Convergence of the PCTL algorithm for solving the discretized 3T energy equations in RHD problems

For solving the three-temperature linear system arising from the radiation hydrodynamics (RHD) problem, Xu et. proposed a physical-variable based coarsening algebraic two level (PCTL) iterative method and verified its efficiency by numerical experiments. However, there is still a lack of quantitative evaluation of the performance of PCTL algorithm, thus we aim to fill in this blank in this paper. By theoretical analysis, we give an estimation on the convergence factor of the PCTL algorithm and show it is independent of the problem size, which provides a theoretical guarantee for solving large-scale problems. Moreover, we also discuss the factors that affect the efficiency of PCTL algorithm and provide a direction for the efficient application of the PCTL algorithm.