28 citations · 162 across the 24 of their papers we have counts for
25 papers
Linearly implicit exponential integrators for damped Hamiltonian PDEs
Murat Uzunca, Bülent Karasözen
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integr…
Reduced-order modeling for Ablowitz-Ladik equation
Murat Uzunca, Bülent Karasözen
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) wit…
Global energy preserving model reduction for multi-symplectic PDEs
Murat Uzunca, Bülent Karasözen, Ayhan Aydın
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…
Nonintrusive model order reduction for cross-diffusion systems
Bulent Karasozen, Murat Uzunca, Gulden Mulayim
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 differ…
Intrusive and non-intrusive reduced order modeling of the rotating thermal shallow water equation
Süleyman Yıldız, Murat Uzunca, Bülent Karasözen
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equat…
Structure-preserving reduced-order modelling of Korteweg de Vries equation
Bulent Karasozen, Murat Uzunca, Suleyman Yildiz
Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized i…
Structure-preserving Reduced Order Modeling of non-traditional Shallow Water Equation
Süleyman Yıldız, Murat Uzunca, Bülent Karasözen
An energy preserving reduced order model is developed for the nontraditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in the noncanonical Hamiltonian/Pois…
Structure preserving reduced order modeling for gradient systems
Tuğba Akman Yıldız, Murat Uzunca, Bülent Karasözen
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 f…
Energy preserving model order reduction of the nonlinear Schrödinger equation
Bülent Karasözen, Murat Uzunca
An energy preserving reduced order model is developed for two dimensional nonlinear Schrödinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE i…
Reduced Order Optimal Control of the Convective FitzHugh-Nagumo Equation
Bülent Karasözen, Murat Uzunca, Tuğba Küçükseyhan
In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposit…
Reduced-Order Modeling for Heston Stochastic Volatility Model
Sinem Kozpınar, Murat Uzunca, Bülent Karasözen
In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pri…
Energy stable model order reduction for the Allen-Cahn equation
Murat Uzunca, Bülent Karasözen
The Allen-Cahn equation is a gradient system, where the free-energy functional decreases monotonically in time. We develop an energy stable reduced order model (ROM) for a gradient…
Moving Mesh Discontinuous Galerkin Methods for PDEs with Traveling Waves
Murat Uzunca, Bülent Karasözen, Tuğba Küçükseyhan
In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh stra…
Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equation
Bülent Karasözen, Murat Uzunca, Tuğba Küçükseyhan
We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) eq…
Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation
Murat Uzunca, Bülent Karasözen, Ayşe Sarıaydın Filibelioğlu
We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization f…
Optimal Control of Convective FitzHugh-Nagumo Equation
Murat Uzunca, Tuğba Küçükseyhan, Hamdullah Yücel +1
We investigate smooth and sparse optimal control problems for convective FitzHugh-Nagumo equation with travelling wave solutions in moving excitable media. The cost function includ…
Structure preserving integration and model order reduction of skew-gradient reaction-diffusion systems
Bülent Karasözen, Tuğba Küçükseyhan, Murat Uzunca
Activator-inhibitor FitzHugh-Nagumo (FHN) equation is an example for reaction-diffusion equations with skew-gradient structure. We discretize the FHN equation using symmetric inter…
Energy stable interior penalty discontinuous Galerkin finite element method for Cahn-Hilliard equation
Bülent Karasözen, Ayşe Sarıaydın Filibelioğlu, Murat Uzunca
An energy stable conservative method is developed for the Cahn--Hilliard (CH) equation with the degenerate mobility. The CH equation is discretized in space with the mass conservin…
Time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction mechanism
Bülent Karasözen, Murat Uzunca
In this work, we apply a time-space adaptive discontinuous Galerkin method using the elliptic reconstruction technique with a robust (in Péclet number) elliptic error estimator in…
A Matlab Tutorial for Diffusion-Convection-Reaction Equations using DGFEM
Murat Uzunca, Bülent Karasözen
We present a collection of MATLAB routines using discontinuous Galerkin finite elements method (DGFEM) for solving steady-state diffusion-convection-reaction equations. The code em…
Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations
Murat Uzunca, Bülent Karasözen, Murat Manguoğlu
In this work, we apply the adaptive discontinuous Galerkin (DGAFEM) method to the convection dominated non-linear, quasi-stationary diffusion-convection-reaction equations. We prop…
Model Order Reduction for Nonlinear Schrödinger Equation
Bülent Karasözen, Canan Akkoyunlu, Murat Uzunca
We apply the proper orthogonal decomposition (POD) to the nonlinear Schrödinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite d…
Energy Stable Discontinuous Galerkin Finite Element Method for the Allen-Cahn Equation
Bülent Karasözen, Ayşe Sarıaydın Filibelioğlu, Murat Uzunca
Allen--Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals is discretized using symmetric interior penalty discontinuous Gal…
Space-Time Discontinuous Galerkin Solution of Convection Dominated Optimal Control Problems
Tuğba Akman, Bülent Karasözen
In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with…