We consider a threshold-type algorithm for curvature-dependent motions (CDM for short) of hypersurfaces. This algorithm was numerically studied by Kimura - Notsu [
Citation: |
[1] |
G. Barles and C. Georgelin, A simple proof of convergence for an approximation scheme for computing motion by mean curvature, SIAM J. Numer. Anal., 32 (1995), 484-500.
doi: 10.1137/0732020.![]() ![]() ![]() |
[2] |
J. Bence, B. Merriman and S. Osher, Diffusion generated motion by mean curvature, in "Computational Crystal Growers Workshop", J. Taylor ed., Selected Lectures in Math., Amer. Math. Soc., Province, 1992.
![]() |
[3] |
A. Chambolle, An algorithm for mean curvature motion, Interfaces Free Bound., 6 (2004), 195-218.
![]() ![]() |
[4] |
A. Chambolle and M. Novaga, Approximation of the anisotropic mean curvature flow, Math. Models Methods Appl. Sci., 17 (2007), 833-844.
doi: 10.1142/S0218202507002121.![]() ![]() ![]() |
[5] |
A. Chambolle and M. Novaga, Implicit time discretization of the mean curvature flow with a discontinuous forcing term, Interfaces Free Bound., 10 (2008), 283-300.
![]() ![]() |
[6] |
M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. A. M. S., 27 (1992), 1-67.
doi: 10.1090/S0273-0979-1992-00266-5.![]() ![]() ![]() |
[7] |
S. Esedoḡlu, S.J. Ruuth and R. Tsai, Diffusion generated motion using the signed distance function, J. Comp. Phys., 229 (2010), 1017-1042.
doi: 10.1016/j.jcp.2009.10.002.![]() ![]() ![]() |
[8] |
T. Eto, Y. Giga and K. Ishii, An area minimizing scheme for anisotropic mean curvature flow, Adv. Differential Equations, 17 (2012), 1031-1084.
![]() ![]() |
[9] |
L.C. Evans, Convergence of an algorithm for mean curvature motion, Indiana Univ. Math. J., 42 (1993), 533-557.
doi: 10.1512/iumj.1993.42.42024.![]() ![]() ![]() |
[10] |
L.C. Evans and J. Spruck, Motion of level sets by mean curvature Ⅱ, Trans. Amer. Math. Soc., 330 (1992), 321-332.
doi: 10.1090/S0002-9947-1992-1068927-8.![]() ![]() ![]() |
[11] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1983.
![]() ![]() |
[12] |
K. Ishii and M. Kimura, Convergence of a threshold-type algorithm using the signed distance function, Interfaces Free Bound., 18 (2016), 479-522.
doi: 10.4171/IFB/371.![]() ![]() ![]() |
[13] |
M. Kimura and H. Notsu, A level set method using the signed distance function, Japan J. Indust. Appl. Math., 19 (2002), 415-446.
doi: 10.1007/BF03167487.![]() ![]() ![]() |
[14] |
S. Koike, A Beginner's Guide to the Theory of Viscosity Solutions, MSJ Memoirs, 13. Mathematical Society of Japan, Tokyo, 2004.
![]() ![]() |
[15] |
F. Leoni, Convergence of an approximation scheme for curvature-dependent motion of sets, SIAM J. Numer. Anal., 39 (2001), 1115-1131.
doi: 10.1137/S0036142900370459.![]() ![]() ![]() |
[16] |
R.Z. Mohammad and K. Švadlenka, Multiphase volume-preserving interface motion via localized signed distance vector scheme, Discrete and Continuous Dynamical Systems, Series S, 8 (2015), 969-988.
doi: 10.3934/dcdss.2015.8.969.![]() ![]() ![]() |
[17] |
L. Vivier, Convergence of an approximation scheme for computing motions with curvature dependent velocities, Differential Integral Equations, 13 (2000), 1263-1288.
![]() ![]() |
Graphs of
Graphs of of