Optimal boundary control of the unsteady Burgers equation with simultaneous space-time discretization

The optimality system for boundary controlled unsteady Burgers equation is transformed after linearization into a biharmonic equation in the space-time domain. It is then discretized in space and time simultaneously, so that standard finite element software can be easily implemented. Numerical experiments with and without control constraint problems confirm the applicability of this approach. Copyright (C) 2013 John Wiley & Sons, Ltd.


Solving optimal control problems for the unsteady Burgers equation in COMSOL Multiphysics
YILMAZ, FİKRİYE NURAY; Karasözen, Bülent (2011-06-15)
The optimal control of unsteady Burgers equation without constraints and with control constraints are solved using the high-level modelling and simulation package COMSOL Multiphysics. Using the first-order optimality conditions, projection and semi-smooth Newton methods are applied for solving the optimality system. The optimality system is solved numerically using the classical iterative approach by integrating the state equation forward in time and the adjoint equation backward in time using the gradient ...
Effective-mass Klein-Gordon-Yukawa problem for bound and scattering states
Arda, Altug; Sever, Ramazan (2011-09-01)
Bound and scattering state solutions of the effective-mass Klein-Gordon equation are obtained for the Yukawa potential with any angular momentum l. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated as well as for the constant mass case. Bound state solutions of the Coulomb potential are also studied as a limiting case. Analytical and numerical results are compared with the ones obtained before. (C) 2011 American Institute of Physics. [doi:10.1063/1.3641246]
Exact solution of Schrodinger equation for Pseudoharmonic potential
Sever, Ramazan; TEZCAN, CEVDET; Aktas, Metin; Yesiltas, Oezlem (2008-02-01)
Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of l and n with n <= 5 for some diatomic molecules.
Numerical solution of nonlinear reaction-diffusion and wave equations
Meral, Gülnihal; Tezer, Münevver; Department of Mathematics (2009)
In this thesis, the two-dimensional initial and boundary value problems (IBVPs) and the one-dimensional Cauchy problems defined by the nonlinear reaction- diffusion and wave equations are numerically solved. The dual reciprocity boundary element method (DRBEM) is used to discretize the IBVPs defined by single and system of nonlinear reaction-diffusion equations and nonlinear wave equation, spatially. The advantage of DRBEM for the exterior regions is made use of for the latter problem. The differential quad...
Distributed optimal control of viscous Burgers' equation via a high-order, linearization, integral, nodal discontinuous Gegenbauer-Galerkin method
Elgindy, Kareem T.; Karasözen, Bülent (2020-01-01)
We developed a novel direct optimization method to solve distributed optimal control of viscous Burgers' equation over a finite-time horizon by minimizing the distance between the state function and a desired target state profile along with the energy of the control. Through a novel linearization strategy, well-conditioned integral reformulations, optimal Gegenbauer barycentric quadratures, and nodal discontinuous Galerkin discretizations, the method reduces such optimal control problems into finite-dimensi...
Citation Formats
B. Karasözen, “Optimal boundary control of the unsteady Burgers equation with simultaneous space-time discretization,” OPTIMAL CONTROL APPLICATIONS & METHODS, pp. 423–434, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30230.