Parallel Guaranteed Quality Delaunay Uniform Mesh Refinement

We present a theoretical framework for developing parallel guaranteed quality Delaunay mesh generation software that allows us to use commercial off-the-shelf sequential Delaunay meshers for two-dimensional geometries. In this paper, we describe our approach for constructing uniform meshes, that is, the meshes in which all elements have approximately the same size. Our uniform distributed- and shared-memory implementations are based on a simple (block) coarse-grained mesh decomposition. Our method requires only local communication, which is bulk and structured as opposed to fine and unpredictable communication of the other existing practical parallel guaranteed quality mesh generation and refinement techniques. Our experimental data show that on a cluster of more than 100 workstations we can generate about 0.9 billion elements in less than 5 minutes in the absence of work-load imbalances. Preliminary results for this paper were presented in [A. N. Chernikov and N. P. Chrisochoides, “Practical and efficient point insertion scheduling method for parallel guaranteed quality Delaunay refinement,” in Proceedings of the 18th Annual International Conference on Supercomputing, ACM Press, New York, 2004, pp. 48-57]. Our work in progress includes extending the presented approach, which can efficiently generate only uniform meshes, to nonuniform graded meshes.