Graded Delaunay Decoupling Method for Parallel Guaranteed Quality Planar Mesh Generation

We present a method for creating large 2D graded, guaranteed quality, 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 guaranteed quality. This work extents our previous result on the uniform Delaunay Decoupling method [19], by allowing the element size to be governed by a sizing function, or a background mesh, and thus to produce large graded meshes. The graded Delaunay decoupling method demonstrates high efficiency, ten billion elements can be created in five minutes, with very small over-refinement (about 2%), and also results high speed-ups. This parallelization approach is effective, using off-the-self, well tested and fine tuned, sequential mesh generation libraries without modification.