Motion by intrinsic Laplacian of curvature

Interfaces and Free Boundaries

Volumn 1, Issue 1, 1999, Pages 107-123

  Chopp, David L ^a   Sethian, J A ^b  

^a Northwestern University   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005091671     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/6     Document Type: Article

References (30)

1. ADALSTEINSSON, D. & SETHIAN, J. A. A fast level set method for propagating interfaces. J. Comput. Phys. 118(2), (1995) 269-277.
2. ADALSTEINSSON, D. & SETHIAN, J. A. A unified level set approach to etching, deposition and lithography i: Algorithms and two-dimensional simulations. J. Comput. Phys. 120(1), (1995) 128-144.
3. ADALSTEINSSON, D. & SETHIAN, J. A. A unified level set approach to etching, deposition and lithography ii: Three-dimensional simulations. J. Comput. Phys. 122(2):348-366, 1995.
4. ADALSTEINSSON, D. & SETHIAN, J. A. The fast construction of extension velocities in level set methods. J. Comput. Phys. 148, (1999) 2-22.
5. ADALSTEINSSON, D. & SETHIAN, J. A. A unified level set approach to etching, deposition and lithography iii: Complex simulations and multiple effects. J. Comput. Phys. 138(1), (1997) 193-223.
6. CAHN, J. W., ELLIOTT, C. M., & NOVICK-COHEN, A. The Cahn-Hilliard equation with a concentration depedendent mobility: Motion by minus the Laplacian of the mean curvature. Eur. J. Appl. Math. 7, (1996) 287-301.
7. CAHN, J. W. and TAYLOR, J. E. Surface motion by surface diffusion. Acta Metallur. Mater. 42, (1994) 1045-1063.
8. CHOPP, D. L. Flow under geodesic curvature. Technical Report CAM 92-23, UCLA, May 1992.
9. CHOPP, D. L. Computing minimal surfaces via level set curvature flow. J. Comput. Phys. 106, (1993) 77-91.
10. CHOPP, D. L. & SETHIAN, J. A. Flow under curvature: Singularity formation, minimal surfaces, and geodesics. J. Exp. Math. 2(4), (1993) 235-255.
11. COLEMAN, B. D., FALK, R. S., & MOAKHER, M. Space-time finite element methods for surface diffusion with applications to the theory of the stability of cylinders. SIAM J. Computing 17(6), (1996) 1434-1448.
12. DAVI, F. & GURTIN, M. E. On the motion of a phase interface by surface diffusion. J. Appl. Math. Phys. 41, (1990) 782-811.
13. ELLIOTT, C. M. & GARCKE, H. Existence results for diffusive surface motion laws. Adv. Math. Sci. Appl. 7(1), (1997) 467-490.
14. ESCHER, J., MAYER, U. F., & SIMONETT, G. The surface diffusion flow for immersed hypersurfaces. SIAM J. Math. Anal. 29(6), (1998) 1419-1433.
15. EVANS, L. C., SONER, H. M., & SOUGANIDIS, P. E. Phase transitions and generalized motion by mean curvature. Commun. Pure Appl. Math. 45(9), (1992) 1097-1123.
16. GIGA, Y. & ITO, K. On pinching of curves moved by surface diffusion. Comm. Appl. Anal. 2(3), (1998) 393-405.
17. HUANG, H., GILMER, G. H., & DIAZ DE LA RUBIA, T. An atomistic simulator for thin film deposition in three dimensions. preprint, 1997.
18. MALLADI, R., SETHIAN, J. A., & VEMURI, B. C. Evolutionary fronts for topology-independent shape modeling and recovery. in Proceedings of Third European Conference on Computer Vision, Stockholm, Sweden, Lecture Notes in Computer Science, volume 800, pp. 3-13, (1994).
19. MULLINS, W. W. Theory of thermal grooving. J. Appl. Phy. 28, (1957) 333-339.
20. OSHER, S. & SETHIAN, J. A. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulation. J. Comput. Phys. 79, (1998) 12-49.
21. SETHIAN, J. A. An Analysis of Flame Propagation. PhD thesis, Dept. of Mathematics, University of California, Berkeley (1982).
22. SETHIAN, J. A. Curvature and the evolution of fronts. Comm. Math. Phys. 101, (1985) 487-499.
23. SETHIAN, J. A. Numerical methods for propagating fronts. in Concus, P. & Finn, R. (eds), Variational Methods for Free Surface Interfaces. Springer-Verlag, NY (1987).
24. SETHIAN, J. A. Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws. J. Differen. Geom. 31, (1990) 131-161.
25. SETHIAN, J. A. Level Set Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision and Material Science. Cambridge University Press, Cambridge (1996).
26. SETHIAN, J. A. A marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. USA 93(4), (1996) 1591-1595.
27. STUMPF, R. & SCHEFFLER, M. Ab Initio calculations of energies and self-diffusion on flat and stepped surfaces of Al and their implications on crystal growth. Phys. Rev. B 53, (1996).
28. SUSSMAN, M., SMEREKA, P., & OSHER, S. J. A level set method for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, (1994) 146-159.
29. VAN DE VORST, G. A. L. Modelling and Numerical Simulation of Viscous Sintering. PhD thesis, Eindhoven University of Technology (1994).
30. ZHU, J. & SETHIAN, J. A. Projection methods coupled to level set interface techniques. J. Comput. Phys. 102, (1992) 128-138.