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Displaying similar documents to “Forced anisotropic mean curvature flow of graphs in relative geometry”

Computational studies of non-local anisotropic Allen-Cahn equation

Michal Beneš, Shigetoshi Yazaki, Masato Kimura (2011)

Mathematica Bohemica

Similarity:

The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by Rubinstein and Sternberg in 1992 is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We study this motion approximately by the mentioned PDE, generalize the problem by including anisotropy and discuss the computational results obtained.

Gaussian curvature based tangential redistribution of points on evolving surfaces

Medľa, Matej, Mikula, Karol

Similarity:

There exist two main methods for computing a surface evolution, level-set method and Lagrangian method. Redistribution of points is a crucial element in a Lagrangian approach. In this paper we present a point redistribution that compress quads in the areas with a high Gaussian curvature. Numerical method is presented for a mean curvature flow of a surface approximated by quads.

Diffuse-interface treatment of the anisotropic mean-curvature flow

Michal Beneš (2003)

Applications of Mathematics

Similarity:

We investigate the motion by mean curvature in relative geometry by means of the modified Allen-Cahn equation, where the anisotropy is incorporated. We obtain the existence result for the solution as well as a result concerning the asymptotical behaviour with respect to the thickness parameter. By means of a numerical scheme, we can approximate the original law, as shown in several computational examples.