Optimal Right Restricted Additive Schwarz Preconditioners for the Three-Dimensional Flux-Limited Multi-Group Radiation Diffusion Equations

Source abstract

When addressing the flux-limited multi-group radiation diffusion equations on a static spherically symmetric bounded geometry, the robust, efficient and scalable iterative solution strategies are sorely needed for dealing with large-scale sparse ill-conditioned linear systems of equations. Preconditioning is at the heart of significantly improving their convergence rates and thus markedly decreasing the overall computational burden. This article is concerned with the optimal exact and inexact right restricted additive Schwarz preconditioning algorithms with reasonable approximation assumptions for the involved submatrix inverses, algebraic multigrid subsolves and field-of-values equivalence analyses. Their sequential and two-layer hierarchical parallel implementations are taken into consideration within the JXPAMG software package. We evaluate their numerical robustness, computational efficiencies and parallel scalability by applying them to a realistic three-dimensional unstructured coupled simulation targeted at hydrodynamic instabilities during the inertial confinement fusion capsule implosion deceleration phase. Quantitative results demonstrate that they, carried out on China’s Tianhe-Xingyi supercomputer, achieve superior performance compared with several existing popular monolithic and block preconditioning strategies.