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 the nonlinear Klein–Gordon equation Uzunca, Murat; Karasözen, Bülent (2025-05-01) We present energy-preserving linearly implicit integrators for the nonlinear Klein–Gordon equation, based on the polarization of the polynomial functions. They are symmetric, second-order accurate in time and space, and un...
Reduced-order modeling for Ablowitz–Ladik equation Uzunca, Murat; Karasözen, Bülent (2023-11-01) In this paper, reduced-order models (ROMs) are constructed for the Ablowitz–Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schrödinger equation (NLSE) with and without damping. Both ALEs are non-c...
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...

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