging"},{"key":"2779_CR25","doi-asserted-by":"crossref","unstructured":"Bonnetier, E., Dapogny, C., Vogelius, M.S.: Small perturbations in the type of boundary conditions for an elliptic operator. J. Math. Pures Appl. (2022)","DOI":"10.1016\/j.matpur.2022.09.003"},{"key":"2779_CR26","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10659-007-9107-3","volume":"91","author":"B Bourdin","year":"2008","unstructured":"Bourdin, B., Francfort, G.A., Marigo, J.-J.: The variational approach to fracture. J. Elast. 91, 5\u2013148 (2008)","journal-title":"J. Elast."},{"key":"2779_CR27","unstructured":"Brakke, K.: The motion of a surface by its mean curvature. Princeton University"},{"key":"2779_CR28","doi-asserted-by":"crossref","unstructured":"Brito-Pacheco, C.: Rodin, 1 (2023)","DOI":"10.1109\/ISBI56570.2024.10635639"},{"key":"2779_CR29","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0022-0396(91)90147-2","volume":"90","author":"L Bronsard","year":"1991","unstructured":"Bronsard, L., Kohn, R.V.: Motion by mean curvature as the singular limit of Ginzburg\u2013Landau dynamics. J. Differ. Equ. 90, 211\u2013237 (1991)","journal-title":"J. Differ. Equ."},{"key":"2779_CR30","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1002\/fld.2730","volume":"70","author":"C Bui","year":"2012","unstructured":"Bui, C., Dapogny, C., Frey, P.: An accurate anisotropic adaptation method for solving the level set advection equation. Int. J. Numer. Meth. Fluids 70, 899\u2013922 (2012)","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"2779_CR31","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1017\/S0956792505006182","volume":"16","author":"M Burger","year":"2005","unstructured":"Burger, M., Osher, S.J.: A survey on level set methods for inverse problems and optimal design. Eur. J. Appl. Math. 16, 263\u2013301 (2005)","journal-title":"Eur. J. Appl. Math."},{"key":"2779_CR32","doi-asserted-by":"crossref","unstructured":"Campen, M., Kobbelt, L.: Exact and robust (self-) intersections for polygonal meshes. In: Computer Graphics Forum, vol.\u00a029, Wiley Online Library, pp.\u00a0397\u2013406 (2010)","DOI":"10.1111\/j.1467-8659.2009.01609.x"},{"key":"2779_CR33","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","volume":"10","author":"TF Chan","year":"2001","unstructured":"Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10, 266\u2013277 (2001)","journal-title":"IEEE Trans. Image Process."},{"key":"2779_CR34","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/0022-0396(92)90146-E","volume":"96","author":"X Chen","year":"1992","unstructured":"Chen, X.: Generation and propagation of interfaces for reaction\u2013diffusion equations. J. Differ. Equ. 96, 116\u2013141 (1992)","journal-title":"J. Differ. Equ."},{"key":"2779_CR35","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1071\/WF9930031","volume":"3","author":"N Cheney","year":"1993","unstructured":"Cheney, N., Gould, J., Catchpole, W.: The influence of fuel, weather and fire shape variables on fire-spread in grasslands. Int. J. Wildland Fire 3, 31\u201344 (1993)","journal-title":"Int. J. Wildland Fire"},{"key":"2779_CR36","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1006\/jcph.2001.6960","volume":"175","author":"L-T Cheng","year":"2002","unstructured":"Cheng, L.-T., Burchard, P., Merriman, B., Osher, S.: Motion of curves constrained on surfaces using a level-set approach. J. Comput. Phys. 175, 604\u2013644 (2002)","journal-title":"J. Comput. Phys."},{"key":"2779_CR37","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/10586458.1993.10504566","volume":"2","author":"DL Chopp","year":"1993","unstructured":"Chopp, D.L., Sethian, J.A.: Flow under curvature: singularity formation, minimal surfaces, and geodesics. Exp. Math. 2, 235\u2013255 (1993)","journal-title":"Exp. Math."},{"key":"2779_CR38","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.cag.2014.09.021","volume":"46","author":"AN Christiansen","year":"2015","unstructured":"Christiansen, A.N., B\u00e6rentzen, J.A., Nobel-J\u00f8rgensen, M., Aage, N., Sigmund, O.: Combined shape and topology optimization of 3D structures. Comput. Graph. 