Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations
Year: 2018
Author: Xiaoqiang Yue, Shi Shu, Junxian Wang, Zhiyang Zhou
Communications in Computational Physics, Vol. 23 (2018), Iss. 2 : pp. 540–560
Abstract
Inspired by [Q. Y. Hu, S. Shu and J. X. Wang, Math. Comput., 79 (272) (2010): 2059-2078], we firstly present two nonoverlapping domain decomposition (DD) preconditioners Bah and Bsmh about the preserving-symmetry finite volume element (SFVE) scheme for solving two-dimensional three-temperature radiation diffusion equations with strongly discontinuous coefficients. It's worth mentioning that both Bah and Bsmh involve a SFVE sub-system with respect to a simple coarse space and SFVE sub-systems which are self-similar to the original SFVE system but embarrassingly parallel. Next, the nearly optimal estimation O((1+logdh)3) on condition numbers is proved for the resulting preconditioned systems, where d and h respectively denote the maximum diameters in coarse and fine grids. Moreover, we present algebraic and parallel implementations of Bah and Bsmh, develop parallel PCG solvers, and provide the numerical results validating the aforementioned theoretical estimations and stating the good algorithmic and parallel scalabilities.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0065
Communications in Computational Physics, Vol. 23 (2018), Iss. 2 : pp. 540–560
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: 2-D 3-T radiation diffusion equations nonoverlapping domain decomposition simple coarse space condition number parallel scalability.
Author Details
Xiaoqiang Yue Email
Shi Shu Email
Junxian Wang Email
Zhiyang Zhou Email
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