Volume 2, Issue 1
A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection

Lin-Bo Zhang

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 65-89.

Published online: 2009-02

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  • Abstract

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid (http://lsec.cc.ac.cn/phg/), a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the bisectioning refinement procedure.

  • Keywords

Adaptive refinement, bisection, tetrahedral mesh, parallel algorithm, MPI.

  • AMS Subject Headings

65Y05, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-65, author = {}, title = {A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {1}, pages = {65--89}, abstract = {

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid (http://lsec.cc.ac.cn/phg/), a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the bisectioning refinement procedure.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6016.html} }
TY - JOUR T1 - A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 65 EP - 89 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6016.html KW - Adaptive refinement, bisection, tetrahedral mesh, parallel algorithm, MPI. AB -

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid (http://lsec.cc.ac.cn/phg/), a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simultaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the bisectioning refinement procedure.

Lin-Bo Zhang. (2020). A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection. Numerical Mathematics: Theory, Methods and Applications. 2 (1). 65-89. doi:
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