46, 25\u201335 (2015)","journal-title":"Comput. Graph."},{"key":"2779_CR39","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/s00158-013-0983-9","volume":"49","author":"AN Christiansen","year":"2014","unstructured":"Christiansen, A.N., Nobel-J\u00f8rgensen, M., Aage, N., Sigmund, O., B\u00e6rentzen, J.A.: Topology optimization using an explicit interface representation. Struct. Multidiscip. Optim. 49, 387\u2013399 (2014)","journal-title":"Struct. Multidiscip. Optim."},{"key":"2779_CR40","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511606205","volume-title":"Computational Fluid Dynamics","author":"TJ Chung","year":"2002","unstructured":"Chung, T.J., et al.: Computational Fluid Dynamics. Cambridge University Press, Cambridge (2002)"},{"key":"2779_CR41","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719208","volume-title":"The Finite Element Method for Elliptic Problems","author":"PG Ciarlet","year":"2002","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems, vol. 40. SIAM, Philadelphia (2002)"},{"key":"2779_CR42","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1142\/S0218202506001212","volume":"16","author":"G-H Cottet","year":"2006","unstructured":"Cottet, G.-H., Maitre, E.: A level set method for fluid-structure interactions with immersed surfaces. Math. Models Methods Appl. Sci. 16, 415\u2013438 (2006)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"2779_CR43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-1992-00266-5","volume":"27","author":"MG Crandall","year":"1992","unstructured":"Crandall, M.G., Ishii, H., Lions, P.-L.: User\u2019s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27, 1\u201367 (1992)","journal-title":"Bull. Am. Math. Soc."},{"key":"2779_CR44","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.jcp.2014.01.005","volume":"262","author":"C Dapogny","year":"2014","unstructured":"Dapogny, C., Dobrzynski, C., Frey, P.: Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems. J. Comput. Phys. 262, 358\u2013378 (2014)","journal-title":"J. Comput. Phys."},{"key":"2779_CR45","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.5802\/crmath.498","volume":"361","author":"C Dapogny","year":"2023","unstructured":"Dapogny, C., Feppon, F.: Shape optimization using a level set based mesh evolution method: an overview and tutorial. C. R. Math. 361, 1267\u20131332 (2023)","journal-title":"C. R. Math."},{"key":"2779_CR46","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10092-011-0051-z","volume":"49","author":"C Dapogny","year":"2012","unstructured":"Dapogny, C., Frey, P.: Computation of the signed distance function to a discrete contour on adapted triangulation. Calcolo 49, 193\u2013219 (2012)","journal-title":"Calcolo"},{"key":"2779_CR47","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s00211-020-01140-0","volume":"146","author":"C Dapogny","year":"2020","unstructured":"Dapogny, C., Lebbe, N., Oudet, E.: Optimization of the shape of regions supporting boundary conditions. Numer. Math. 146, 51\u2013104 (2020)","journal-title":"Numer. Math."},{"key":"2779_CR48","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1090\/S0002-9947-1995-1672406-7","volume":"347","author":"P De Mottoni","year":"1995","unstructured":"De Mottoni, P., Schatzman, M.: Geometrical evolution of developed interfaces. Trans. Am. Math. Soc. 347, 1533\u20131589 (1995)","journal-title":"Trans. Am. Math. Soc."},{"key":"2779_CR49","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719826","volume-title":"Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization","author":"MC Delfour","year":"2011","unstructured":"Delfour, M.C., Zol\u00e9sio, J.-P.: Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization. SIAM, Philadelphia (2011)"},{"key":"2779_CR50","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2022.111415","volume":"467","author":"Y Deng","year":"2022","unstructured":"Deng, Y., Zhang, W., Liu, Z., Zhu, J., Korvink, J.G.: Topology optimization for surface flows. J. Comput. Phys. 467, 111415 (2022)","journal-title":"J. Comput. Phys."