{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:34:50Z","timestamp":1726014890285},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030115388"},{"type":"electronic","value":"9783030115395"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-11539-5_3","type":"book-chapter","created":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T15:26:23Z","timestamp":1552058783000},"page":"28-34","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical Solving a Boundary Value Problem for the Eikonal Equation"],"prefix":"10.1007","author":[{"given":"Alexander G.","family":"Churbanov","sequence":"first","affiliation":[]},{"given":"Petr N.","family":"Vabishchevich","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,26]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Belyaev, A.G., Fayolle, P.A.: On variational and PDE-based distance function approximations. In: Computer Graphics Forum, vol. 34, pp. 104\u2013118. Wiley Online Library (2015)","DOI":"10.1111\/cgf.12611"},{"key":"3_CR2","first-page":"15","volume":"47","author":"T Bhattacharya","year":"1989","unstructured":"Bhattacharya, T., DiBenedetto, E., Manfredi, J.: Limits as \n \n \n \n $$p \\rightarrow \\infty $$\n of \n \n \n \n $$\\triangle _p u_p = f$$\n and related extremal problems. Rend. Sem. Mat. Univ. Polytec. Torino 47, 15\u201368 (1989)","journal-title":"Rend. Sem. Mat. Univ. Polytec. Torino"},{"key":"3_CR3","volume-title":"Some Classes of Partial Differential Equations","author":"AV Bitzadze","year":"1981","unstructured":"Bitzadze, A.V.: Some Classes of Partial Differential Equations. Nauka, Moscow (1981). (in Russian)"},{"key":"3_CR4","volume-title":"Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light","author":"M Born","year":"2005","unstructured":"Born, M., Wolf, E.: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, Cambridge (2005)"},{"issue":"12","key":"3_CR5","doi-asserted-by":"publisher","first-page":"2545","DOI":"10.1016\/j.camwa.2013.09.009","volume":"66","author":"Q Cai","year":"2014","unstructured":"Cai, Q., Kollmannsberger, S., Sala-Lardies, E., Huerta, A., Rank, E.: On the natural stabilization of convection dominated problems using high order Bubnov-Galerkin finite elements. Comput. Math. Appl. 66(12), 2545\u20132558 (2014)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"3_CR6","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/0045-7825(73)90019-4","volume":"2","author":"PG Ciarlet","year":"1973","unstructured":"Ciarlet, P.G., Raviart, P.A.: Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Eng. 2(1), 17\u201331 (1973)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"3_CR7","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1145\/2516971.2516977","volume":"32","author":"K Crane","year":"2013","unstructured":"Crane, K., Weischedel, C., Wardetzky, M.: Geodesics in heat: a new approach to computing distance based on heat flow. ACM Trans. Graph. (TOG) 32(5), 152 (2013)","journal-title":"ACM Trans. Graph. (TOG)"},{"issue":"5","key":"3_CR8","doi-asserted-by":"publisher","first-page":"2468","DOI":"10.1137\/100788951","volume":"33","author":"Z Fu","year":"2011","unstructured":"Fu, Z., Jeong, W.K., Pan, Y., Kirby, R.M., Whitaker, R.T.: A fast iterative method for solving the eikonal equation on triangulated surfaces. SIAM J. Sci. Comput. 33(5), 2468\u20132488 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"3_CR9","doi-asserted-by":"publisher","first-page":"C473","DOI":"10.1137\/120881956","volume":"35","author":"Z Fu","year":"2013","unstructured":"Fu, Z., Kirby, R.M., Whitaker, R.T.: A fast iterative method for solving the eikonal equation on tetrahedral domains. SIAM J. Sci. Comput. 35(5), C473\u2013C494 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"3_CR10","series-title":"Applied Mathematical Sciences","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-44588-5","volume-title":"Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations","author":"A Gilles","year":"2006","unstructured":"Gilles, A., Pierre, K.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Applied Mathematical Sciences, 2nd edn. Springer, New York (2006). \n https:\/\/doi.org\/10.1007\/978-0-387-44588-5","edition":"2"},{"key":"3_CR11","unstructured":"G\u00f3mez, J.V., Alvarez, D., Garrido, S., Moreno, L.: Fast methods for eikonal equations: an experimental survey. arXiv preprint \n arXiv:1506.03771\n \n (2015)"},{"key":"3_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1007\/978-3-642-02256-2_9","volume-title":"Scale Space and Variational Methods in Computer Vision","author":"KS Gurumoorthy","year":"2009","unstructured":"Gurumoorthy, K.S., Rangarajan, A.: A Schr\u00f6dinger equation for the fast computation of approximate euclidean distance functions. In: Tai, X.