A Delaunay Meshing Algorithm with “Built-in” Concurrency

Most Delaunay refinement-based meshing algorithms maintain a vertex-free “buffer zone” enclosing the edges and faces in the mesh boundary to guarantee a lower bound on edge lengths. To maintain this buffer zone, vertex insertions on or near the domain boundary must be strictly ordered—it is this ordering requirement that makes parallelization difficult. In this paper, we show that it is possible to enforce a minimum edge length condition locally and without strict ordering by searching the circumball conflict set for boundary edges and faces that are too close to a new vertex. We use the circumball conflict set as the basis of a new algorithm that can provably generate meshes whose tetrahedra have a maximum circumradius to shortest edge ratio of 2 when meshing polyhedral domains without acute boundary angles. The algorithm does not impose an order on vertex insertions, so we can prove correctness even in the case of concurrently inserted vertices. The result is a guaranteedquality Delaunay meshing algorithm that is specifically designed for parallelization; i.e. concurrency is “built-in”.