Substructuring Preconditioners with a Simple Coarse Space for 2-D 3-T Radiation Diffusion Equations (Communications in Computational Physics, 2018)
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 equationswith strongly discontinuous coefficients. It's worth mentioning that both $B^a_h$ and $B^{sm}_h$ involve a SFVE sub-system with respect to a simple coarse space and SFVE sub-systemswhich are self-similar to the original SFVE system but embarrassingly parallel. Next,the nearly optimal estimation $\mathcal{O}$((1+log$\frac{d}{h}$)3) on condition numbers is proved for theresulting preconditioned systems, where d and h respectively denote the maximumdiameters in coarse and fine grids. Moreover, we present algebraic and parallel implementationsof  $B^a_h$ and $B^{sm}_h$, develop parallel PCG solvers, and provide the numericalresults validating the aforementioned theoretical estimations and stating the good algorithmicand parallel scalabilities.
Keywords: 2-D 3-T radiation diffusion equations; nonoverlapping domain decomposition; simple coarse space; condition number; parallel scalability.