{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T01:40:14Z","timestamp":1649209214666},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,2,25]],"date-time":"2014-02-25T00:00:00Z","timestamp":1393286400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s00211-014-0613-5","type":"journal-article","created":{"date-parts":[[2014,2,24]],"date-time":"2014-02-24T21:01:15Z","timestamp":1393275675000},"page":"339-375","source":"Crossref","is-referenced-by-count":3,"title":["Analysis of high order fast interface tracking methods"],"prefix":"10.1007","volume":"128","author":[{"given":"Olof","family":"Runborg","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,2,25]]},"reference":[{"issue":"5","key":"613_CR1","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1137\/S0036142994260872","volume":"33","author":"P Albrecht","year":"1996","unstructured":"Albrecht, P.: The Runge-Kutta theory in a nutshell. SIAM J. Numer. Anal. 33(5), 1712\u20131735 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"613_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0962492904000169","volume":"13","author":"H-J Bungartz","year":"2004","unstructured":"Bungartz, H.-J., Griebel, M.: Sparse grids. Acta Numer. 13, 1\u2013121 (2004)","journal-title":"Acta Numer."},{"key":"613_CR3","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1017\/S1446788700027932","volume":"3","author":"JC Butcher","year":"1963","unstructured":"Butcher, J.C.: Coefficients for the study of Runge-Kutta integration processes. J. Austral. Math. Soc. 3, 185\u2013201 (1963)","journal-title":"J. Austral. Math. Soc."},{"key":"613_CR4","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.jcp.2006.07.032","volume":"220","author":"E Cand\u00e8s","year":"2006","unstructured":"Cand\u00e8s, E., Ying, L.: Fast geodesics computations with the phase flow method. J. Comput. Phys. 220, 6\u201318 (2006)","journal-title":"J. Comput. Phys."},{"key":"613_CR5","doi-asserted-by":"crossref","unstructured":"Cavaretta, A.S., Dahmen, W., Micchelli, C.A.: Stationary subdivision. Memoirs Amer. Math. Soc. 93(453), (1991)","DOI":"10.1090\/memo\/0453"},{"issue":"5","key":"613_CR6","doi-asserted-by":"crossref","first-page":"1388","DOI":"10.1137\/0522089","volume":"22","author":"I Daubechies","year":"1991","unstructured":"Daubechies, I., Lagarias, J.C.: Two-scale difference equations I. Existence and global regularity of solutions. SIAM J. Math. Anal. 22(5), 1388\u20131410 (1991)","journal-title":"SIAM J. Math. Anal."},{"issue":"4","key":"613_CR7","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1137\/0523059","volume":"23","author":"I Daubechies","year":"1992","unstructured":"Daubechies, I., Lagarias, J.C.: Two-scale difference equations II. Local regularity, infinite products of matrices and fractals. SIAM J. Math. Anal. 23(4), 1031\u20131079 (1992)","journal-title":"SIAM J. Math. Anal."},{"key":"613_CR8","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s00365-003-0543-4","volume":"20","author":"I Daubechies","year":"2004","unstructured":"Daubechies, I., Runborg, O., Sweldens, W.: Normal multiresolution approximation of curves. Constr. Approx. 20, 399\u2013463 (2004)","journal-title":"Constr. Approx."},{"key":"613_CR9","first-page":"44","volume-title":"Interpolation dyadique. Fractals. dimensions non enti\u00e8res et applications","author":"G Deslauriers","year":"1987","unstructured":"Deslauriers, G., Dubuc, S.: Interpolation dyadique. Fractals. dimensions non enti\u00e8res et applications, pp. 44\u201355. Masson, Paris (1987)"},{"key":"613_CR10","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/0167-8396(87)90001-X","volume":"4","author":"N Dyn","year":"1987","unstructured":"Dyn, N., Levin, D., Gregory, J.: A 4-point interpolatory subdivision scheme for curve design. Comput. Aided Geom. Des. 4, 257\u2013268 (1987)","journal-title":"Comput. Aided Geom. Des."},{"issue":"3","key":"613_CR11","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1137\/S1064827595293600","volume":"19","author":"J Glimm","year":"1998","unstructured":"Glimm, J., Grove, J.W., Li, X.L., Shyue, K.-M., Zeng, Y., Zhang, Q.: Three-dimensional front tracking. SIAM J. Sci. Comput. 19(3), 703\u2013727 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"613_CR12","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0196-8858(81)90040-3","volume":"2","author":"J Glimm","year":"1981","unstructured":"Glimm, J., Isaacson, E., Marchesin, D., McBryan, O.: Front tracking for hyperbolic systems. Adv. Appl. Math 2, 91\u2013119 (1981)","journal-title":"Adv. Appl. Math"},{"key":"613_CR13","doi-asserted-by":"crossref","unstructured":"Guskov, I., Vidimce, K., Sweldens, W., Schr\u00f6der, P.: Normal meshes. In: Computer graphics (SIGGRAPH \u201900 Proceedings), pp. 259\u2013268 (2000)","DOI":"10.1145\/344779.344831"},{"issue":"6","key":"613_CR14","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1007\/s10208-011-9104-6","volume":"11","author":"S Harizanov","year":"2011","unstructured":"Harizanov, S., Oswald, P., Shingel, T.: Normal multi-scale transforms for curves. Found. Comput. Math. 11(6), 617\u2013656 (2011)","journal-title":"Found. Comput. Math."