{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T22:23:00Z","timestamp":1770070980309,"version":"3.49.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,3,27]],"date-time":"2017-03-27T00:00:00Z","timestamp":1490572800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673221"],"award-info":[{"award-number":["61673221"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Jiangsu Province (CN)","award":["16KJB110012"],"award-info":[{"award-number":["16KJB110012"]}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["16303114"],"award-info":[{"award-number":["16303114"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002920","name":"Research Grants Council, University Grants Committee","doi-asserted-by":"publisher","award":["16309316"],"award-info":[{"award-number":["16309316"]}],"id":[{"id":"10.13039\/501100002920","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,1]]},"DOI":"10.1007\/s10915-017-0424-9","type":"journal-article","created":{"date-parts":[[2017,3,27]],"date-time":"2017-03-27T18:58:57Z","timestamp":1490641137000},"page":"70-96","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Lagrangian Coherent Structures Extraction"],"prefix":"10.1007","volume":"74","author":[{"given":"Guoqiao","family":"You","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4549-2761","authenticated-orcid":false,"given":"Shingyu","family":"Leung","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,27]]},"reference":[{"issue":"11","key":"424_CR1","doi-asserted-by":"crossref","first-page":"3162","DOI":"10.1063\/1.869433","volume":"9","author":"V Artale","year":"1997","unstructured":"Artale, V., Boffetta, G., Celani, A., Cencini, M., Vulpiani, A.: Dispersion of passive tracers in closed basins: beyond the diffusion coefficient. Phys. Fluids 9(11), 3162\u20133171 (1997)","journal-title":"Phys. Fluids"},{"key":"424_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0305-4470\/30\/1\/003","volume":"30","author":"E Aurell","year":"1997","unstructured":"Aurell, E., Boffetta, G., Crisanti, A., Paladin, G., Vulpiani, A.: Predictability in the large: an extension of the concept of Lyapunov exponent. J. Phys. A: Math. Gen. 30, 1\u201326 (1997)","journal-title":"J. Phys. A: Math. Gen."},{"key":"424_CR3","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.jcp.2006.07.032","volume":"220","author":"EJ Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E.J., Ying, L.: Fast geodesics computation with the phase flow method. J. Comput. Phys. 220, 6\u201318 (2006)","journal-title":"J. Comput. Phys."},{"key":"424_CR4","doi-asserted-by":"crossref","first-page":"254019","DOI":"10.1088\/1751-8113\/46\/25\/254019","volume":"46","author":"M Cencini","year":"2013","unstructured":"Cencini, M., Vulpiani, A.: Finite size Lyapunov exponent: review on applications. J. Phys. A: Math. Theor. 46, 254019 (2013)","journal-title":"J. Phys. A: Math. Theor."},{"key":"424_CR5","volume-title":"Ray Method in Seismology","author":"V Cerveny","year":"1977","unstructured":"Cerveny, V., Molotkov, I.A., Psencik, I.: Ray Method in Seismology. Univerzita Karlova Press, Praha (1977)"},{"key":"424_CR6","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1002\/cpa.3160050303","volume":"5","author":"R Courant","year":"1952","unstructured":"Courant, R., Issacson, E., Rees, M.: On the solution of nonlinear hyperbolic differential equations by finite differences. Commun. Pure Appl. Math. 5, 243\u2013255 (1952)","journal-title":"Commun. Pure Appl. Math."},{"key":"424_CR7","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/0021-9045(77)90011-9","volume":"21","author":"C Boor de","year":"1977","unstructured":"de Boor, C., Swartz, B.: Piecewise monotone interpolation. J. Approx. Theory 21, 411\u2013416 (1977)","journal-title":"J. Approx. Theory"},{"key":"424_CR8","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.compstruc.2004.04.024","volume":"83","author":"D Enright","year":"2005","unstructured":"Enright, D., Losasso, F., Fedkiw, R.: A fast and accurate semi-Lagrangian particle level set method. Comput. Struct. 