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Annihilation of two interfaces in a hybrid system
Distance function and extension in normal direction for implicitly defined interfaces
1. | Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovak Republic, Slovak Republic, Slovak Republic |
References:
[1] |
D. Adalsteinsson and J. Sethian, The fast construction of extension velocities in level set methods, J. Comput. Phys., 148 (1999), 2-22.
doi: 10.1006/jcph.1998.6090. |
[2] |
T. D. Aslam, A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys., 193 (2004), 349-355.
doi: 10.1016/j.jcp.2003.08.001. |
[3] |
S. Fomel, Traveltime Computation with the Linearized Eikonal Equation, Technical report, SEP 94, 1997. |
[4] |
P. Frolkovič, Flux-based level set method for extrapolation along characteristics using immersed interface formulation, In P. Struk, editor, Magia, Slovak University of Technology, Bratislava, (2010), 15-26. |
[5] |
S. Hysing and S. Turek, The Eikonal equation: numerical efficiency vs. algorithmic complexity on quadrilateral grids, In Proceedings of Algoritmy, 2005, (2005), 22-31. |
[6] |
S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003.
doi: 10.1007/b98879. |
[7] |
E. Rouy and A. Tourin, A viscosity solutions approach to shape-from-shading, SIAM J. Num. Anal., 29 (1992), 867-884.
doi: 10.1137/0729053. |
[8] |
J. Sethian, A fast marching level set method for monotonically advancing fronts, Proc. Nat. Acad. Sci., 93 (1996), 1591-1595.
doi: 10.1073/pnas.93.4.1591. |
[9] |
J. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999. |
[10] |
H. Zhao, A fast sweeping method for eikonal equations, Math. Comput., 74 (2005), 603-627.
doi: 10.1090/S0025-5718-04-01678-3. |
[11] |
H. Zhao, T. Chan, B. Merriman and S. Osher, A variational level set approach to multiphase motion, J. Comput. Phys., 127 (1996), 179-195.
doi: 10.1006/jcph.1996.0167. |
show all references
References:
[1] |
D. Adalsteinsson and J. Sethian, The fast construction of extension velocities in level set methods, J. Comput. Phys., 148 (1999), 2-22.
doi: 10.1006/jcph.1998.6090. |
[2] |
T. D. Aslam, A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys., 193 (2004), 349-355.
doi: 10.1016/j.jcp.2003.08.001. |
[3] |
S. Fomel, Traveltime Computation with the Linearized Eikonal Equation, Technical report, SEP 94, 1997. |
[4] |
P. Frolkovič, Flux-based level set method for extrapolation along characteristics using immersed interface formulation, In P. Struk, editor, Magia, Slovak University of Technology, Bratislava, (2010), 15-26. |
[5] |
S. Hysing and S. Turek, The Eikonal equation: numerical efficiency vs. algorithmic complexity on quadrilateral grids, In Proceedings of Algoritmy, 2005, (2005), 22-31. |
[6] |
S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003.
doi: 10.1007/b98879. |
[7] |
E. Rouy and A. Tourin, A viscosity solutions approach to shape-from-shading, SIAM J. Num. Anal., 29 (1992), 867-884.
doi: 10.1137/0729053. |
[8] |
J. Sethian, A fast marching level set method for monotonically advancing fronts, Proc. Nat. Acad. Sci., 93 (1996), 1591-1595.
doi: 10.1073/pnas.93.4.1591. |
[9] |
J. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999. |
[10] |
H. Zhao, A fast sweeping method for eikonal equations, Math. Comput., 74 (2005), 603-627.
doi: 10.1090/S0025-5718-04-01678-3. |
[11] |
H. Zhao, T. Chan, B. Merriman and S. Osher, A variational level set approach to multiphase motion, J. Comput. Phys., 127 (1996), 179-195.
doi: 10.1006/jcph.1996.0167. |
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