A Preconditioned GMRES Method for Elliptic PDE-constrained Optimization Problems

Author

Cong-Yi Zhu ; Yu-Mei Huang

Author_Institution

Sch. of Math. & Stat., Lanzhou Univ., Lanzhou, China

fYear

2014

fDate

15-16 Nov. 2014

Firstpage

711

Lastpage

713

Abstract

In this paper, we consider the system of linear equations resulted from the elliptic PDE-constrained optimization distributed control problems. A new preconditioner is constructed and the preconditioned Generalized Minimum Residual (GMRES) method is applied to solve the linear system. Theoretical analysis and numerical experimental result show that the proposed preconditioned GMRES method is competitive to the existing preconditioned Krylov subspace methods appearing in the literature for this problem.

Keywords

distributed control; elliptic equations; linear systems; optimisation; partial differential equations; elliptic PDE-constrained optimization distributed control problems; linear equation system; preconditioned GMRES method; preconditioned Krylov subspace methods; preconditioned generalized minimum residual method; Decentralized control; Educational institutions; Eigenvalues and eigenfunctions; Equations; Linear systems; Optimization; Symmetric matrices; distributed control problem; eigenvalues and eigenvectors; preconditioning matrix; spectral distribution; the GMRES method;

fLanguage

English

Publisher

ieee

Conference_Titel

Computational Intelligence and Security (CIS), 2014 Tenth International Conference on

Conference_Location

Kunming

Print_ISBN

978-1-4799-7433-7

Type

conf

DOI

10.1109/CIS.2014.76

Filename

7016990