AMCF for a torus

Volume preserving mean curvature flow in three space dimensions

Uwe F. Mayer

System:	Hewlett-Packard HP-UX 9000/725
Computation time:	About 2 hours, 40 minutes to reach the singularity
	Another 12 hours, 50 minutes afterwards
Scale:	Major radius = 3, minor radius = 1, time step = 0.01
Vertices:	Initially 512, finally 546
Facets:	Initially 1024, finally 1088
Comment:	The interface becomes singular after 516 steps.
	The center vertices where identified in an appropriate manner after
	500 steps to extend the flow to after the singularity.

After 0000 time steps.

After 0100 time steps.

After 0200 time steps.

After 0300 time steps.

After 0400 time steps.

After 0500 time steps.

The interface becomes singular. Identifying all
vertices at the center belonging to a top facet
and all those belonging to a bottom facet yields
the following picture (having two vertices at the
center) from which the computations are restarted.
After 0500 time steps.

After 0510 time steps.

After 0520 time steps.

After 0530 time steps.

After 0550 time steps.

After 0600 time steps.

After 0700 time steps.

After 1000 time steps.

After 2250 time steps.

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mayer@math.utah.edu
Last updated: 01/29/97

After 0000 time steps.	After 0100 time steps.
After 0200 time steps.	After 0300 time steps.
After 0400 time steps.	After 0500 time steps.
The interface becomes singular. Identifying all vertices at the center belonging to a top facet and all those belonging to a bottom facet yields the following picture (having two vertices at the center) from which the computations are restarted.	After 0500 time steps.
After 0510 time steps.	After 0520 time steps.
After 0530 time steps.	After 0550 time steps.
After 0600 time steps.	After 0700 time steps.
After 1000 time steps.	After 2250 time steps.