83, 479\u2013490 (2005)","journal-title":"Comput. Struct."},{"key":"424_CR9","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1137\/0717021","volume":"17","author":"FN Fritsch","year":"1980","unstructured":"Fritsch, F.N., Carlson, R.E.: Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 17, 238\u2013246 (1980)","journal-title":"SIAM J. Numer. Anal."},{"key":"424_CR10","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/S0167-2789(00)00199-8","volume":"149","author":"G Haller","year":"2001","unstructured":"Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Phys. D 149, 248\u2013277 (2001)","journal-title":"Phys. D"},{"key":"424_CR11","first-page":"3368","volume":"13","author":"G Haller","year":"2001","unstructured":"Haller, G.: Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence. Phys. Fluids A 13, 3368\u20133385 (2001)","journal-title":"Phys. Fluids A"},{"key":"424_CR12","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1016\/S0167-2789(00)00142-1","volume":"147","author":"G Haller","year":"2000","unstructured":"Haller, G., Yuan, G.: Lagrangian coherent structures and mixing in two-dimensional turbulence. Phys. D 147, 352\u2013370 (2000)","journal-title":"Phys. D"},{"issue":"3\u20134","key":"424_CR13","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.ocemod.2010.12.006","volume":"36","author":"I Hermandez-Carrasco","year":"2011","unstructured":"Hermandez-Carrasco, I., Lopex, C., Hernansez-Garcia, E., Turiel, A.: How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics? Ocean Model. 36(3\u20134), 208\u2013218 (2011)","journal-title":"Ocean Model."},{"key":"424_CR14","unstructured":"Huynh, H.T.: Accurate monotone cubic interpolation. NASA Technical Memorandum 103789 (1991)"},{"key":"424_CR15","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1002\/nme.1296","volume":"63","author":"F Lekien","year":"2005","unstructured":"Lekien, F., Marsden, J.E.: Tricubic interpolation in three dimensions. Int. J. Numer. Methods Eng. 63, 455\u2013471 (2005)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"424_CR16","doi-asserted-by":"crossref","first-page":"065404","DOI":"10.1063\/1.2740025","volume":"48","author":"F Lekien","year":"2007","unstructured":"Lekien, F., Shadden, S.C., Marsden, J.E.: Lagrangian coherent structures in $$n$$ n -dimensional systems. J. Math. Phys. 48, 065404 (2007)","journal-title":"J. Math. Phys."},{"key":"424_CR17","doi-asserted-by":"crossref","first-page":"2857","DOI":"10.1016\/j.jcp.2010.12.036","volume":"230","author":"M Lentine","year":"2011","unstructured":"Lentine, M., Gretarsson, J.T., Fedkiw, R.: An unconditionally stable fully conservative semi-Lagrangian method. J. Comput. Phys. 230, 2857\u20132879 (2011)","journal-title":"J. Comput. Phys."},{"key":"424_CR18","doi-asserted-by":"crossref","first-page":"2551","DOI":"10.1175\/1520-0493(1995)123<2551:TDMCSL>2.0.CO;2","volume":"123","author":"LM Leslie","year":"1995","unstructured":"Leslie, L.M., Pursuer, R.J.: Three-dimensional mass-conserving semi-Lagrangian scheme employing forward trajectories. Mon. Weather Rev. 123, 2551\u20132566 (1995)","journal-title":"Mon. Weather Rev."},{"key":"424_CR19","doi-asserted-by":"crossref","first-page":"2533","DOI":"10.1103\/PhysRevE.61.2533","volume":"61","author":"T Letz","year":"2000","unstructured":"Letz, T., Kantz, H.: Characterization of sensitivity to finite perturbations. Phys. Rev. E. 61, 2533 (2000)","journal-title":"Phys. Rev. E."},{"key":"424_CR20","doi-asserted-by":"crossref","first-page":"3500","DOI":"10.1016\/j.jcp.2011.01.046","volume":"230","author":"S Leung","year":"2011","unstructured":"Leung, S.: An Eulerian approach for computing the finite time Lyapunov exponent. J. Comput. Phys. 230, 3500\u20133524 (2011)","journal-title":"J. Comput. Phys."