Numerical Examples

A uniform grid is deformed dynamically to a grid clustered around a pair of circles. A constraint is imposed on the adaptation in that a particular grid line always remains a line. In this case it is grid line whose initial endpoints are a=(0,0.5) and b=(1,0.5). The endpoints of the line move according to the following:

The circles are located with centers at (0.5,0.2) and (0.5,0.8) and radius 0.1.

A 40 x 40 grid was used on the unit square [0,1] x [0,1]. The time step dt = 0.05. The final time was t = 3.0

This material is based upon work supported by the National Science Foundation under Grant No. 9732742.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.