Graded Delaunay decoupling method for parallel guaranteed quality planar mesh generation

We present a method for creating large two-dimensional graded Delaunay meshes on parallel machines. The method decouples the mesh generation procedure for each subdomain and thus eliminates the communication between processors, while the final mesh is of the same guaranteed quality as in the sequential case. This work extends our previous result on the uniform Delaunay decoupling method [L. Linardakis and N. Chrisochoides, SIAM J. Sci. Comput., 27 (2006), pp. 1394 1423], by allowing the element size to be governed by a sizing function, or a background mesh. The graded Delaunay decoupling method can produce in parallel very large graded meshes efficiently, demonstrating high speedup and scalability. Ten billion elements can be created in five minutes with small overrefinement (about 2%). The decoupling parallelization approach is effective, using off-the-shelf, well-tested, and fine-tuned sequential mesh generation libraries without modification.