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 0 time steps.
after 0 steps
After 100 time steps.
after 100 steps

After 200 time steps.
after 200 steps
After 300 time steps.
after 300 steps

After 400 time steps.
after 400 steps
After 500 time steps.
after 500 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 500 time steps.
after 501 steps

After 510 time steps.
after 510 steps
After 520 time steps.
after 520 steps

After 530 time steps.
after 530 steps
After 550 time steps.
after 550 steps

After 600 time steps.
after 600 steps
After 700 time steps.
after 700 steps

After 1000 time steps.
after 1000 steps
After 2250 time steps.
after 2250 steps

Back

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

After 0 time steps.	After 100 time steps.
After 200 time steps.	After 300 time steps.
After 400 time steps.	After 500 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 500 time steps.
After 510 time steps.	After 520 time steps.
After 530 time steps.	After 550 time steps.
After 600 time steps.	After 700 time steps.
After 1000 time steps.	After 2250 time steps.