Publication Details




Parallel Delaunay Refinement for Restricted Polyhedral Domains


Demian Nave, Nikos Chrisochoides and Paul Chew.


Published in Computational Geometry: Theory and Applications, Volume 28, pages 191 -- 215, 2004




We describe a distributed memory parallel Delaunay refinement algorithm for polyhedral domains which can generate meshes containing tetrahedra with circumradius to shortest edge ratio less than 2, as long as the angle separating any two incident segments and/or facets is between 90 and 270 degrees. Input to our implementation is an element--wise partitioned, conforming Delaunay mesh of a restricted polyhedral domain which has been distributed to the processors of a parallel system. The submeshes of the distributed mesh are then independently refined by concurrently inserting new mesh vertices.Our algorithm allows a new mesh vertex to affect both the submesh tetrahedralizations and the submesh interfaces induced by the partitioning. This flexibility is crucial to ensure mesh quality, but it introduces unpredictable and variable latencies due to long delays in gathering remote data required for updating mesh data structures. In our experiments, more than 80% of this latency was masked with computation due to the fine--grained concurrency of our algorithm.Our experiments also show that the algorithm is efficient in practice, even for certain domains whose boundaries do not conform to the theoretical limits imposed by the algorithm. The algorithm we describe is the first step in the development of much more sophisticated guaranteed--quality parallel mesh generation algorithms.




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