Paper Info
Title
An DRCS preconditioning iterative method for a constrained fractional optimal control problem
Abstract
The optimal control problem constrained by a fractional diffusion equation arises in a great deal of applications. Fast and efficient numerical methods for solving such kinds of problems have attracted much attention in recent years. In this paper, we consider an optimal control problem constrained by a fractional diffusion equation (FDE). After the state and costate equations are derived, the closed form of the optimal control variable is then given. The decoupled gradient projection method is applied to solve the coupled system of the state and costate equations to obtain the solution of the optimal control problem. The second-order Crank-Nicolson method as well as the weighted and shifted Grunwald difference (CN-WSGD) methods are utilized to discretize these two equations. We get the discretized state and costate equations as systems of linear equations with both coefficient matrices having the structure of the sum of a diagonal and a Toeplitz matrix. A diagonal and a R.Chan's circulant splitting (DRCS) preconditioner is developed and combined in the Krylov subspace methods to solve the resulting discretized linear systems. Theoretical analysis of spectral distributions of the preconditioned matrix is also given. Numerical results exhibit that the proposed preconditioner can significantly improve the convergence of the Krylov subspace iteration methods.
Year
DOI
Venue
2021
10.1007/s40314-021-01654-9
COMPUTATIONAL & APPLIED MATHEMATICS
Keywords
DocType
Volume
Optimal control problem, Fractional diffusion equation, Preconditioner, Krylov subspace methods, Spectral distribution
Journal
40
Issue
ISSN
Citations 
8
2238-3603
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Shi-Ping Tang100.68
Yu-Mei Huang225811.83