Engineering with Computers

, Volume 22, Issue 2, pp 75–93 | Cite as

Embarrassingly parallel mesh refinement by edge subdivision

  • David C. ThompsonEmail author
  • Philippe P. Pébay
Original Article


We have previously proposed a new technique for the communication-free adaptive refinement of tetrahedral meshes that works for all configurations. Implementations of the scheme must deal with all possible geometric configurations, which results in a large number of cases that in turn result in practical programming issues. In this article, we address this issue with a Python script that generates C++ code using the symmetric group \({\mathfrak{S}}_{4}\) acting over canonical topological and geometric configurations. We then analyze the performance of the technique by characterizing (a) mesh quality, (b) execution time and parallel speedup, and (c) traits of the algorithm that could affect quality or execution time differently for different meshes and different mesh refinement strategies. This article also details the method used to debug the many subdivision templates that the algorithm relies upon. Mesh quality is on par with other similar refinement schemes, and we suggest a more elaborate technique that may substantially improve mesh quality. We show that throughput on modern hardware can exceed 600,000 output tetrahedra per second per processor, and that the method is embarrassingly parallel—assuming the application has partitioned the input properly.


Adaptive tetrahedral tessellation Parallel mesh refinement Streaming subdivision Symmetric groups 



David C. Thompson and Philippe P. Pébay were supported by the United States Department of Energy, Office of Defense Programs. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the United States Department of Energy under contract DE-AC04-94-AL85000.


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Copyright information

© Springer-Verlag London Limited 2006

Authors and Affiliations

  1. 1.Sandia National Laboratories, MS 9152LivermoreUSA

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