{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:39:28Z","timestamp":1772296768287,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,2,17]],"date-time":"2018-02-17T00:00:00Z","timestamp":1518825600000},"content-version":"tdm","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":["11701287"],"award-info":[{"award-number":["11701287"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20171071"],"award-info":[{"award-number":["BK20171071"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"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":[[2018,9]]},"DOI":"10.1007\/s10915-018-0669-y","type":"journal-article","created":{"date-parts":[[2018,2,17]],"date-time":"2018-02-17T00:53:21Z","timestamp":1518828801000},"page":"1407-1435","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An Improved Eulerian Approach for the Finite Time Lyapunov Exponent"],"prefix":"10.1007","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9413-5691","authenticated-orcid":false,"given":"Guoqiao","family":"You","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shingyu","family":"Leung","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,2,17]]},"reference":[{"key":"669_CR1","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1007\/s11012-016-0364-8","volume":"52","author":"MG Badas","year":"2017","unstructured":"Badas, M.G., Domenichini, F., Querzoli, G.: Quantification of the blood mixing in the left ventricle using finite time Lyapunov exponents. Meccania 52, 529\u2013544 (2017)","journal-title":"Meccania"},{"key":"669_CR2","doi-asserted-by":"publisher","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":"669_CR3","doi-asserted-by":"publisher","first-page":"545","DOI":"10.2514\/1.35223","volume":"46","author":"BM Cardwell","year":"2008","unstructured":"Cardwell, B.M., Mohseni, K.: Vortex shedding over two-dimensional airfoil: where do the particles come from? AIAA J. 46, 545\u2013547 (2008)","journal-title":"AIAA J."},{"key":"669_CR4","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1051\/m2an\/1989230405651","volume":"23","author":"G Chavent","year":"1989","unstructured":"Chavent, G., Cockburn, B.: The local projection p0 p1-discontinuous-Galerkin finite element method for scalar conservation laws. RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r. 23, 565\u2013592 (1989)","journal-title":"RAIRO Mod\u00e9l. Math. Anal. Num\u00e9r."},{"key":"669_CR5","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1006\/jcph.1998.5892","volume":"141","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The Runge\u2013Kutta discontinuous Galerkin finite element method for conservation laws V: multidimensional systems. J. Comput. Phys. 141, 199\u2013224 (1998)","journal-title":"J. Comput. Phys."},{"key":"669_CR6","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1023\/A:1012873910884","volume":"16","author":"B Cockburn","year":"2001","unstructured":"Cockburn, B., Shu, C.-W.: Runge\u2013Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16, 173\u2013261 (2001)","journal-title":"J. Sci. Comput."},{"key":"669_CR7","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1109\/TVCG.2007.70551","volume":"13","author":"C Garth","year":"2007","unstructured":"Garth, C., Gerhardt, F., Tricoche, X., Hagen, H.: Efficient computation and visualization of coherent structures in fluid flow applications. IEEE Trans. Vis. Comput. Graph. 13, 1464\u20131471 (2007)","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"669_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-88606-8_1","volume-title":"Visualization of Coherent Structures in Transient 2D Flows","author":"C Garth","year":"2009","unstructured":"Garth, C., Li, G.S., Tricoche, X., Hansen, C.D., Hagen, H.: Visualization of Coherent Structures in Transient 2D Flows. Springer, Berlin (2009)"},{"key":"669_CR9","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1090\/S0025-5718-98-00913-2","volume":"67","author":"S Gottlieb","year":"1998","unstructured":"Gottlieb, S., Shu, C.-W.: Total variation diminishing Runge\u2013Kutta schemes. Math. Comput. 67, 73\u201385 (1998)","journal-title":"Math. Comput."},{"key":"669_CR10","doi-asserted-by":"publisher","first-page":"017510","DOI":"10.1063\/1.3270045","volume":"20","author":"MA Green","year":"2010","unstructured":"Green, M.A., Rowley, C.W., Smiths, A.J.: Using hyperbolic Lagrangian coherent structures to investigate vortices in biospired fluid flows. Chaos 20, 017510 (2010)","journal-title":"Chaos"},{"key":"669_CR11","doi-asserted-by":"publisher","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. Physica D 149, 248\u2013277 (2001)","journal-title":"Physica D"},{"key":"669_CR12","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":"669_CR13","doi-asserted-by":"publisher","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. Physica D 147, 352\u2013370 (2000)","journal-title":"Physica D"},{"key":"669_CR14","doi-asserted-by":"crossref","unstructured":"Kuhn, A., Rossl, C., Weinkauf, T., Theisel, H.: A benchmark for evaluating FTLE computations. In: IEEE Pacific Visualization Symposium, pp. 121\u2013128. IEEE Computer Society (2012)","DOI":"10.1109\/PacificVis.2012.6183582"},{"key":"669_CR15","doi-asserted-by":"crossref","unstructured":"Lekien, F., Leonard, N.: Dynamically consistent Lagrangian coherent structures. In: Experimental Chaos: 8-th Experimental Chaos Conference, pp. 132\u2013139 (2004)","DOI":"10.1063\/1.1846469"},{"key":"669_CR16","doi-asserted-by":"publisher","first-page":"017505","DOI":"10.1063\/1.3278516","volume":"20","author":"F Lekien","year":"2010","unstructured":"Lekien, F., Ross, S.D.: The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. Chaos 20, 017505 (2010)","journal-title":"Chaos"},{"key":"669_CR17","doi-asserted-by":"publisher","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                      \n                    \n                    $$n$$\n                    \n                      \n                        n\n                      \n                    \n                  -dimensional systems. J. Math. Phys. 48, 065404 (2007)","journal-title":"J. Math. Phys."