A ROBUST MULTIGRID METHOD FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS

被引：34
|
作者：
Schoeberl, Joachim [1 ]
Simon, Rene [2 ]
Zulehner, Walter [3 ]
机构：
[1] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria
[2] Univ Duisburg Essen, Fac Math, D-47057 Duisburg, Germany
[3] Johannes Kepler Univ Linz, Inst Computat Math, A-4040 Linz, Austria
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 04期
基金：
奥地利科学基金会;
关键词：
multigrid methods; all-at-once methods; robust methods; elliptic optimal control; PDE constrained optimization; PDE-CONSTRAINED OPTIMIZATION; KRYLOV-SCHUR METHODS; PRECONDITIONERS; SMOOTHERS; SYSTEMS; SOLVER;
D O I：
10.1137/100783285
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the discretized optimality system of a special class of elliptic optimal control problems and propose an all-at-once multigrid method for solving this discretized system. Under standard assumptions the convergence of the multigrid method and the robustness of the convergence rates with respect to the involved parameter are shown. Numerical experiments are presented for illustrating the theoretical results.
引用
收藏
页码：1482 / 1503
页数：22
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