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Volume 9, Issue 1
Multigrid Multi-Level Domain Decomposition

Sheng Zhang & Hong-Ci Huang

J. Comp. Math., 9 (1991), pp. 17-27.

Published online: 1991-09

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  • Abstract

The domain decomposition method in this paper is based on PCG (Preconditioned Conjugate Gradient method). If $N$ is the number of subdomains, the number of sub-problems solved parallelly in a PCG step is $\frac{4}{3}(1-\frac{1}{4^{\log N+1}})N$. The condition number of the preconditioned system does not exceed $O(1+\log N)^3$. It is completely independent of the mesh size. The number of iterations required, to decrease the energy norm of the error by a fixed factor, is proportional to $O(1+\log N)^{\frac{3}{2}}$ .

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@Article{JCM-9-17, author = {Zhang , Sheng and Huang , Hong-Ci}, title = {Multigrid Multi-Level Domain Decomposition}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {1}, pages = {17--27}, abstract = {

The domain decomposition method in this paper is based on PCG (Preconditioned Conjugate Gradient method). If $N$ is the number of subdomains, the number of sub-problems solved parallelly in a PCG step is $\frac{4}{3}(1-\frac{1}{4^{\log N+1}})N$. The condition number of the preconditioned system does not exceed $O(1+\log N)^3$. It is completely independent of the mesh size. The number of iterations required, to decrease the energy norm of the error by a fixed factor, is proportional to $O(1+\log N)^{\frac{3}{2}}$ .

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9374.html} }
TY - JOUR T1 - Multigrid Multi-Level Domain Decomposition AU - Zhang , Sheng AU - Huang , Hong-Ci JO - Journal of Computational Mathematics VL - 1 SP - 17 EP - 27 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9374.html KW - AB -

The domain decomposition method in this paper is based on PCG (Preconditioned Conjugate Gradient method). If $N$ is the number of subdomains, the number of sub-problems solved parallelly in a PCG step is $\frac{4}{3}(1-\frac{1}{4^{\log N+1}})N$. The condition number of the preconditioned system does not exceed $O(1+\log N)^3$. It is completely independent of the mesh size. The number of iterations required, to decrease the energy norm of the error by a fixed factor, is proportional to $O(1+\log N)^{\frac{3}{2}}$ .

Zhang , Sheng and Huang , Hong-Ci. (1991). Multigrid Multi-Level Domain Decomposition. Journal of Computational Mathematics. 9 (1). 17-27. doi:
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