求解鞍点问题的新Bramble-Pasciak预条件子
new Bramble-Pasciak-like preconditioner forsaddle point problems
本文提出了一个新的Bramble-Pasciak型预条件子. 原系统经这种预条件子处理后, 转换成了关于某种内积对称正定的系统, 后者能用Bramble-Pasciak共轭梯度(BPCG)方法求解. 基于相应矩阵的谱条件数分析, 导出了 新预条件子的拟最优参数. 关于Stokes问题的数值实验验证了文中的理论结果.
In this paper, a new Bramble-Pasciak-like preconditioner with parameter is proposedfor solving the saddle point problem. The saddle point problem canbe reformulated as a symmetric and positive definite system withrespect to some inner product and thus can be solved byBramble-Pasciak conjugate gradient (BPCG) method. Based on thespectral condition number of the associated system, thequasi-optimal parameters can be obtained to improve the convergencerate of the BPCG method. Numerical experiments on the Stokes problemare given to illustrate our theoretical results.
黎稳、彭小飞
数学
鞍点问题Bramble-Pasciak型预条件子Bramble-Pasciak共轭梯度方法谱条件数收敛速度
Saddle point problemsBramble-Pasciak-like preconditionerBramble-Pasciak conjugategradient methodspectral condition numberconvergencerate
黎稳,彭小飞.求解鞍点问题的新Bramble-Pasciak预条件子[EB/OL].(2011-07-04)[2025-08-19].http://www.paper.edu.cn/releasepaper/content/201107-22.点此复制
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