Analysis of block matrix preconditioners for elliptic optimal control problems
نویسندگان
چکیده
منابع مشابه
Analysis of block matrix preconditioners for elliptic optimal control problems
In this paper, we describe and analyse several block matrix iterative algorithms for solving a saddle point linear system arising from the discretization of a linear-quadratic elliptic control problem with Neumann boundary conditions. To ensure that the problem is well posed, a regularization term with a parameter is included. The first algorithm reduces the saddle point system to a symmetric p...
متن کاملAnalysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems
In this paper, we describe block matrix algorithms for the iterative solution of large scale linear-quadratic optimal control problems arising from the optimal control of parabolic partial differential equations over a finite control horizon. We describe three iterative algorithms. The first algorithm employs a CG method for solving a symmetric positive definite reduced linear system involving ...
متن کاملDomain Decomposition Preconditioners for Linear–quadratic Elliptic Optimal Control Problems
We develop and analyze a class of overlapping domain decomposition (DD) preconditioners for linear-quadratic elliptic optimal control problems. Our preconditioners utilize the structure of the optimal control problems. Their execution requires the parallel solution of subdomain linear-quadratic elliptic optimal control problems, which are essentially smaller subdomain copies of the original pro...
متن کاملHierarchical-Matrix Preconditioners for Parabolic Optimal Control Problems
Hierarchical (H)-matrices approximate full or sparse matrices using a hierarchical data sparse format. The corresponding H-matrix arithmetic reduces the time complexity of the approximate H-matrix operators to almost optimal while maintains certain accuracy. In this paper, we represent a scheme to solve the saddle point system arising from the control of parabolic partial differential equations...
متن کاملNeumann-Neumann Domain Decomposition Preconditioners for Linear-Quadratic Elliptic Optimal Control Problems
We present a class of domain decomposition (DD) preconditioners for the solution of elliptic linear-quadratic optimal control problems. Our DD preconditioners are extensions of Neumann–Neumann DD preconditioners, which have been successfully applied to the solution of single PDEs. The DD preconditioners are based on a decomposition of the optimality conditions for the elliptic linear-quadratic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2007
ISSN: 1070-5325,1099-1506
DOI: 10.1002/nla.526