Bülent Karasözen

E-mail

bulent@metu.edu.tr

Department

ORCID

0000-0003-1037-5431

Scopus Author ID

6603369633

Web of Science Researcher ID

K-1879-2014

Linearly implicit methods for Allen-Cahn equation Uzunca, Murat; Karasözen, Bülent (2023-08-01) It is well known that the Allen-Cahn equation satisfies a nonlinear stability property, i.e., the free-energy functional decreases in time. Linearly implicit integrators have been developed for energy-preserving methods fo...
Global energy preserving model reduction for multi-symplectic PDEs Uzunca, Murat; Karasözen, Bülent; Aydın, Ayhan (2023-01-01) © 2022 Elsevier Inc.Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global e...
Nonintrusive model order reduction for cross-diffusion systems Karasözen, Bülent; Mülayim, Gülden; Uzunca, Murat (2022-12-01) In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tenso...
Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation Yıldız, Süleyman; Karasözen, Bülent; Uzunca, Murat (2022-05-15) In this paper, we investigate projection-based intrusive and data-driven model order reduction in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form. Discretizatio...
Energy preserving reduced-order modeling of the rotating thermal shallow water equation Karasözen, Bülent; Ylldlz, S.; Uzunca, M. (2022-05-01) © 2022 Author(s).In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity...
Structure-preserving reduced-order modeling of Korteweg–de Vries equation Uzunca, Murat; Karasözen, Bülent; Yıldız, Süleyman (2021-10-01) Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg–de Vries (KdV) equations in Hamiltonian form. The semi-discretization in space by finite differences is based on the Hami...
Reduced order modelling of nonlinear cross-diffusion systems Karasözen, Bülent; Uzunca, Murat; Yıldız, Süleyman (2021-07-15) 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 formation of the patte...
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...
Structure-preserving Reduced Order Modeling of non-traditional Shallow Water Equation Uzunca, Murat; Karasözen, Bülent; Yıldız, Süleyman (Springer, London/Berlin , 2021-04-01) An energy- preserving reduced -order model (ROM) is developed for the non-traditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in the noncanonical Hamiltonian/Poisson form is discretized in space ...
Pricing European and American options under Heston model using discontinuous Galerkin finite elements Kozpınar, Sinem; 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...

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