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Distance function and extension in normal direction for implicitly defined interfaces

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  • In this paper we present a novel application of extrapolation procedure for three popular numerical algorithms to compute the distance function for an interface that is given only implicitly. The methods include the fast marching method [8], the fast sweeping method [10] and the linearization method [10]. The extrapolation procedure removes the necessity of a special initialization procedure for the grid nodes next to the interface that is used so far with the methods, thus it represents a natural extension of these methods. The extrapolation procedure can be used also for an extension of a function that is defined only locally on the interface in the direction given by the gradient of distance function [2].
    Mathematics Subject Classification: Primary: 35L50, 76M12; Secondary: 65L20.


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  • [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.


    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.


    S. Fomel, Traveltime Computation with the Linearized Eikonal Equation, Technical report, SEP 94, 1997.


    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.


    S. Hysing and S. Turek, The Eikonal equation: numerical efficiency vs. algorithmic complexity on quadrilateral grids, In Proceedings of Algoritmy, 2005, (2005), 22-31.


    S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003.doi: 10.1007/b98879.


    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.


    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.


    J. Sethian, Level Set Methods and Fast Marching Methods, Cambridge University Press, 1999.


    H. Zhao, A fast sweeping method for eikonal equations, Math. Comput., 74 (2005), 603-627.doi: 10.1090/S0025-5718-04-01678-3.


    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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