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Semi-implicit Alternating Discrete Duality Finite Volume Scheme for Curvature Driven Level Set Equation

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Book cover Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

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Abstract

Linear semi-implicit Alternating Discrete Duality Finite Volume (ADDFV) numerical scheme for the solution of regularized curvature driven level set equation is presented. The scheme requires in each time step to solve algebraic system with a half number of unknowns than necessary in standard DDFV scheme. The stability estimations are proved and comparisons for one numerical experiment are provided.

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References

  1. Andreianov, B., Boyer, F., Hubert, F.: Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Numer. Meth. Part. D. E. 23(1), 145–195 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Deckelnick, K., Dziuk, G.: Error estimates for a semi-implicit fully discrete finite element scheme for the mean curvature flow of graphs. Interfaces Free Bound. 2, 341–359 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Domelevo, K., Omnès, P.: A finite volume method for the laplace equation on almost arbitrary two-dimensional grids. M2AN. Math. Model. Numer. Anal. 39(6), 1203–1249 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Evans, L.C., Spruck, J.: Motion of level sets by mean curvature I. J. Differ. Geom. 33, 635–681 (1991)

    MATH  MathSciNet  Google Scholar 

  5. Eymard, R., Handlovičová, A., Mikula, K.: Study of a finite volume scheme for the regularized mean curvature flow level set equation. IMA J. Numer. Anal. 31(3), 813–846 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  6. Handlovičová, A., Kotorová, D.: Convergence of a semi-implicit discrete duality finite volume scheme for the curvature driven level set equation in 2d. Kybernetika 49(6), 829–854 (2013)

    MATH  Google Scholar 

  7. Handlovičová, A., Mikula, K., Sgallari, F.: Semi-implicit complementary volume scheme for solving level set like equations in image processing and curve evolution. Numer. Math. 93, 675–695 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hermeline, F.: A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160(2), 481–499 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Mikula, K., Sarti, A., Sgallari, F.: Co-volume method for Riemannian mean curvature flow in subjective surfaces multiscale segmentation. Comput. Visual. Sci. 9(1), 23–31 (2006)

    Article  MathSciNet  Google Scholar 

  10. Oberman, A.: A convergent monotone difference scheme for motion of level sets by mean curvature. Numer. Math. 99(2), 365–379 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Sethian, J.: Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and material science. Cambridge University Press, New York (1999)

    MATH  Google Scholar 

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Acknowledgments

This work was supported by grants APVV-0184-10 and VEGA 1/1137/12.

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Authors and Affiliations

  1. Department of Mathematics, Slovak University of Technology, Radlinského 11, 813 68, Bratislava, Slovakia

    Angela Handlovičová & Peter Frolkovič

Authors
  1. Angela Handlovičová
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  2. Peter Frolkovič
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Corresponding author

Correspondence to Angela Handlovičová .

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Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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Handlovičová, A., Frolkovič, P. (2014). Semi-implicit Alternating Discrete Duality Finite Volume Scheme for Curvature Driven Level Set Equation. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_32

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