OOF: Finite Element Analysis of Microstructures
/adaptive_mesh/smooth
Synopsis
Smooth attempts to smooth out gradients in node density. Repeatedly refining a region of the mesh can lead to a high density of nodes in that region and a low density of nodes nearby. This is sometimes undesirable and can lead to artifacts in the finite element solution. To reduce the gradients, smooth moves each node to the average position of its neighbors, if doing so does not increase E. On each iteration of the procedure, each node is addressed exactly once, but in a random order.[31]
Figure 4.2. Effect of the smooth function shows the results of three smoothing iterations applied to a simple mesh. This example has no material inhomogeneity--the only contribution to E comes from Eshape.
Outputs
On each iteration, ppm2oof prints the change in the mesh-energy and the fraction of attempted moves that were actually performed.
[31] An alternative implementation would be to effectively move all nodes at once, computing each node's new position from the old positions of its neighbors. This method is more difficult to program, requires more storage, and has little gain in efficiency. The implemented random method still converges exponentially fast.