},{"key":"424_CR21","doi-asserted-by":"crossref","unstructured":"Leung, S.: A backward phase flow method for the finite time Lyapunov exponent. Chaos 23, 043132 (2013)","DOI":"10.1063\/1.4847175"},{"key":"424_CR22","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1088\/0266-5611\/23\/2\/019","volume":"23","author":"S Leung","year":"2007","unstructured":"Leung, S., Qian, J.: Transmission traveltime tomography based on paraxial Liouville equations and level set formulations. Inverse Probl. 23, 799\u2013821 (2007)","journal-title":"Inverse Probl."},{"key":"424_CR23","doi-asserted-by":"crossref","first-page":"2951","DOI":"10.1016\/j.jcp.2009.01.007","volume":"228","author":"S Leung","year":"2009","unstructured":"Leung, S., Qian, J.: Eulerian Gaussian beams for Schr\u00f6dinger equations in the semi-classical regime. J. Comput. Phys. 228, 2951\u20132977 (2009)","journal-title":"J. Comput. Phys."},{"key":"424_CR24","doi-asserted-by":"crossref","first-page":"8888","DOI":"10.1016\/j.jcp.2010.08.015","volume":"229","author":"S Leung","year":"2010","unstructured":"Leung, S., Qian, J.: The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schr\u00f6dinger equation. J. Comput. Phys. 229, 8888\u20138917 (2010)","journal-title":"J. Comput. Phys."},{"key":"424_CR25","doi-asserted-by":"crossref","first-page":"SM61","DOI":"10.1190\/1.2752136","volume":"72","author":"S Leung","year":"2007","unstructured":"Leung, S., Qian, J., Burridge, R.: Eulerian Gaussian beams for high frequency wave propagation. Geophysics 72, SM61\u2013SM76 (2007)","journal-title":"Geophysics"},{"key":"424_CR26","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1006\/jcph.1994.1187","volume":"115","author":"XD Liu","year":"1994","unstructured":"Liu, X.D., Osher, S.J., Chan, T.: Weighted essentially nonoscillatory schemes. J. Comput. Phys. 115, 200\u2013212 (1994)","journal-title":"J. Comput. Phys."},{"key":"424_CR27","unstructured":"Mills, P.: Following the vapour trail: A study of chaotic mixing of water vapour in the upper troposphere. Thesis, University of Bremen, Germany (2004)"},{"key":"424_CR28","doi-asserted-by":"crossref","first-page":"2020","DOI":"10.1016\/j.cageo.2008.12.015","volume":"35","author":"P Mills","year":"2009","unstructured":"Mills, P.: Isoline retrieval: an optimal sounding method for validation of advected contours. Comput. Geosci. 35, 2020\u20132031 (2009)","journal-title":"Comput. Geosci."},{"issue":"1","key":"424_CR29","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.jcp.2004.04.019","volume":"200","author":"C Min","year":"2004","unstructured":"Min, C.: Local level set methods in high dimension and codimension. J. Comput. Phys. 200(1), 368\u2013382 (2004)","journal-title":"J. Comput. Phys."},{"key":"424_CR30","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/j.jcp.2006.11.034","volume":"225","author":"C Min","year":"2007","unstructured":"Min, C., Gibou, F.: A second order accurate level set method on non-graded adaptive cartesian grids. J. Comput. Phys. 225, 300\u2013321 (2007)","journal-title":"J. Comput. Phys."},{"key":"424_CR31","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.jcp.2016.06.017","volume":"322","author":"M Mirzadeh","year":"2016","unstructured":"Mirzadeh, M., Guittet, A., Burstedde, C., Gibou, F.: Parallel level-set methods on adaptive tree-based grids. J. Comput. Phys. 322, 345\u2013364 (2016)","journal-title":"J. Comput. Phys."},{"key":"424_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/b98879","volume-title":"Level Set Methods and Dynamic Implicit Surfaces","author":"SJ Osher","year":"2003","unstructured":"Osher, S.J., Fedkiw, R.P.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2003)"},{"key":"424_CR33","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"SJ Osher","year":"1988","unstructured":"Osher, S.J., 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":"424_CR34","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1137\/0728049","volume":"28","author":"SJ Osher","year":"1991","unstructured":"Osher, S.J., Shu, C.W.: High-order essentially nonoscillatory schemes for Hamilton\u2013Jacobi equations. SIAM J. Numer. Anal. 28, 907\u2013922 (1991)","journal-title":"SIAM J. Numer. Anal."