  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.
