基于局部信息优先的代数多重网格粗化策略

A Grid Coarsening Strategy for Algebraic Multigrid Method Based on Local Information Priority Principle

网格粗化是实施代数多重网格方法的重要步骤之一。在网格粗化过程中,当出现多个最大集合势相同的网格点时,经典网格粗化策略中的集合势并不能精确表征网格点的整体强弱连接强度,导致网格粗化路径不唯一并影响后续求解阶段的计算效率。为克服这一不足,本文提出了一种基于局部信息优先原则的网格粗化策略,并发展了基于局部信息的整体强弱连接系数判别法和基于局部信息的二次粗化阈值判别法两种实施方法。数值计算表明:与经典网格粗化策略相比,本文提出的网格粗化策略可精确表征网格点之间的整体强弱连接强度,有效优化网格粗化路径,并在一定程度上提高了求解阶段的计算效率。

Grid coarsening is one of the most important procedures to implement the algebraic multigrid（AMG） method.In the process of grid coarsening,if the potential coarse-points（C-points）having the same maximum influence measure are not unique,the influence measure in the classical Ruge-Stúben（C-RS） coarsening strategy is not able to accurately describe the overall strength of strong connection.In this situation,several grid coarsening routines may exist,which would result in the non-uniqueness of grid distribution and exert effect on the computational efficiency of subsequent solution phase.To overcome this limitation,a grid coarsening strategy based on local information priority principle（LIPP-RS） is proposed and two corresponding implementation methods are developed in this paper：overall strong connection coefficient method and secondary coarsening threshold method.Calculation results of two numerical examples indicate that：compared with the C-RS coarsening strategy,the LIPP-RS strategy can accurately reflect the degree of overall strong connection strength,effectively optimize grid coarsening routines and improve the computational efficiency of solution phase to some extent.