Dynamic Parallel 3D Delaunay Triangulation

Abstract

Delaunay meshing is a popular technique for mesh generation. Usually, the mesh has to be refined so that certain fidelity and quality criteria are met. Delaunay refinement is achieved by dynamically inserting and removing points in/from a Delaunay triangulation. In this paper, we present a robust parallel algorithm for computing Delaunay triangulations in three dimensions. Our triangulator offers fully dynamic parallel insertions and removals of points and is thus suitable for mesh refinement. As far as we know, ours is the first method that parallelizes point removals, an operation that significantly slows refinement down. Our shared memory implementation makes use of a custom memory manager and light-weight locks which greatly reduce the communication and synchronization cost. We also employ a contention policy which is able to accelerate the execution times even in the presence of high number of rollbacks. Evaluation on synthetic and real data shows the effectiveness of our method on widely used multi-core SMPs.