Simultaneous Mesh Generation and Partitioning for Delaunay Meshes

In this paper, we present a new approach for the parallel generation and partitioning of unstructured 3D Delaunay meshes. The new approach couples the mesh generation and partitioning problems into a single optimization problem. Traditionally, these two problems are solved separately, first generating the mesh (usually sequentially) and then partitioning the mesh, either sequentially or in parallel. In the traditional approach, the overheads due to I/O and data movement exceed 50% of the total execution time. Even if parallel partitioning schemes are employed, data movement, synchronization, and data structure translation overheads are high; for applications which require frequent remeshing (e.g. crack growth simulations), these overheads are prohibitive. We present a method for solving the mesh partitioning and placement problem simultaneously with the mesh generation problem. By eliminating unnecessary and redundant cache, local, and remote memory accesses, we can speed up the generation and redistribution process, for very large meshes, by almost an order of magnitude compared to traditional approaches. Our results show that we can achieve nearly perfect equi-distribution of mesh elements over the processors, while maintaining reasonably good separator size, all while improving the quality of the mesh by eliminating many of the problems inherent in traditional parallel constrained mesh generation.