A New Relaxed Splitting Preconditioner for Multidimensional Multi-Group Radiation Diffusion Equations

Abstract

Motivated by the ideas of Frigo et al. [SIAM J. Sci. Comput. 41 (2019) B694–B720], we develop a novel relaxed splitting preconditioner and consider its parallel implementation. Fully-coupled fully-implicit linearised algebraic systems arising from the multidimensional multi-group radiation diffusion equations are solved by using algebraic multigrid subsolvers. Spectral properties of the relaxed splitting right-preconditioned matrix are studied. This allows to introduce an easily implementable algebraic selection strategy for finding the corresponding relaxation parameter. Numerical experiments show that the new preconditioner outperforms some existing popular preconditioners in robustness and efficiency and is well scalable both algorithmically and in parallel.