Multithread parallelization of Lepp-bisection algorithms

  • Authors:

  • Maria-Cecilia Rivara;Pedro Rodriguez;Rafael Montenegro;Gaston Jorquera

  • Affiliations:

  • Department of Computer Science, University of Chile, Santiago, Chile;Department of Computer Science, University of Chile, Santiago, Chile and Department of Information Systems, University of Bio-Bio, Concepción, Chile;University of Las Palmas de Gran Canaria, University Institute for Intelligent Systems and Numerical Applications for Engineering, Spain;Department of Computer Science, University of Chile, Santiago, Chile

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2012

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Abstract

Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge. The process is repeated until triangle t is destroyed. We discuss the algorithm, related synchronization issues, and the properties inherited from the serial algorithm. We present an empirical study that shows that a reasonably efficient parallel method with good scalability was obtained.