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| 二维三温辐射扩散方程组两层预条件子的自适应求解 | |
| 引用本文： | 周志阳,徐小文,舒适,冯春生,莫则尧. 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 |
| 作者姓名： | 周志阳 徐小文 舒适 冯春生 莫则尧 |
| 作者单位： | 1. 湘潭大学数学与计算科学学院科学工程计算与数值仿真湖南省重点实验室, 湘潭市, 411105;2. 北京应用物理与计算数学研究所高性能计算中心计算物理重点实验室, 北京, 100094 |
| 基金项目： | 国家重点基础研究专项经费，国家自然科学基金，湖南省科学技术厅科技计划重点项目 |
| 摘 要： | 针对实际应用中若干典型三温线性系统,分析求解二维三温辐射扩散方程离散线性系统的代数两层预条件子(PCTL)的算法效率.结果表明,PCTL的算法效率与三个温度之间的耦合强度以及单温子系统对角占优性强弱程度有很大关系.为此,通过刻画三温线性系统的耦合强度和单温子系统对角占优性特征,提出一种PCTL中子系统的自适应求解算法.数值结果表明,可以显著改善PCTL的算法效率.对于实际数值模拟应用中37个典型三温线性系统,相对于经典AMG算法,算法整体加速2.5倍.数值实验表明算法具有很强的鲁棒性. |
| 关 键 词： | 二维三温方程 辐射扩散 代数多重网格(AMG) 预条件子 自适应 |
| 收稿时间： | 2011-09-20 |
| 修稿时间： | 2012-01-17 |
An Adaptive Two-level Preconditioner for 2-D 3-T Radiation Diffusion Equations |
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| ZHOU Zhiyang , XU Xiaowen , SHU Shi , FENG Chunsheng , MO Zeyao. An Adaptive Two-level Preconditioner for 2-D 3-T Radiation Diffusion Equations[J]. Chinese Journal of Computational Physics, 2012, 29(4): 475-483 | |
| Authors: | ZHOU Zhiyang XU Xiaowen SHU Shi FENG Chunsheng MO Zeyao |
| Affiliation: | 1. School of Mathematics and Computational Science, Xiangtan University, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Hunan 411105, China;2. High Performance Computing Center, Computation Physics Laboratory, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China |
| Abstract: | Performance of physical-variable based coarsening two-level(PCTL) preconditioner is analyzed for typical linear systems discretizated from two-dimensional(2-D) radiative diffusion equations with photon,electron,ion temperatures(3-T).It reveals that performance of PCTL strongly depends on both coupling of three temperatures and diagonally dominance of three diagonal sub-matrices of coefficient matrix.An adaptive algorithm for sub linear systems in PCTL is proposed.Numerical results show efficiency and robustness of the method.For 37 2-D 3-T linear systems in simulations,PCTL based on the algorithm speeds up 2.5 times compared with classical algebraic multigrid(AMG) preconditioners. |
| Keywords: | 2-D 3-T radiation diffusion algebraic multigrid(AMG) preconditioner adaptive |
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