},{"key":"2779_CR51","volume-title":"Mathematical Aspects of Discontinuous Galerkin Methods","author":"DA Di Pietro","year":"2011","unstructured":"Di Pietro, D.A., Ern, A.: Mathematical Aspects of Discontinuous Galerkin Methods, vol. 69. Springer, Berlin (2011)"},{"key":"2779_CR52","doi-asserted-by":"crossref","unstructured":"Dobrzynski, C., Frey, P.: Anisotropic Delaunay mesh adaptation for unsteady simulations. In: Proceedings of the 17th International Meshing Roundtable. Springer, pp.\u00a0177\u2013194 (2008)","DOI":"10.1007\/978-3-540-87921-3_11"},{"key":"2779_CR53","first-page":"214","volume":"74","author":"A Doi","year":"1991","unstructured":"Doi, A., Koide, A.: An efficient method of triangulating equi-valued surfaces by using tetrahedral cells. IEICE Trans. Inf. Syst. 74, 214\u2013224 (1991)","journal-title":"IEICE Trans. Inf. Syst."},{"key":"2779_CR54","first-page":"425","volume":"21","author":"Q Du","year":"2020","unstructured":"Du, Q., Feng, X.: The phase field method for geometric moving interfaces and their numerical approximations. Handb. Numer. Anal. 21, 425\u2013508 (2020)","journal-title":"Handb. Numer. Anal."},{"key":"2779_CR55","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/0021-9991(92)90173-V","volume":"98","author":"LJ Durlofsky","year":"1992","unstructured":"Durlofsky, L.J., Engquist, B., Osher, S.: Triangle based adaptive stencils for the solution of hyperbolic conservation laws. J. Comput. Phys. 98, 64\u201373 (1992)","journal-title":"J. Comput. Phys."},{"key":"2779_CR56","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1093\/imanum\/drl023","volume":"27","author":"G Dziuk","year":"2007","unstructured":"Dziuk, G., Elliott, C.M.: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, 262\u2013292 (2007)","journal-title":"IMA J. Numer. Anal."},{"key":"2779_CR57","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1017\/S0962492913000056","volume":"22","author":"G Dziuk","year":"2013","unstructured":"Dziuk, G., Elliott, C.M.: Finite element methods for surface PDEs. Acta Numer. 22, 289\u2013396 (2013)","journal-title":"Acta Numer."},{"key":"2779_CR58","volume-title":"Regularity Theory for Mean Curvature Flow","author":"K Ecker","year":"2012","unstructured":"Ecker, K.: Regularity Theory for Mean Curvature Flow, vol. 57. Springer, Berlin (2012)"},{"key":"2779_CR59","doi-asserted-by":"crossref","unstructured":"Feppon, F., Allaire, G., Dapogny, C., Jolivet, P.: Topology optimization of thermal fluid\u2013structure systems using body-fitted meshes and parallel computing. J. Comput. Phys 109574 (2020)","DOI":"10.1016\/j.jcp.2020.109574"},{"key":"2779_CR60","doi-asserted-by":"crossref","unstructured":"Filippi, J.-B., Bosseur, F., Grandi, D.: ForeFire: open-source code for wildland fire spread models. Advances in forest fire research\u2019.(Ed. DX Viegas) (Imprensa da Universidade de Coimbra: Coimbra, Portugal) (2014)","DOI":"10.14195\/978-989-26-0884-6_29"},{"key":"2779_CR61","doi-asserted-by":"crossref","first-page":"2633","DOI":"10.1016\/j.proci.2012.07.022","volume":"34","author":"J-B Filippi","year":"2013","unstructured":"Filippi, J.-B., Pialat, X., Clements, C.B.: Assessment of ForeFire\/Meso-NH for wildland fire\/atmosphere coupled simulation of the FireFlux experiment. Proc. Combust. Inst. 34, 2633\u20132640 (2013)","journal-title":"Proc. Combust. Inst."},{"key":"2779_CR62","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1071\/WF03010","volume":"12","author":"MA Finney","year":"2003","unstructured":"Finney, M.A.: Calculation of fire spread rates across random landscapes. Int. J. Wildland Fire 12, 167\u2013174 (2003)","journal-title":"Int. J. Wildland Fire"},{"key":"2779_CR63","doi-asserted-by":"crossref","unstructured":"Frey, P.J., George, P.