【摘要】 辐射扩散问题广泛出现在天体物理学和惯性约束聚变等多物理耦合领域,基于问题的物理与代数特征的AMG法已成为当今多重网格法研究领域的热点.本文重点针对三温辐射扩散方程组的线性化离散系统,首先给出了一种常见的UA-AMG预条件算法及相应的PGMRES解法器T2T2-ILU(0)-V-FGMRES.进一步,为改善该解法器的计算性能,对不同离散系统凝练了若干物理和代数特征,设计了基于这些特征的自适应UA-AMG预条件算法,并研制了相应的PGMRES解法器Adapt-UA-AMG-FGMRES.数值实验表明:新解法器具有更好的稳健性和计算效率,与解法器T2T2-ILU(0)-V-FGMRES和HMIS-V-FGMRES(在基于几种常见非聚集型粗化算法的AMG预条件子中计算性能最好)相比CPU时间分别减少了约49.1%和25.3%.上述算法设计思想容易推广到多群辐射扩散方程组等更一般的模型问题中.更多还原

【Abstract】 Radiation diffusion problems are widespread in multi-physics coupling fields such as astrophysics and inertial confinement fusion.Algebraic Multigrid(AMG) methods based on the physical and algebraic features of a problem have become a hot topic in the field of multigrid research.This paper proposes T2T2-ILU(0)-V-FGMRES solver for efficiently solving linearized discrete systems derived from three-temperature radiation diffusion equations.This solver is a PGMRES solver employing a common unsmoothed aggregation AMG(UA-AMG) preconditioner.Furthermore,several physical and algebraic features are extracted from different discrete systems to enhance the computational performance.Based on these features,we develop an adaptive UA-AMG preconditioned FGMRES solver,termed Adapt-UA-AMG-FGMRES.Numerical experiments show that the new solver exhibits better robustness and computational efficiency.Compared to the T2T2-ILU(0)-V-FGMRES and HMIS-V-FGMRES solvers(best common non-aggregation AMG preconditioners),the CPU time of the new solver is reduced by approximately 49.1% and 25.3%,respectively.It should be noted that the algorithmic design principles can be easily extended to more general model problems,such as multi-group radiative diffusion equations.更多还原