scholarly journals Finite Element and Split Bregman Methods for Solving a Family of Optimal Control Problem with Partial Differential Equation Constraint

2020 ◽  
Vol 15 (1) ◽  
pp. 11
Author(s):  
Mahmoud Lotfi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Split Bregman ◽  
Partial Differential ◽  
Equation Constraint

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.

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

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