},{"key":"613_CR15","unstructured":"Henrici, P.: Discrete variable methods in ordinary differential equations. Wiley, New York, London (1962)"},{"key":"613_CR16","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0021-9991(81)90145-5","volume":"39","author":"CW Hirt","year":"1981","unstructured":"Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201\u2013225 (1981)","journal-title":"J. Comput. Phys."},{"key":"613_CR17","unstructured":"Hosea, M.E.: A new recurrence for computing Runge-Kutta truncation error coefficients. SIAM J. Numer. Anal. 32(6), 1989\u20132001 (1995)"},{"key":"613_CR18","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1111\/j.1365-246X.1996.tb00021.x","volume":"125","author":"G Lambar\u00e9","year":"1996","unstructured":"Lambar\u00e9, G., Lucio, P.S., Hanyga, A.: Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of ray field. Geophys. J. Int. 125, 584\u2013598 (1996)","journal-title":"Geophys. J. Int."},{"issue":"1","key":"613_CR19","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-Jacobi formulations. J. Comput. Phys. 79(1), 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"key":"613_CR20","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1023\/A:1027315032100","volume":"20","author":"P Oswald","year":"2004","unstructured":"Oswald, P.: Smoothness of nonlinear subdivision schemes. Adv. Comp. Math 20, 401\u2013423 (2004)","journal-title":"Adv. Comp. Math"},{"key":"613_CR21","doi-asserted-by":"crossref","unstructured":"Oswald, P.: Normal multi-scale transforms for surfaces. In: Proceedings of the 7th international conference on Curves and Surfaces, pp. 527\u2013542. Springer-Verlag Berlin, Heidelberg (2012)","DOI":"10.1007\/978-3-642-27413-8_34"},{"issue":"2","key":"613_CR22","doi-asserted-by":"crossref","first-page":"365","DOI":"10.4310\/CMS.2009.v7.n2.a5","volume":"7","author":"O Runborg","year":"2009","unstructured":"Runborg, O.: Fast interface tracking via a multiresolution representation of curves and surfaces. Commun. Math. Sci. 7(2), 365\u2013398 (2009)","journal-title":"Commun. Math. Sci."},{"key":"613_CR23","doi-asserted-by":"crossref","unstructured":"Sepasian, N., Vilanova, A., Florack, L., Ter Haar Romeny, B.M.: A ray tracing method for geodesic based tractography in diffusion tensor images. In CVPRW \u201908. IEEE Computer Society conference on computer vision and pattern recognition, pp. 1\u20136 (2008)","DOI":"10.1109\/CVPRW.2008.4563002"},{"key":"613_CR24","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0021-9991(92)90307-K","volume":"100","author":"SO Unverdi","year":"1992","unstructured":"Unverdi, S.O., Tryggvason, G.: A front tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25\u201337 (1992)","journal-title":"J. Comput. Phys."},{"issue":"8","key":"613_CR25","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1190\/1.1443499","volume":"58","author":"V Vinje","year":"1993","unstructured":"Vinje, V., Iversen, E., Gj\u00f8ystdal, H.: Traveltime and amplitude estimation using wavefront construction. Geophysics 58(8), 1157\u20131166 (1993)","journal-title":"Geophysics"},{"key":"613_CR26","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.cagd.2005.06.003","volume":"22","author":"J Wallner","year":"2005","unstructured":"Wallner, J., Dyn, N.: Convergence and $$C^1$$ C 1 analysis of subdivision schemes on manifolds by proximity. Comput. Aided Geom. Des. 22, 593\u2013622 (2005)","journal-title":"Comput. Aided Geom. Des."},{"key":"613_CR27","doi-asserted-by":"crossref","unstructured":"Welch, J.E., Harlow, F.W., Shannon, J.P., Daly, B.J.: The MAC method: a computing technique for solving viscous, incompressible, transient fluid flow problems involving free surfaces. Los Alalmos Scientific Laboratory, Report LA-3425 (1966)","DOI":"10.2172\/4563173"},{"key":"613_CR28","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s00365-004-0581-6","volume":"22","author":"G Xie","year":"2005","unstructured":"Xie, G., Yu, T.P.-Y.: Smoothness analysis of nonlinear subdivision schemes of homoegeneous and affine invariant type. Constr. Approx. 22, 219\u2013254 (2005)","journal-title":"Constr. Approx."},{"key":"613_CR29","unstructured":"Zenger, C.: Sparse grids. In: Hackbusch, W. (ed.) Parallel algorithms for partial differential equations, volume 31 of Notes on numerical fluid mechanics, pp. 241\u2013251. Vieweg Verlag, Braunschweig (1991)"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-014-0613-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-014-0613-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-014-0613-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,27]],"date-time":"2022-03-27T15:32:37Z","timestamp":1648395157000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-014-0613-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,25]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["613"],"URL":"https:\/\/doi.org\/10.1007\/s00211-014-0613-5","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2,25]]}}}