Non-Averaged Mean Curvature Flow in two space dimensions

Uwe F. Mayer

System:AMD Phenom IIX4 830 2.8GHz, Windows 7, Cygwin
Computation time:About 2.5 minutes
Scale:Thickness of spiral = 0.5, initial discretization edge length about 0.078, time step = 0.00001
Nodes:Initially 975, finally 32
Edge threshold:Eliminated edge if length is less than 0.01
Comment:The closed curve unwinds before it shrinks to a round point.


The initial configuration.
after 0 steps
After 25,000 time steps.
after 25,000 steps

After 50,000 time steps.
after 50,000 steps
After 75,000 time steps.
after 75,000 steps

After 100,000 time steps.
after 100,000 steps
After 125,000 time steps.
after 125,000 steps

After 150,000 time steps.
after 150,000 steps
After 175,000 time steps.
after 175,000 steps

After 200,000 time steps.
after 200,00 steps
After 225,000 time steps.
after 225,000 steps

After 250,000 time steps.
after 250,000 steps
After 275,000 time steps.
after 275,000 steps

After 283,500 time steps.
after 282,500 steps
After 295,000 time steps.
after 295,000 steps

After 297,500 time steps.
after 297,500 steps
After 299,000 time steps.
after 299,000 steps

After 300,000 time steps.
after 300,000 steps
The interface has shrunk
to a round point.

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mayer@math.utah.edu
Last updated: Sun Jul 31 16:18:37 PDT 2016