-L.: Mesh generation: application to finite elements. ISTE (2007)","DOI":"10.1002\/9780470611166"},{"key":"2779_CR64","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1016\/j.cma.2016.10.019","volume":"313","author":"T-P Fries","year":"2017","unstructured":"Fries, T.-P., Omerovi\u0107, S., Sch\u00f6llhammer, D., Steidl, J.: Higher-order meshing of implicit geometries-Part I: Integration and interpolation in cut elements. Comput. Methods Appl. Mech. Eng. 313, 759\u2013784 (2017)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2779_CR65","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.cma.2017.07.037","volume":"326","author":"T-P Fries","year":"2017","unstructured":"Fries, T.-P., Sch\u00f6llhammer, D.: Higher-order meshing of implicit geometries, Part II: Approximations on manifolds. Comput. Methods Appl. Mech. Eng. 326, 270\u2013297 (2017)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2779_CR66","volume-title":"Surface Evolution Equations","author":"Y Giga","year":"2006","unstructured":"Giga, Y.: Surface Evolution Equations. Springer, Berlin (2006)"},{"key":"2779_CR67","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s10915-005-9012-5","volume":"29","author":"JB Greer","year":"2006","unstructured":"Greer, J.B.: An improvement of a recent Eulerian method for solving PDEs on general geometries. J. Sci. Comput. 29, 321\u2013352 (2006)","journal-title":"J. Sci. Comput."},{"key":"2779_CR68","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611972030","volume-title":"Elliptic Problems in Nonsmooth Domains","author":"P Grisvard","year":"2011","unstructured":"Grisvard, P.: Elliptic Problems in Nonsmooth Domains. SIAM, Philadelphia (2011)"},{"key":"2779_CR69","doi-asserted-by":"crossref","unstructured":"Henrot, A., Pierre, M.: Shape Variation and Optimization, EMS Tracts in Mathematics, vol. 28 (2018)","DOI":"10.4171\/178"},{"key":"2779_CR70","doi-asserted-by":"crossref","unstructured":"Ilmanen, T.: Generalized flow of sets by mean curvature on a manifold. Indiana Univ. Math. J. 671\u2013705 (1992)","DOI":"10.1512\/iumj.1992.41.41036"},{"key":"2779_CR71","doi-asserted-by":"crossref","first-page":"2126","DOI":"10.1137\/S106482759732455X","volume":"21","author":"G-S Jiang","year":"2000","unstructured":"Jiang, G.-S., Peng, D.: Weighted ENO schemes for Hamilton\u2013Jacobi equations. SIAM J. Sci. Comput. 21, 2126\u20132143 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"2779_CR72","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1006\/gmip.1997.0442","volume":"59","author":"R Kimmel","year":"1997","unstructured":"Kimmel, R.: Intrinsic scale space for images on surfaces: the geodesic curvature flow. Graph. Models Image Process. 59, 365\u2013372 (1997)","journal-title":"Graph. Models Image Process."},{"key":"2779_CR73","doi-asserted-by":"crossref","first-page":"8431","DOI":"10.1073\/pnas.95.15.8431","volume":"95","author":"R Kimmel","year":"1998","unstructured":"Kimmel, R., Sethian, J.A.: Computing geodesic paths on manifolds. Proc. Natl. Acad. Sci. 95, 8431\u20138435 (1998)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"2779_CR74","doi-asserted-by":"crossref","first-page":"2703","DOI":"10.1002\/smll.200900934","volume":"5","author":"HC Ko","year":"2009","unstructured":"Ko, H.C., Shin, G., Wang, S., Stoykovich, M.P., Lee, J.W., Kim, D.-H., Ha, J.S., Huang, Y., Hwang, K.-C., Rogers, J.A.: Curvilinear electronics formed using silicon membrane circuits and elastomeric transfer elements. Small 5, 2703\u20132709 (2009)","journal-title":"Small"},{"key":"2779_CR75","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1145\/37402.37422","volume":"21","author":"WE Lorensen","year":"1987","unstructured":"Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. ACM Siggraph Comput. Graph. 21, 163\u2013169 (1987)","journal-title":"ACM Siggraph Comput. Graph."},{"key":"2779_CR76","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s10915-008-9196-6","volume":"35","author":"CB Macdonald","year":"2008","unstructured":"Macdonald, C.B., Ruuth, S.J.: Level set equations on surfaces via the closest point method. J. Sci. Comput. 