-C., M\u00f8rken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 100\u2013111. Springer, Heidelberg (2009). \n https:\/\/doi.org\/10.1007\/978-3-642-02256-2_9"},{"issue":"5","key":"3_CR13","doi-asserted-by":"publisher","first-page":"2512","DOI":"10.1137\/060670298","volume":"30","author":"WK Jeong","year":"2008","unstructured":"Jeong, W.K., Whitaker, R.T.: A fast iterative method for eikonal equations. SIAM J. Sci. Comput. 30(5), 2512\u20132534 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"3_CR14","first-page":"406","volume":"27","author":"SN Kru\u017ekov","year":"1975","unstructured":"Kru\u017ekov, S.N.: Generalized solutions of the Hamilton-Jacobi equations of eikonal type. I. Formulation of the problems; existence, uniqueness and stability theorems; some properties of the solutions. Sb.: Math. 27(3), 406\u2013446 (1975)","journal-title":"Sb.: Math."},{"issue":"3","key":"3_CR15","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1137\/0913045","volume":"13","author":"FW Letniowski","year":"1992","unstructured":"Letniowski, F.W.: Three-dimensional Delaunay triangulations for finite element approximations to a second-order diffusion operator. SIAM J. Sci. Stat. Comput. 13(3), 765\u2013770 (1992)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"3_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5282-5","volume-title":"Maximum Principles in Differential Equations","author":"MH Protter","year":"2012","unstructured":"Protter, M.H., Weinberger, H.F.: Maximum Principles in Differential Equations. Springer, New York (2012). \n https:\/\/doi.org\/10.1007\/978-1-4612-5282-5"},{"key":"3_CR17","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-34467-4","volume-title":"Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems","author":"H Roos","year":"2008","unstructured":"Roos, H., Stynes, M., Tobiska, L.: Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems. Springer Series in Computational Mathematics, vol. 24. Springer, Heidelberg (2008). \n https:\/\/doi.org\/10.1007\/978-3-540-34467-4"},{"key":"3_CR18","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03359-3","volume-title":"Galerkin Finite Element Methods for Parabolic Problems","author":"V Thom\u00e9e","year":"2006","unstructured":"Thom\u00e9e, V.: Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics. Springer, Berlin (2006). \n https:\/\/doi.org\/10.1007\/978-3-662-03359-3"},{"issue":"2","key":"3_CR19","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1137\/S0036142901396533","volume":"41","author":"YHR Tsai","year":"2003","unstructured":"Tsai, Y.H.R., Cheng, L.T., Osher, S., Zhao, H.K.: Fast sweeping algorithms for a class of Hamilton-Jacobi equations. SIAM J. Numer. Anal. 41(2), 673\u2013694 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"3_CR20","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1109\/9.412624","volume":"40","author":"J Tsitsiklis","year":"1995","unstructured":"Tsitsiklis, J.: Fast marching methods. IEEE Trans. Autom. Control 40, 1528\u20131538 (1995)","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Lecture Notes in Computer Science","Finite Difference Methods. Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-11539-5_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T10:20:19Z","timestamp":1558347619000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-11539-5_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030115388","9783030115395"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-11539-5_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"26 January 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FDM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Finite Difference Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lozenetz","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bulgaria","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 June 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 June 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fdm2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/parallel.bas.bg\/dpa\/FDM2018\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}