摘要
针对由Galerkin有限元离散椭圆PDE-约束优化问题产生的具有特殊结构的3×3块线性鞍点系统,提出了一个预条件子并给出了预处理矩阵特征值及特征向量的具体表达形式.数值结果表明了该预条件子能够有效地加速Krylov子空间方法的收敛速率,同时也验证了理论结果.
For the special 3-by-3 block linear equations arising from the Galerkin finite element discretizations of elliptic PDE-constrained optimization problems, a preconditioner is proposed and the explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrix are derived. Numerical results show that the preconditioner is effec- tively used to accelerate the convergence rate of Krylov subspace methods and match well with the theoretical results as well.
出处
《计算数学》
CSCD
北大核心
2017年第1期70-80,共11页
Mathematica Numerica Sinica
基金
国家自然科学基金项目(11071041)
福建自然科学基金项目(2016J01005)
关键词
PDE-约束优化问题
鞍点矩阵
预条件子
特征值
特征向量
PDE-constrained optimization problem
saddle point matrix
precondition-er
eigenvalue
eigenvector
