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Perform Lloyd relaxation on a mesh and its dual
.
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Perform Lloyd relaxation on a mesh and its dual
.
Briefly, Lloyd relaxation is a technique to smooth out a mesh. The centroid of each cell is computed from its vertex positions, then vertices are placed at the average of their connected cells' centroids, and the process iterates until convergence.
In the parallel algorithm, an extra ghost layer of cells is exchanged. This allows us to compute the centroids for boundary cells on each processor where they appear; this eliminates the need for one round of data exchange (for those centroids) between processors. New vertex positions must be sent from owning processors to processors sharing those vertices. Convergence is measured as the maximum distance moved by any vertex.