},{"key":"424_CR35","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/0021-9045(74)90066-5","volume":"12","author":"E Passow","year":"1974","unstructured":"Passow, E.: Piecewise monotone spline interpolation. J. Approx. Theory 12, 240\u2013241 (1974)","journal-title":"J. Approx. Theory"},{"key":"424_CR36","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1016\/j.jcp.2003.12.017","volume":"197","author":"J Qian","year":"2004","unstructured":"Qian, J., Leung, S.: A level set based Eulerian method for paraxial multivalued traveltimes. J. Comput. Phys. 197, 711\u2013736 (2004)","journal-title":"J. Comput. Phys."},{"key":"424_CR37","volume-title":"Level Set Methods","author":"JA Sethian","year":"1996","unstructured":"Sethian, J.A.: Level Set Methods. Cambridge University Press, Cambridge (1996)"},{"key":"424_CR38","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.physd.2005.10.007","volume":"212","author":"SC Shadden","year":"2005","unstructured":"Shadden, S.C., Lekien, F., Marsden, J.E.: Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Phys. D 212, 271\u2013304 (2005)","journal-title":"Phys. D"},{"key":"424_CR39","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BFb0096355","volume-title":"Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Lecture Notes in Mathematics","author":"CW Shu","year":"1998","unstructured":"Shu, C.W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Cockburn, B., Johnson, C., Shu, C.W., Tadmor, E. (eds.) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Lecture Notes in Mathematics, vol. 1697, pp. 325\u2013432. Springer, Berlin (1998)"},{"key":"424_CR40","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/0021-9991(92)90018-T","volume":"101","author":"PK Smolarkiewicz","year":"1992","unstructured":"Smolarkiewicz, P.K., Grell, G.A.: A class of monotone interpolation schemes. J. Comput. Phys. 101, 431\u2013440 (1992)","journal-title":"J. Comput. Phys."},{"key":"424_CR41","doi-asserted-by":"crossref","first-page":"2206","DOI":"10.1175\/1520-0493(1991)119<2206:SLISFA>2.0.CO;2","volume":"119","author":"A Staniforth","year":"1991","unstructured":"Staniforth, A., Cote, J.: Semi-Lagrangian integration schemes for atmospheric model\u2014a review. Mon. Weather Rev. 119, 2206\u20132223 (1991)","journal-title":"Mon. Weather Rev."},{"key":"424_CR42","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.jcp.2006.05.008","volume":"220","author":"L Ying","year":"2006","unstructured":"Ying, L., Cand\u00e8s, E.J.: The phase flow method. J. Comput. Phys. 220, 184\u2013215 (2006)","journal-title":"J. Comput. Phys."},{"key":"424_CR43","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.jcp.2014.01.034","volume":"264","author":"G You","year":"2014","unstructured":"You, G., Leung, S.: An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems. J. Comput. Phys. 264, 112\u2013132 (2014)","journal-title":"J. Comput. Phys."},{"key":"424_CR44","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.jcp.2014.02.014","volume":"266","author":"G You","year":"2014","unstructured":"You, G., Leung, S.: VIALS: an Eulerian tool based on total variation and the level set method for studying dynamical systems. J. Comput. Phys. 266, 139\u2013160 (2014)","journal-title":"J. Comput. Phys."},{"key":"424_CR45","doi-asserted-by":"crossref","unstructured":"You, G., Wong, T., Leung, S.: Eulerian methods for visualizing continuous dynamical systems using Lyapunov exponents. SIAM J. Sci. Comput. 39(2), A415\u2013A437 (2017)","DOI":"10.1137\/16M1066890"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0424-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0424-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0424-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T03:09:29Z","timestamp":1568948969000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0424-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,27]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["424"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0424-9","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,27]]}}}