@Article{CiCP-23-2,
author = {},
title = {Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {23},
number = {2},
pages = {540--560},
abstract = {<p style="text-align: justify;">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 $B^a_h$ and $B^{sm}_h$ about the preserving-symmetry finite volume element (SFVE)
scheme for solving two-dimensional three-temperature radiation diffusion equations
with strongly discontinuous coefficients. It&#39;s worth mentioning that both<span style="text-align: justify;">&nbsp;$B^a_h$ and $B^{sm}_h$&nbsp;</span>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&nbsp;$\mathcal{O}$((1+log$\frac{d}{h}$)<sup>3</sup>) 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 &nbsp;$B^a_h$ and $B^{sm}_h$, develop parallel PCG solvers, and provide the numerical
results validating the aforementioned theoretical estimations and stating the good algorithmic
and parallel scalabilities.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0065},
url = {https://global-sci.com/article/80020/substructuring-preconditioners-with-a-simple-coarse-space-for-2-d-3-t-radiation-diffusion-equations}
}