The Delaunay triangulation used by `meshtool` would be an ideal way to
refine the working mesh, as well as making a coarse mesh for initial
download. Unfortunately, adding a new node to an existing Delaunay
triangulation may have global consequences; it is not possible to predict
in advance how much of the current mesh should be replaced to accommodate the
new node. Doing this in parallel requires an enormous amount of communication
to make sure that the processors do not tread on each others' toes
[Williams:89c].

DIME uses the algorithm of Rivara [Rivara:84a;89a] for refinement of the mesh, which is well suited to loosely synchronous parallel operation, but results in a triangulation which is not a Delaunay triangulation, and thus lacks some desirable properties. The process of topological relaxation changes the connectivity of the mesh to make it a Delaunay triangulation.

It is usually desirable to avoid triangles in the mesh which have particularly acute angles, and topological relaxation will reduce this tendency. Another method of doing this is by moving the nodes toward the average position of their neighboring nodes; a physical analogy would be to think of the edges of the mesh as damped springs and allowing the nodes to move under the action of the springs.

Wed Mar 1 10:19:35 EST 1995