},{"key":"669_CR18","doi-asserted-by":"publisher","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":"669_CR19","doi-asserted-by":"publisher","first-page":"043132","DOI":"10.1063\/1.4847175","volume":"23","author":"S Leung","year":"2013","unstructured":"Leung, S.: The backward phase flow method for the Eulerian finite time Lyapunov exponent computations. Chaos 23, 043132 (2013)","journal-title":"Chaos"},{"key":"669_CR20","doi-asserted-by":"publisher","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":"669_CR21","doi-asserted-by":"publisher","first-page":"2436","DOI":"10.1242\/jeb.026740","volume":"212","author":"D Lipinski","year":"2009","unstructured":"Lipinski, D., Mohseni, K.: Flow structures and fluid transport for the hydromedusae Sarsia tubulosa and Aequorea victoria. J. Exp. Biol. 212, 2436\u20132447 (2009)","journal-title":"J. Exp. Biol."},{"key":"669_CR22","doi-asserted-by":"publisher","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":"669_CR23","doi-asserted-by":"publisher","first-page":"017511","DOI":"10.1063\/1.3271340","volume":"20","author":"S Lukens","year":"2010","unstructured":"Lukens, S., Yang, X., Fauci, L.: Using Lagrangian coherent structures to analyze fluid mixing by cillia. Chaos 20, 017511 (2010)","journal-title":"Chaos"},{"key":"669_CR24","doi-asserted-by":"publisher","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":"669_CR25","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1137\/030601673","volume":"28","author":"J Qian","year":"2006","unstructured":"Qian, J., Leung, S.: A local level set method for paraxial multivalued geometric optics. SIAM J. Sci. Comput. 28, 206\u2013223 (2006)","journal-title":"SIAM J. Sci. Comput."},{"key":"669_CR26","doi-asserted-by":"publisher","first-page":"2481","DOI":"10.1175\/2009JAS2865.1","volume":"66","author":"T Sapsis","year":"2009","unstructured":"Sapsis, T., Haller, G.: Inertial particle dynamics in a hurricane. J. Atmos. Sci. 66, 2481\u20132492 (2009)","journal-title":"J. Atmos. Sci."},{"key":"669_CR27","doi-asserted-by":"publisher","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. Physica D 212, 271\u2013304 (2005)","journal-title":"Physica D"},{"key":"669_CR28","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/BFb0096355","volume-title":"Advanced Numerical Approximation of Nonlinear Hyperbolic Equations","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":"669_CR29","doi-asserted-by":"publisher","first-page":"017502","DOI":"10.1063\/1.3276061","volume":"20","author":"W Tang","year":"2010","unstructured":"Tang, W., Chan, P.W., Haller, G.: Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong international airport. Chaos 20, 017502 (2010)","journal-title":"Chaos"},{"key":"669_CR30","doi-asserted-by":"publisher","first-page":"017508","DOI":"10.1063\/1.3273054","volume":"20","author":"W Tang","year":"2010","unstructured":"Tang, W., Peacock, T.: Lagrangian coherent structures and internal wave attractors. Chaos 20, 017508 (2010)","journal-title":"Chaos"},{"key":"669_CR31","doi-asserted-by":"publisher","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":"669_CR32","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1007\/s10915-017-0424-9","volume":"74","author":"G You","year":"2018","unstructured":"You, G., Leung, S.: Eulerian based interpolation schemes for flow map construction and line integral computation with applications to coherent structures extraction. J. Sci. Comput. 74, 70\u201396 (2018)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"669_CR33","doi-asserted-by":"publisher","first-page":"A415","DOI":"10.1137\/16M1066890","volume":"39","author":"G You","year":"2017","unstructured":"You, G., Wong, T., Leung, S.: Eulerian methods for visualizating continuous dynamical systems using Lyapunov exponents. SIAM J. Sci. Comput. 39(2), A415\u2013A437 (2017)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-0669-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0669-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0669-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,16]],"date-time":"2019-02-16T22:07:28Z","timestamp":1550354848000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-0669-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,17]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["669"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-0669-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,17]]},"assertion":[{"value":"13 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 February 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 February 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}