Tim Laux (University of Berkeley): A gradient-flow approach to thresholding for codimension-two mean-curvature flow

Mittwoch, 10.01.2018 16:00 im Raum M5
Mathematik und Informatik

The thresholding scheme is an efficient numerical scheme for mean curvature flow with natural extensions to mutliphase systems as well as higher codimensions. In this talk I will present the first convergence proof for the scheme in codimension two. It is well-known that for hypersurfaces, the scheme is compatible with the gradient-flow structure of mean-curvature flow in the sense that it satisfies a minimizing movements principle (Esedoglu-Otto ?15). I will show that an analogous principle holds true for thresholding in codimension two. In particular, the scheme dissipates an energy reminiscent of the Ginzburg-Landau energy of a vortex filament. The main ingredient for the (short-time) convergence result is a sharp energy bound away from the smooth mean-curvature flow. As opposed to previous results on hypersurfaces (L.-Otto ?16, ?17), this result is unconditional. If time permits, I will demonstrate how this variational viewpoint facilities the design of new schemes. This is joint work with Aaron Yip (Purdue).

Angelegt am Dienstag, 07.11.2017 11:00 von cgiet_01
Geändert am Mittwoch, 20.12.2017 15:10 von cgiet_01
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