Seminár z kvalitatívnej teórie diferenciálnych rovníc

Seminar on Qualitative Theory of Differential Equations

Štvrtok 30.10.2014 o 14:00, poslucháreň M-223

Daniel Ševčovič (KAMŠ):

Tangential redistribution for mean-curvature driven evolution of surfaces and curves

Abstrakt:

The main goal of this talk is to investigate tangential redistribution of points on evolving immersed manifolds.

More precisely, we will analyze motion of surfaces or curves evolved in the normal direction by the curvature.

Although the tangential velocity has no impact on the shape of evolved manifolds, it is an important issue

in numerical approximation of any evolution model, since the quality of the mesh has a significant impact on the

result of the computation. We analyze the volume-oriented and length-oriented tangential redistribution methods.

We apply the proposed techniques to the particular case of mean curvature evolution of surfaces in $\mathbb{R}^3$.

We explain the numerical approximation of the model and present several experiments illustrating the performance

of the redistribution techniques. This is a joint work based on the joint paper with M.Remesikova, K.Mikula

and P.Sarkoci: Manifold evolution with tangential redistribution of points, SIAM J. Sci. Comput. 36-4 (2014).