35, 219\u2013240 (2008)","journal-title":"J. Sci. Comput."},{"key":"2779_CR77","doi-asserted-by":"crossref","first-page":"4330","DOI":"10.1137\/080740003","volume":"31","author":"CB Macdonald","year":"2010","unstructured":"Macdonald, C.B., Ruuth, S.J.: The implicit closest point method for the numerical solution of partial differential equations on surfaces. SIAM J. Sci. Comput. 31, 4330\u20134350 (2010)","journal-title":"SIAM J. Sci. Comput."},{"key":"2779_CR78","doi-asserted-by":"crossref","first-page":"1723","DOI":"10.1016\/S0017-9310(01)00249-6","volume":"45","author":"J Margerit","year":"2002","unstructured":"Margerit, J., S\u00e9ro-Guillaume, O.: Modelling forest fires. Part II: reduction to two-dimensional models and simulation of propagation. Int. J. Heat Mass Transf. 45, 1723\u20131737 (2002)","journal-title":"Int. J. Heat Mass Transf."},{"key":"2779_CR79","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2167076.2167082","volume":"31","author":"MK Misztal","year":"2012","unstructured":"Misztal, M.K., B\u00e6rentzen, J.A.: Topology-adaptive interface tracking using the deformable simplicial complex. ACM Trans. Graph. 31, 1\u201312 (2012)","journal-title":"ACM Trans. Graph."},{"key":"2779_CR80","doi-asserted-by":"crossref","unstructured":"Moes, N., Remacle, J.-F., Lambrechts, J., Le, B., Chevaugeon, N.: The eXtreme Mesh deformation approach (X-MESH) for the Stefan phase change model. J. Comput. Phys. 111878 (2023)","DOI":"10.1016\/j.jcp.2022.111878"},{"key":"2779_CR81","volume-title":"Applied Shape Optimization for Fluids","author":"B Mohammadi","year":"2010","unstructured":"Mohammadi, B., Pironneau, O.: Applied Shape Optimization for Fluids. Oxford University Press, Oxford (2010)"},{"key":"2779_CR82","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5802\/crmeca.100","volume":"350","author":"D Morvan","year":"2022","unstructured":"Morvan, D., Accary, G., Meradji, S., Frangieh, N.: Fifty years of progress in wildland fire modelling: from empirical to fully physical CFD models. C. R. M\u00e9c. 350, 1\u20139 (2022)","journal-title":"C. R. M\u00e9c."},{"key":"2779_CR83","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/S0168-9274(98)00030-0","volume":"29","author":"H Munthe-Kaas","year":"1999","unstructured":"Munthe-Kaas, H.: High order Runge\u2013Kutta methods on manifolds. Appl. Numer. Math. 29, 115\u2013127 (1999)","journal-title":"Appl. Numer. Math."},{"key":"2779_CR84","unstructured":"Murat, F., Simon, J.: Sur le contr\u00f4le par un domaine g\u00e9om\u00e9trique, Pr\u00e9-publication du Laboratoire d\u2019Analyse Num\u00e9rique 76015 (1976)"},{"key":"2779_CR85","doi-asserted-by":"crossref","first-page":"2788","DOI":"10.1063\/1.1488599","volume":"14","author":"TG Myers","year":"2002","unstructured":"Myers, T.G., Charpin, J.P., Chapman, S.J.: The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface. Phys. Fluids 14, 2788\u20132803 (2002)","journal-title":"Phys. Fluids"},{"key":"2779_CR86","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1006\/jcph.1996.5584","volume":"133","author":"CF Ollivier-Gooch","year":"1997","unstructured":"Ollivier-Gooch, C.F.: Quasi-ENO schemes for unstructured meshes based on unlimited data-dependent least-squares reconstruction. J. Comput. Phys. 133, 6\u201317 (1997)","journal-title":"J. Comput. Phys."},{"key":"2779_CR87","volume-title":"Level Set Methods and Dynamic Implicit Surfaces","author":"S Osher","year":"2006","unstructured":"Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces, vol. 153. Springer, Berlin (2006)"},{"key":"2779_CR88","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S Osher","year":"1988","unstructured":"Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton\u2013Jacobi formulations. J. Comput. Phys. 79, 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"key":"2779_CR89","volume-title":"Finite Element Methods for Fluids","author":"O Pironneau","year":"1989","unstructured":"Pironneau, O.: Finite Element Methods for Fluids. Wiley, Chichester (1989)"},{"key":"2779_CR90","unstructured":"Rothermel, R.C.: A mathematical model for predicting fire spread in wildland fuels, vol.