{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:43:37Z","timestamp":1787330617443,"version":"build-2736575974"},"reference-count":16,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>We introduce a new level set method for motion in normal direction. It is based on a formulation in the form of a second order forward-backward diffusion equation. The equation is discretized by the finite volume method. We propose a semi-implicit time discretization taking into account the forward diffusion part of the solution in an implicit way, while the backward diffusion part is treated explicitly. When forward diffusion dominates, a straightforward reconstruction of the solution is used, while larger (smoothing) stencils are used when backward diffusion dominates. The method is precise on coarse grids and is second order accurate for smooth solutions. Numerical experiments show an optimal coupling of time and space steps with $\\tau=h$, and no stronger CFL condition is required. Numerical tests with the scheme are discussed on representative examples.<\/jats:p>","DOI":"10.1137\/09075946x","type":"journal-article","created":{"date-parts":[[2010,5,28]],"date-time":"2010-05-28T18:33:35Z","timestamp":1275071615000},"page":"1527-1544","source":"Crossref","is-referenced-by-count":17,"title":["A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach"],"prefix":"10.1137","volume":"32","author":[{"given":"Karol","family":"Mikula","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mario","family":"Ohlberger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,5,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:1999149"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/060651203"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100322"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/070685038"},{"key":"R5","unstructured":"O. Drblikov\u00e1 and K. Mikula,\n                      Semi-implicit diamond-cell finite volume scheme for 3D nonlinear tensor diffusion in coherence enhancing image filtering\n                      , Finite Volumes for Complex Applications V: Problems and Perspectives, R. Eymard and J. M.Herard, eds., ISTE and Wiley, London, 2008, pp. 343\u2013350."},{"key":"R6","doi-asserted-by":"crossref","unstructured":"R. Eymard, T. Gallouet, and R. Herbin,\n                      Finite volume methods\n                      , Handbook of Numerical Analysis, Vol. VII: Solution of Equations in\n                      R\n                      , North-Holland, Amsterdam, 2000, pp. 713-1020.","DOI":"10.1016\/S1570-8659(00)07005-8"},{"key":"R7","unstructured":"C. Erath,\n                      Adaptive Finite Volume Methode\n                      , Diploma thesis, Vienna University of Technology, Vienna, Austria, 2005 (in German)."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-002-0089-1"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2006.06.002"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/050646561"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/s002080050179"},{"key":"R12","unstructured":"Z. Kriv\u00e1 and K. Mikula,\n                      Adaptive diamond cell finite volume method in image processing\n                      , in Proceedings of ALGORITMY 2009\u201418th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, Slovak University of Technology, 2009, pp. 121\u2013133."},{"key":"R13","unstructured":"K. Mikula and M. Ohlberger,\n                      A new class of implicit-inflow\/explicit-outflow schemes for solving variable velocity advection equations\n                      , to appear."},{"key":"R14","unstructured":"S. Osher and R. Fedkiw,\n                      Level Set Methods and Dynamic Implicit Surfaces\n                      , Appl. Math. Sci. 153, Springer, Berlin, 2000."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90002-2"},{"key":"R16","unstructured":"J. A. Sethian,\n                      Level Set Methods and Fast Marching Methods, Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science\n                      , Cambridge University Press, New York, 1999."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/09075946X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:15:59Z","timestamp":1787328959000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/09075946X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/09075946X"],"URL":"https:\/\/doi.org\/10.1137\/09075946x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}