Delaunay Decoupling Method for Parallel Guaranteed Quality Planar Mesh Refinement

Creating in parallel guaranteed quality large unstructured meshes is a challenging problem. Parallel mesh generation procedures decompose the original mesh generation problem into smaller subproblems that can be solved in parallel. The subproblems can be treated as either completely or partially coupled, or they can be treated as completely decoupled. In this paper we present a parallel guaranteed quality Delaunay method for 2-dimensional domains which is based on the complete decoupling of the subproblems. As a result the method eliminates the communication and the synchronization during the meshing of the subproblems. Moreover, it achieves 100% code reuse of existing, fine-tuned, and well-tested sequential mesh generators. The approach we describe in this paper presents for the first time an effective way to create in parallel guaranteed quality meshes with billions of elements in a few hundreds of seconds, and at the same time demonstrates that these meshes can be generated in an efficient and scalable way. Our performance data indicate superlinear speedups.