\u00a0115, Intermountain Forest & Range Experiment Station, Forest Service, US (1972)"},{"key":"2779_CR91","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1016\/j.jcp.2007.10.009","volume":"227","author":"SJ Ruuth","year":"2008","unstructured":"Ruuth, S.J., Merriman, B.: A simple embedding method for solving partial differential equations on surfaces. J. Comput. Phys. 227, 1943\u20131961 (2008)","journal-title":"J. Comput. Phys."},{"key":"2779_CR92","volume-title":"Geometric Partial Differential Equations and Image Analysis","author":"G Sapiro","year":"2006","unstructured":"Sapiro, G.: Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, Cambridge (2006)"},{"key":"2779_CR93","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1016\/S0017-9310(01)00248-4","volume":"45","author":"O S\u00e9ro-Guillaume","year":"2002","unstructured":"S\u00e9ro-Guillaume, O., Margerit, J.: Modelling forest fires. Part I: a complete set of equations derived by extended irreversible thermodynamics. Int. J. Heat Mass Transf. 45, 1705\u20131722 (2002)","journal-title":"Int. J. Heat Mass Transf."},{"key":"2779_CR94","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1073\/pnas.93.4.1591","volume":"93","author":"JA Sethian","year":"1996","unstructured":"Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591\u20131595 (1996)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"2779_CR95","volume-title":"Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science","author":"JA Sethian","year":"1999","unstructured":"Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, vol. 3. Cambridge University Press, Cambridge (1999)"},{"key":"2779_CR96","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/0021-9991(88)90177-5","volume":"77","author":"C-W Shu","year":"1988","unstructured":"Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439\u2013471 (1988)","journal-title":"J. Comput. Phys."},{"key":"2779_CR97","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58106-9","volume-title":"Introduction to Shape Optimization","author":"J Sokolowski","year":"1992","unstructured":"Sokolowski, J., Zol\u00e9sio, J.-P.: Introduction to Shape Optimization. Springer, Berlin (1992)"},{"key":"2779_CR98","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1137\/S0036142901389025","volume":"40","author":"RJ Spiteri","year":"2002","unstructured":"Spiteri, R.J., Ruuth, S.J.: A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 40, 469\u2013491 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"2779_CR99","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1006\/jcph.1999.6194","volume":"151","author":"J Strain","year":"1999","unstructured":"Strain, J.: Semi-Lagrangian methods for level set equations. J. Comput. Phys. 151, 498\u2013533 (1999)","journal-title":"J. Comput. Phys."},{"key":"2779_CR100","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1071\/WF06142","volume":"18","author":"AL Sullivan","year":"2009","unstructured":"Sullivan, A.L.: Wildland surface fire spread modelling, 1990\u20132007. 2: Empirical and quasi-empirical models. Int. J. Wildland Fire 18, 369\u2013386 (2009)","journal-title":"Int. J. Wildland Fire"},{"key":"2779_CR101","volume":"72","author":"P Tang","year":"2005","unstructured":"Tang, P., Qiu, F., Zhang, H., Yang, Y.: Phase separation patterns for diblock copolymers on spherical surfaces: a finite volume method. Phys. Rev. E 72, 016710 (2005)","journal-title":"Phys. Rev. E"},{"key":"2779_CR102","doi-asserted-by":"crossref","unstructured":"Tian, L., Macdonald, C.B., Ruuth, S.J.: Segmentation on surfaces with the closest point method. In: 2009 16th IEEE International Conference on Image Processing (ICIP), IEEE, pp.\u00a03009\u20133012 (2009)","DOI":"10.1109\/ICIP.2009.5414447"},{"key":"2779_CR103","doi-asserted-by":"crossref","DOI":"10.1016\/j.tws.2020.107349","volume":"160","author":"EA Tr\u00e4ff","year":"2021","unstructured":"Tr\u00e4ff, E.A., Sigmund, O., Aage, N.: Topology optimization of ultra high resolution shell structures. Thin-Walled Struct. 