For solving the discretized three-temperature energy linear systems, Xu et al. proposed a physical-variable based coarsening two-level iterative method (PCTL algorithm) in 2009 and verified its efficiency by numerical experiments in practical applications. In this paper, we study in detail the specific convergence property of the PCTL algorithm based on the theory of algebraic multigrid method (AMG),and give a reasonable upper bound on the convergence factor, which provides a theoretical guarantee for the PCTL algorithm. Moreover, we also analyse the algebraic features that affect the convergence of the PCTL algorithm, such as diagonal dominance and coupling strength, hoping provides theoretical guidance for the applications and algorithm optimization of the PCTL algorithm.

翻译：针对离散化三温能量线性系统的求解，Xu等人于2009年提出了基于物理变量的粗化双层迭代方法(PCTL算法)，并通过实际应用中的数值实验验证了其有效性。本文基于代数多重网格法(AMG)理论，详细研究了PCTL算法的具体收敛性质，给出了收敛因子的合理上界，为PCTL算法提供了理论保证。此外，我们还分析了影响PCTL算法收敛性的代数特征，如对角占优性和耦合强度，以期为PCTL算法的应用与算法优化提供理论指导。