Bülent Karasözen

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Structure-preserving reduced-order modeling of Korteweg–de Vries equation
Uzunca, Murat; Karasözen, Bülent; Yıldız, Süleyman (2021-10-01)
© 2021 International Association for Mathematics and Computers in Simulation (IMACS)Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg–de Vries (KdV) equations in Hamiltoni...
Reduced order modelling of nonlinear cross-diffusion systems
Karasözen, Bülent; Mülayim, Gülden; Uzunca, Murat; Yıldız, Süleyman (2021-07-15)
© 2021 Elsevier Inc.In this work, we present reduced-order models (ROMs) for a nonlinear cross-diffusion problem from population dynamics, the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The fo...
Learning reduced-order dynamics for parametrized shallow water equations from data
Yildiz, Suleyman; Goyal, Pawan; Benner, Peter; Karasözen, Bülent (2021-05-01)
This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation. We consider the shallow water equation in non-traditiona...
Pricing European and American options under Heston model using discontinuous Galerkin finite elements
Kozpınar, Sinem; Uzunca, Murat; Karasözen, Bülent (2020-11-01)
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM s...
Structure preserving model order reduction of shallow water equations
Karasözen, Bülent; Yildiz, Suleyman; UZUNCA, MURAT (2020-07-01)
In this paper, we present two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of t...
Earthquake location methods
Karasozen, Ezgi; Karasözen, Bülent (2020-04-06)
Earthquake location is a well-defined inverse problem to which the mathematical fundamentals of existing methodologies were established nearly a century ago. However, in quantitative seismology, achieving accurate, bias-fr...
Reduced order optimal control of the convective FitzHugh-Nagumo equations
Karasözen, Bülent; UZUNCA, MURAT; KÜÇÜKSEYHAN, TUĞBA (2020-02-15)
In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the c...
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 ...
High-order integral nodal discontinuous Gegenbauer-Galerkin method for solving viscous Burgers' equation
Elgindy, Kareem T.; Karasözen, Bülent (2019-10-03)
We present a high-order integral nodal discontinuous Galerkin (DG) method to solve Burgers' equation. The method lays the first stone of a novel class of integral nodal DG methods exhibiting exponential convergence rates i...
Structure preserving reduced order modeling for gradient systems
Akman Yildiz, Tugba; UZUNCA, MURAT; Karasözen, Bülent (2019-04-15)
Minimization of energy in gradient systems leads to formation of oscillatory and Turing patterns in reaction-diffusion systems. These patterns should be accurately computed using fine space and time meshes over long time h...
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