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Volume 28, Issue 6
A Coarsening Algorithm on Adaptive Grids by the Newest Vertex Bisection and Its Applications

Long Chen & Chensong Zhang

DOI: 10.4208/jcm.1004-m3172

J. Comp. Math., 28 (2010), pp. 767-789.

Published online: 2010-12

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  • Abstract

In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimensions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.

  • Keywords

Adaptive finite element method, Coarsening, Newest vertex bisection, Multilevel preconditioning.

  • AMS Subject Headings

65M55, 65N55, 65N22, 65F10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-767, author = {Long Chen and Chensong Zhang}, title = {A Coarsening Algorithm on Adaptive Grids by the Newest Vertex Bisection and Its Applications}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {6}, pages = {767--789}, abstract = {

In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimensions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1004-m3172}, url = {http://global-sci.org/intro/article_detail/jcm/8549.html} }
TY - JOUR T1 - A Coarsening Algorithm on Adaptive Grids by the Newest Vertex Bisection and Its Applications AU - Long Chen & Chensong Zhang JO - Journal of Computational Mathematics VL - 6 SP - 767 EP - 789 PY - 2010 DA - 2010/12 SN - 28 DO - http://doi.org/10.4208/jcm.1004-m3172 UR - https://global-sci.org/intro/article_detail/jcm/8549.html KW - Adaptive finite element method, Coarsening, Newest vertex bisection, Multilevel preconditioning. AB -

In this paper, an efficient and easy-to-implement coarsening algorithm is proposed for adaptive grids obtained using the newest vertex bisection method in two dimensions. The new coarsening algorithm does not require storing the binary refinement tree explicitly. Instead, the structure is implicitly contained in a special ordering of triangular elements. Numerical experiments demonstrate that the proposed coarsening algorithm is efficient when applied for multilevel preconditioners and mesh adaptivity for time-dependent problems.

Long Chen and Chensong Zhang. (2010). A Coarsening Algorithm on Adaptive Grids by the Newest Vertex Bisection and Its Applications. Journal of Computational Mathematics. 28 (6). 767-789. doi:10.4208/jcm.1004-m3172
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