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Volume 25, Issue 1
Multigrid Algorithm for the Coupling System of Natural Boundary Element Method and Finite Element Method for Unbounded Domain Problems

Sheng Zhang & Dehao Yu

J. Comp. Math., 25 (2007), pp. 13-26.

Published online: 2007-02

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  • Abstract

In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.

  • Keywords

Multigird algorithm, Finite element method, Boundary element method, Coupling, Unbounded domain problem.

  • AMS Subject Headings

65N30, 65N38, 65N22, 65F10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-13, author = {Sheng Zhang and Dehao Yu}, title = {Multigrid Algorithm for the Coupling System of Natural Boundary Element Method and Finite Element Method for Unbounded Domain Problems}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {1}, pages = {13--26}, abstract = {

In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8669.html} }
TY - JOUR T1 - Multigrid Algorithm for the Coupling System of Natural Boundary Element Method and Finite Element Method for Unbounded Domain Problems AU - Sheng Zhang & Dehao Yu JO - Journal of Computational Mathematics VL - 1 SP - 13 EP - 26 PY - 2007 DA - 2007/02 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8669.html KW - Multigird algorithm, Finite element method, Boundary element method, Coupling, Unbounded domain problem. AB -

In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.

Sheng Zhang and Dehao Yu. (2007). Multigrid Algorithm for the Coupling System of Natural Boundary Element Method and Finite Element Method for Unbounded Domain Problems. Journal of Computational Mathematics. 25 (1). 13-26. doi:
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