论文标题
离散的三个温度能量线性系统的两级迭代算法的收敛估计和特征分析
Convergence estimation and characteristic analysis of a two-level iterative algorithm for the discretized three-temperature energy linear systems
论文作者
论文摘要
为了求解离散的三元能量线性系统，Xu等。提出了一种基于物理变量的粗化两级迭代方法（PCTL算法），并在2009年通过数值实验验证了其在实际应用中的效率。在本文中，我们基于代数多机方法（AMG）的理论详细研究了PCTL算法的特定收敛性能，并在收敛因子上给出了合理的上限，该融合因子为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，例如对角线优势和耦合强度，希望PCTL算法的应用和算法优化为理论指导提供理论指导。
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.
