Parallel D–D type domain decomposition algorithm for optimal control problem governed by parabolic partial differential equation

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Bo Zhang ◽  
Jixin Chen ◽  
Danping Yang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Domain Decomposition ◽  
Decomposition Algorithm ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Domain Decomposition Algorithm

AbstractA parallel domain decomposition algorithm for solving an optimal control problem governed by a parabolic partial differential equation is proposed. This algorithm is based upon non-overlapping domain decomposition. In every iteration, the global problem is reduced to solve simultaneously some implicit subproblems on many sub-domains by using explicit flux approximations near inner-boundaries at each time-step. Both

Sparse Grid Collocation Method for an Optimal Control Problem Involving a Stochastic Partial Differential Equation with Random Inputs

2014 ◽  
Vol 4 (2) ◽  
pp. 166-188 ◽  
Author(s):  
Nary Kim ◽  
Hyung-Chun Lee
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Collocation Method ◽  
Galerkin Approximation ◽  
Random Coefficients ◽  
Sparse Grid ◽  
Partial Differential

AbstractIn this article, we propose and analyse a sparse grid collocation method to solve an optimal control problem involving an elliptic partial differential equation with random coefficients and forcing terms. The input data are assumed to be dependent on a finite number of random variables. We prove that an optimal solution exists, and derive an optimality system. A Galerkin approximation in physical space and a sparse grid collocation in the probability space is used. Error estimates for a fully discrete solution using an appropriate norm are provided, and we analyse the computational efficiency. Computational evidence complements the present theory, to show the effectiveness of our stochastic collocation method.

An Efficient Computational Procedure for the Optimization of a Class of Distributed Parameter Systems

1969 ◽  
Vol 91 (2) ◽  
pp. 190-194 ◽  
Author(s):  
D. A. Wismer
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Broad Class ◽  
Distributed Parameter Systems ◽  
Parabolic Partial Differential Equation ◽  
Distributed Parameter ◽  
Total System ◽  
Partial Differential

The optimal control problem for a broad class of distributed parameter systems defined by vector parabolic partial differential equations is considered. The problem is solved by discretizing the spatial domain and then treating the (large) resultant set of ordinary differential equations as a set of independent subsystems. The subsystems are determined by decomposition of the total system into lower-dimensional problems and the necessary conditions for optimality of the overall system are then satisfied by an iterative procedure. With this treatment, the optimal control problem can be solved for larger systems (or finer spatial discretizations) than would otherwise be feasible. An example is given for a system described by a nonlinear parabolic partial differential equation in one space dimension.

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