多群辐射扩散问题特征驱动的并行AMG法  

Feature-driven Parallel Algebraic Multigrid Methods for Multi-group Radiation Diffusion Problems

作　　者：舒适[1] 岳孝强 何剑萌 徐小文[2] 莫则尧[2] SHU Shi;YUE Xiaoqiang;HE Jianmeng;XU Xiaowen;MO Zeyao(School of Mathematics and Computational Science,Xiangtan University,Xiangtan,Hunan 411105,China;Institute of Applied Physics and Computational Mathematics,Beijing 100094,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105 [2]北京应用物理与计算数学研究所,北京100094

出　　处：《计算物理》2024年第1期87-97,共11页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11971414,12371373)资助项目。

摘　　要：对求解多群辐射扩散(MGRD)方程组的大规模离散系统的已有快速算法进行分类,给出相应的综述。基于近年来所设计的关于并行代数多重网格(AMG)方面的工作,形成基于物理量的近似Schur补型与基于物理和代数特征的组合型预条件算法和理论框架,并对这些工作在该框架下的要素进行了刻画。利用上述框架,设计一种具有基本逼近性和低计算复杂度的近似Schur补型预条件子,并建立相应的谱等价理论;对比数值实验表明:新预条件子具有更好的稳健性和计算效率。最后提出需要进一步解决的若干问题。Firstly,a review is given by classifying the existing fast algorithms for solving large-scale discrete linear systems arising from the Multi-Group Radiation Diffusion(MGRD)equations.Secondly,based on our recent work on parallel algebraic multigrid(AMG),two preconditioning algorithms and related theoretical frameworks are developed on a higher level.One is the approximate Schur complement type based on physical quantities and the other is the combined type based on physical and algebraic features,and the relevant components of these works are portrayed within these frameworks.Based on the above framework,a approximate Schur complement preconditioner with fundamental approximation property and low computational complexity is designed,and the corresponding spectral equivalence theory is established.Numerical experiments show that the new preconditioner has better robustness and computational efficiency.Finally,several issues that need to be further addressed are presented.

关 键 词：多群辐射扩散方程组 特征驱动 并行代数多重网格法 预条件子 近似Schur补 

分 类 号：O241.6[理学—计算数学] TP338.6[理学—数学]