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

Convergence estimation and characteristic analysis of a two-level iterative algorithm for the discretized three-temperature energy linear systems