Multithread parallelization of Lepp-bisection algorithms

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...

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Bibliographic Details
Published in:Applied numerical mathematics Vol. 62; no. 4; pp. 473 - 488
Main Authors: Rivara, Maria-Cecilia, Rodriguez, Pedro, Montenegro, Rafael, Jorquera, Gaston
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2012
Subjects:
Algorithms
Charge
Finite element method
Lepp-bisection algorithm
Longest edge bisection
Mathematical analysis
Parallel multithread refinement
Refining
Synchronism
Terminals
Triangles
Triangulation
Triangulation refinement
Finite element method
Parallel multithread refinement
Lepp-bisection algorithm
Triangulation refinement
Longest edge bisection
ISSN:0168-9274, 1873-5460
Online Access:Get full text
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Summary: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.
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ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2011.07.011