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Volume 21, Issue 4
Gauss-Seidel-Type Multigrid Methods

Zhao-Hui Huang & Qian-Shun Chang

J. Comp. Math., 21 (2003), pp. 421-434.

Published online: 2003-08

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  • Abstract

By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time (for one V-cycle and the setup phase) and computational complexity.

  • Keywords

Multigrid methods, Gauss-Seidel solution, Interpolation formula, Convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-421, author = {Huang , Zhao-Hui and Chang , Qian-Shun}, title = {Gauss-Seidel-Type Multigrid Methods}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {4}, pages = {421--434}, abstract = {

By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time (for one V-cycle and the setup phase) and computational complexity.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8884.html} }
TY - JOUR T1 - Gauss-Seidel-Type Multigrid Methods AU - Huang , Zhao-Hui AU - Chang , Qian-Shun JO - Journal of Computational Mathematics VL - 4 SP - 421 EP - 434 PY - 2003 DA - 2003/08 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8884.html KW - Multigrid methods, Gauss-Seidel solution, Interpolation formula, Convergence. AB -

By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time (for one V-cycle and the setup phase) and computational complexity.

Huang , Zhao-Hui and Chang , Qian-Shun. (2003). Gauss-Seidel-Type Multigrid Methods. Journal of Computational Mathematics. 21 (4). 421-434. doi:
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