三温能量方程离散线性系统的两层迭代算法收敛因子估计及特征分析

doi:10.19596/j.cnki.1001-246x.8767

计算物理 ›› 2024, Vol. 41 ›› Issue (1): 122-130.DOI: 10.19596/j.cnki.1001-246x.8767

• 面向超级计算机的性能优化技术与数值并行算法专刊 • 上一篇下一篇

三温能量方程离散线性系统的两层迭代算法收敛因子估计及特征分析

郝悦¹^,²(), 黄思路¹^,², 徐小文¹^,²^,*()

1. 计算物理全国重点实验室, 北京 100088
2. 北京应用物理与计算数学研究所, 北京 100094

收稿日期:2023-05-30 出版日期:2024-01-25 发布日期:2024-02-05
通讯作者: 徐小文
作者简介:郝悦(1993-), 女, 博士, 研究方向为数值代数及其应用, E-mail: hao_yue1993@163.com
基金资助:
国家自然科学基金(62032023);中国博士后科学基金(2022M710461)

Convergence Estimation and Characteristic Analysis of A Two-level Iterative Algorithm for Discretized Three-temperature Energy Linear Systems

Yue HAO¹^,²(), Silu HUANG¹^,², Xiaowen XU¹^,²^,*()

1. Laboratory of Computational Physics, Beijing 100088, China
2. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China

Received:2023-05-30 Online:2024-01-25 Published:2024-02-05
Contact: Xiaowen XU

摘要/Abstract

摘要：

基于代数多重网格(AMG)方法的理论框架, 详细分析基于物理量粗化的两层迭代方法(PCTL)算法的具体收敛性质, 刻画算法收敛因子的合理上界, 为PCTL算法提供理论保证。进一步深入分析影响PCTL算法收敛速度的代数特征, 如对角占优性和耦合强度, 为PCTL算法的应用和算法调优提供了理论指导。

关键词: 三温能量方程组, 基于物理量粗化的两层迭代方法, 代数多重网格方法, 收敛性质, 影响因子

Abstract:

In this paper, we study in detail the specific convergence property of the physical-variable-based coarsening two-level iterative method (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 analyze the algebraic features that affect the convergence of the PCTL algorithm, such as diagonal dominance and coupling strength, hoping to provide theoretical guidance for the applications and algorithm optimization of the PCTL algorithm.

Key words: three temperature energy equation, physical-variable based coarsening two-level iterative method, algebraic multigrid method, convergence, influence factor

中图分类号:

O241

郝悦, 黄思路, 徐小文. 三温能量方程离散线性系统的两层迭代算法收敛因子估计及特征分析[J]. 计算物理, 2024, 41(1): 122-130.

Yue HAO, Silu HUANG, Xiaowen XU. Convergence Estimation and Characteristic Analysis of A Two-level Iterative Algorithm for Discretized Three-temperature Energy Linear Systems[J]. Chinese Journal of Computational Physics, 2024, 41(1): 122-130.

图/表 2

参考文献 21

1	徐小文, 莫则尧, 安恒斌.求解二维三温辐射扩散方程组的一种代数两层迭代方法[J].计算物理,2009,26(1):1-8. DOI
2	HUANG Silu , YUE Xiaoqiang , XU Xiaowen .αSetup-PCTL: An adaptive setup-based two-level preconditioner for sequence of linear systems of three-temperature energy equations[J].Communications in Computational Physics,2023,32(5):1287-1309.
3	SAAD Y .Iterative methods for sparse linear systems[M].2nd ed. Philadelphia: Society for Industrial and Applied Mathematics,2003.
4	AN Hengbin , MO Zeyao , XU Xiaowen , et al.Operator-based preconditioning for the 2-D 3-T energy equations in radiation hydrodynamics simulations[J].Journal of Computational Physics,2019,385,51-74. DOI
5	BALDWIN C , BROWN P N , FALGOUT R , et al.Iterative linear solvers in a 2D radiation-hydrodynamics code: Methods and performance[J].Journal of Computational Physics,1999,154(1):1-40. DOI
6	XU Xiaowen , MO Zeyao .Algebraic interface-based coarsening AMG preconditioner for multi-scale sparse matrices with applications to radiation hydrodynamics computation[J].Numerical Linear Algebra with Applications,2017,24(2):e2078. DOI
7	HU Qiya , ZHAO Lin .Domain decomposition preconditioners for the system generated by discontinuous Galerkin discretization of 2D-3T heat conduction equations[J].Communications in Computational Physics,2017,22(4):1069-1100. DOI
8	YUE Xiaoqiang , SHU Shi , WANG Junxian , et al.Substructuring preconditioners with a simple coarse space for 2-D 3-T radiation diffusion equations[J].Communications in Computational Physics,2018,23(2):540-560.
9	周志阳, 徐小文, 舒适, 等.二维三温辐射扩散方程组两层预条件子的自适应求解[J].计算物理,2012,29(4):475-483. DOI
10	XU Xiaowen , YUE Xiaoqiang , MAO Runzhang , et al.JXPAMG: A parallel algebraic multigrid solver for extreme-scale numerical simulations[J].CCF Transactions on High Performance Computing,2023,5(1):72-83. DOI
11	RUGE J W, STVBEN K. Algebraic multigrid[M]//MCCORMICK S F, ed. Multigrid Methods. Philadelphia: Society for Industrial and Applied Mathematics, 1987: 73-130.
12	FALGOUT R D , VASSILEVSKI P S , ZIKATANOV L T .On two-grid convergence estimates[J].Numerical Linear Algebra with Applications,2005,12(5/6):471-494.
13	MACLACHLAN S P , OLSON L N .Theoretical bounds for algebraic multigrid performance: Review and analysis[J].Numerical Linear Algebra with Applications,2014,21(2):194-220. DOI
14	YUE Xiaoqiang , SHU Shi , XU Xiaowen , et al.An adaptive combined preconditioner with applications in radiation diffusion equations[J].Communications in Computational Physics,2015,18(5):1313-1335. DOI
15	MIHALAS D , MIHALAS B W .Foundations of radiation hydrodynamics[M].New York: Oxford University Press,1984.
16	POMRANING G C .The equations of radiation hydrodynamics[M].Oxford: Pergamon Press,1973.
17	XU Xuefeng , ZHANG Chensong .Convergence analysis of inexact two-grid methods: A theoretical framework[J].SIAM Journal on Numerical Analysis,2022,60(1):133-156. DOI
18	MCCORMICK S F , RUGE J W .Multigrid methods for variational problems[J].SIAM Journal on Numerical Analysis,1982,19(5):924-929. DOI
19	BRANDT A .Algebraic multigrid theory: The symmetric case[J].Applied Mathematics and Computation,1986,19(1/4):23-56.
20	MANDEL J .Algebraic study of multigrid methods for symmetric, definite problems[J].Applied Mathematics and Computation,1988,25(1):39-56. DOI
21	VARGA R S .Matrix iterative analysis[M].Heidelberg: Springer,2000.

三温能量方程离散线性系统的两层迭代算法收敛因子估计及特征分析

Convergence Estimation and Characteristic Analysis of A Two-level Iterative Algorithm for Discretized Three-temperature Energy Linear Systems

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 2

参考文献 21

相关文章 1

编辑推荐

Metrics

作者中心

审稿中心

期刊浏览

期刊介绍