160, 107349 (2021)","journal-title":"Thin-Walled Struct."},{"key":"2779_CR104","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1145\/127719.122749","volume":"25","author":"G Turk","year":"1991","unstructured":"Turk, G.: Generating textures on arbitrary surfaces using reaction\u2013diffusion. Acm Siggraph Comput. Graph. 25, 289\u2013298 (1991)","journal-title":"Acm Siggraph Comput. Graph."},{"key":"2779_CR105","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.advengsoft.2016.11.007","volume":"113","author":"J Vimmr","year":"2017","unstructured":"Vimmr, J., Bubl\u00edk, O., Pecka, A.: A parallel implementation of an implicit discontinuous Galerkin finite element scheme for fluid flow problems. Adv. Eng. Softw. 113, 108\u2013119 (2017)","journal-title":"Adv. Eng. Softw."},{"key":"2779_CR106","doi-asserted-by":"crossref","unstructured":"Witkin, A., Kass, M.: Reaction\u2013diffusion textures. In: Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, pp.\u00a0299\u2013308 (1991)","DOI":"10.1145\/122718.122750"},{"key":"2779_CR107","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.cma.2014.01.014","volume":"272","author":"Q Xia","year":"2014","unstructured":"Xia, Q., Wang, M.Y., Shi, T.: A level set method for shape and topology optimization of both structure and support of continuum structures. Comput. Methods Appl. Mech. Eng. 272, 340\u2013353 (2014)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2779_CR108","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.cma.2018.08.045","volume":"344","author":"Q Ye","year":"2019","unstructured":"Ye, Q., Guo, Y., Chen, S., Lei, N., Gu, X.D.: Topology optimization of conformal structures on manifolds using extended level set methods (X-LSM) and conformal geometry theory. Comput. Methods Appl. Mech. Eng. 344, 164\u2013185 (2019)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2779_CR109","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TPAMI.2010.116","volume":"33","author":"A Zaharescu","year":"2010","unstructured":"Zaharescu, A., Boyer, E., Horaud, R.: Topology-adaptive mesh deformation for surface evolution, morphing, and multiview reconstruction. IEEE Trans. Pattern Anal. Mach. Intell. 33, 823\u2013837 (2010)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"2779_CR110","doi-asserted-by":"crossref","unstructured":"Zhang, Y.-T., Shu, C.-W.: ENO and WENO schemes. In: Handbook of Numerical Analysis, vol.\u00a017. Elsevier, pp.\u00a0103\u2013122 (2016)","DOI":"10.1016\/bs.hna.2016.09.009"},{"key":"2779_CR111","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1090\/S0025-5718-04-01678-3","volume":"74","author":"H Zhao","year":"2005","unstructured":"Zhao, H.: A fast sweeping method for eikonal equations. Math. Comput. 74, 603\u2013627 (2005)","journal-title":"Math. Comput."},{"key":"2779_CR112","unstructured":"Zhao, H.-K., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: Variational and Level Set Methods in Computer Vision, 2001. Proceedings. IEEE Workshop on, IEEE, pp.\u00a0194\u2013201 (2001)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02779-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-024-02779-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02779-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T17:43:13Z","timestamp":1739900593000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-024-02779-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,29]]},"references-count":112,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["2779"],"URL":"https:\/\/doi.org\/10.1007\/s10915-024-02779-9","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2025,1,29]]},"assertion":[{"value":"20 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2025","order":4,"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 not disclosed any competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"73"}}