Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization
Date
2014-05-01
Author
Seymen, Z. Kanar
Yücel, Hamdullah
Karasözen, Bülent
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
218
views
0
downloads
Cite This
We apply two different strategies for solving unsteady distributed optimal control problems governed by diffusion-convection-reaction equations. In the first approach, the optimality system is transformed into a biharmonic equation in the space time domain. The system is then discretized in space and time simultaneously and solved by an equation-based finite element package, i.e., COMSOL Multiphysics. The second approach is a classical gradient-based optimization method to solve the state and adjoint equations and the optimality condition iteratively. The convection-dominated state and adjoint equations are stabilized using the streamline upwind/Petrov-Galerkin (SUPG) method. Numerical results show favorable accuracy and efficiency of the two strategies for unstabilized and stabilized numerical solutions.
Subject Keywords
Optimal Control Problems
,
Stabilized Finite Elements
,
Convection Dominated Problems
,
Pointwise Inequality Constraints
,
COMSOL Multiphysics
URI
https://hdl.handle.net/11511/32525
Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
https://doi.org/10.1016/j.cam.2013.11.006
Collections
Graduate School of Applied Mathematics, Article
Suggestions
OpenMETU
Core
Distributed Optimal Control Problems Governed by Coupled Convection Dominated PDEs with Control Constraints
Yücel, Hamdullah (2013-08-30)
We study the numerical solution of control constrained optimal control problems governed by a system of convection diffusion equations with nonlinear reaction terms, arising from chemical processes. Control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a posteriori error estimates is applied for both approaches.
Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations
Akman, Tugba; Karasözen, Bülent (2014-12-15)
In this paper, the distributed optimal control problem governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We investigate the commutativity properties of the optimize-then-discretize and discretize-then-optimize approaches for the continuous and discontinuo...
Local improvements to reduced-order approximations of optimal control problems governed by diffusion-convection-reaction equation
Akman, Tuğba (2015-07-01)
We consider the optimal control problem governed by diffusion-convection-reaction equation without control constraints. The proper orthogonal decomposition (POD) method is used to reduce the dimension of the problem. The POD method may lack accuracy if the POD basis depending on a set of parameters is used to approximate the problem depending on a different set of parameters. To increase the accuracy and the robustness of the basis, we compute five bases additional to the baseline POD in case of the perturb...
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints
Yücel, Hamdullah; Karasözen, Bülent (2014-01-02)
In this paper, we study a posteriori error estimates of the upwind symmetric interior penalty Galerkin (SIPG) method for the control constrained optimal control problems governed by linear diffusion-convection-reaction partial differential equations. Residual based error estimators are used for the state, the adjoint and the control. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretic...
Boundary value problems for higher order linear impulsive differential equations
Uğur, Ömür; Akhmet, Marat (2006-07-01)
In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered. (c) 2006 Elsevier In...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
Z. K. Seymen, H. Yücel, and B. Karasözen, “Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization,”
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, pp. 146–157, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32525.