On Schwarz-type smoothers for saddle point problems with applications to PDE-constrained optimization problems

被引：16

作者：

Simon, Rene ^{[1
]}

Zulehner, Walter ^{[2
]}

机构：

[1] Johannes Kepler Univ Linz, SFB 013, A-4040 Linz, Austria

[2] Johannes Kepler Univ Linz, Inst Computat Math, A-4040 Linz, Austria

来源：

NUMERISCHE MATHEMATIK | 2009年 / 111卷 / 03期

基金：

奥地利科学基金会;

关键词：

NAVIER-STOKES EQUATIONS; LAGRANGIAN-MULTIPLIERS; TRANSFORMING SMOOTHERS; MULTIGRID SOLUTION; PRECONDITIONERS; CONVERGENCE; SYSTEMS;

D O I：

10.1007/s00211-008-0187-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a (one-shot) multigrid strategy for solving the discretized optimality system (KKT system) of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a certain class of optimal control problems. A rigorous multigrid convergence analysis is presented. Numerical experiments are shown which confirm the theoretical results.

引用

页码：445 / 468

页数：24

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