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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Vydáno v:Applied numerical mathematics Ročník 62; číslo 4; s. 473 - 488
Hlavní autoři: Rivara, Maria-Cecilia, Rodriguez, Pedro, Montenegro, Rafael, Jorquera, Gaston
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.04.2012
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ISSN:0168-9274, 1873-5460
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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.
AbstractList 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.
Author Rivara, Maria-Cecilia
Rodriguez, Pedro
Montenegro, Rafael
Jorquera, Gaston
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  surname: Jorquera
  fullname: Jorquera, Gaston
  email: gjorquera@dcc.uchile.cl
  organization: Department of Computer Science, University of Chile, Santiago, Chile
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Issue 4
Keywords Finite element method
Parallel multithread refinement
Lepp-bisection algorithm
Triangulation refinement
Longest edge bisection
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Snippet Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations...
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SubjectTerms Algorithms
Charge
Finite element method
Lepp-bisection algorithm
Longest edge bisection
Mathematical analysis
Parallel multithread refinement
Refining
Synchronism
Terminals
Triangles
Triangulation
Triangulation refinement
Title Multithread parallelization of Lepp-bisection algorithms
URI https://dx.doi.org/10.1016/j.apnum.2011.07.011
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Volume 62
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