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椭圆PDE-约束优化问题的一个预条件子

柯艺芬, 马昌凤   

  1. 福建师范大学数学与计算机科学学院, 福建省分析数学及其应用重点实验室, 福州 350117
  • 收稿日期:2016-04-11 出版日期:2017-02-15 发布日期:2017-02-17
  • 基金资助:

    国家自然科学基金项目(11071041)和福建自然科学基金项目(2016J01005).

柯艺芬, 马昌凤. 椭圆PDE-约束优化问题的一个预条件子[J]. 计算数学, 2017, 39(1): 70-80.

Ke Yifen, Ma Changfeng. A PRECONDITIONER FOR ELLIPTIC PDE-CONSTRAINED OPTIMIZATION PROBLEMS[J]. Mathematica Numerica Sinica, 2017, 39(1): 70-80.

A PRECONDITIONER FOR ELLIPTIC PDE-CONSTRAINED OPTIMIZATION PROBLEMS

Ke Yifen, Ma Changfeng   

  1. School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou 350117, China
  • Received:2016-04-11 Online:2017-02-15 Published:2017-02-17
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 effectively used to accelerate the convergence rate of Krylov subspace methods and match well with the theoretical results as well.

MR(2010)主题分类: 

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