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| 速度追踪问题中鞍点系统的新分裂迭代 | |
| 引用本文： | 曾闽丽,张国凤.速度追踪问题中鞍点系统的新分裂迭代[J].计算数学,2016,38(4):354-371. |
| 作者姓名： | 曾闽丽 张国凤 |
| 作者单位： | 1. 兰州大学数学与统计学院, 兰州 730000; 2. 莆田学院数学学院, 福建莆田 351100; 3. 兰州大学数学与统计学院, 兰州 730000 |
| 基金项目： | 国家自然科学基金(11271174;11511130015)，福建省自然科学基金(2016J05016)，福建省教育厅基金(JAT160450)和莆田学院校内科研基金(2015061;2016075)资助项目. |
| 摘 要： | 有限元离散一类速度追踪问题后得到具有鞍点结构的线性系统，针对该鞍点系统，本文提出了一种新的分裂迭代技术.证明了新的分裂迭代方法的无条件收敛性，详细分析了新的分裂预条件子对应的预处理矩阵的谱性质.数值结果验证了对于大范围的网格参数和正则参数，新的分裂预条件子在求解有限元离散速度追踪问题得到的鞍点系统时的可行性和有效性. |
| 关 键 词： | 预条件子 谱分析 鞍点系统 速度追踪问题 迭代方法 |
| 收稿时间： | 2015-07-26; |
A NEW SPLITTING ITERATIVE TECHNIQUE FOR THE SADDLE POINT SYSTEM FROM A VELOCITY TRACKING PROBLEM |
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| Zeng Minli,Zhang Guofeng.A NEW SPLITTING ITERATIVE TECHNIQUE FOR THE SADDLE POINT SYSTEM FROM A VELOCITY TRACKING PROBLEM[J].Mathematica Numerica Sinica,2016,38(4):354-371. | |
| Authors: | Zeng Minli Zhang Guofeng |
| Affiliation: | 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China; 2. School of Mathematics, Putian University, Putian 351100, Fujian, China; 3. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China |
| Abstract: | We develop a new splitting iterative method and a splitting preconditioner for the saddle point system arising from the finite element discretization for the velocity tracking problem. It is proved that the new splitting iterative method converges unconditionally. The spectral properties of the matrix preconditioned by the splitting preconditioner are analyzed. Furthermore, the theoretical results are confirmed by numerical experiments, which demonstrate that the new preconditioner is feasible and effective for the the linear system arising from the finite element discretization equations of the velocity tracking problem for a wide range of mesh sizes and regularization parameters. |
| Keywords: | Preconditioner Spectral analysis Saddle point system Velocity tracking problem Iterative method |
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