20 citations · 67 across the 12 of their papers we have counts for
8 papers · 1 filter
Linearly Implicit Global Energy Preserving Reduced-order Models for Cubic Hamiltonian Systems
Süleyman Yildiz, Pawan Goyal, Peter Benner
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving metho…
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…
Energy preserving reduced-order modelling of thermal shallow water equation
Suleyman Yildiz, Murat Uzunca, Bulent Karasozen
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form wi…
Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation
Süleyman Yıldız, Pawan Goyal, Peter Benner +1
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 th…
Reduced order modelling of nonlinear cross-diffusion systems
Bülent Karasözen, Gülden Mülayim, Murat Uzunca +1
In this work, we present a reduced-order model for a nonlinear cross-diffusion problem from population dynamics, for the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volte…
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 Model Order Reduction of Shallow Water Equations
Bülent Karasözen, Süleyman Yıldız, Murat Uzunca
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…