Structure Preserving Integration and Model Order Reduction of Skew Gradient Reaction Diffusion Systems

Karasözen, Bülent
Küçükseyhan, Tuğba


Structure preserving integration and model order reduction of skew-gradient reaction-diffusion systems
Karasözen, Bülent; Uzunca, Murat (2017-11-01)
Activator-inhibitor FitzHugh-Nagumo (FHN) equation is an example for reaction-diffusion equations with skew-gradient structure. We discretize the FHN equation using symmetric interior penalty discontinuous Galerkin (SIPG) method in space and average vector field (AVF) method in time. The AVF method is a geometric integrator, i.e. it preserves the energy of the Hamiltonian systems and energy dissipation of the gradient systems. In this work, we show that the fully discrete energy of the FHN equation satisfie...
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 horizons to reach the spatially inhomogeneous steady state. In this paper, a reduced order model (ROM) is developed which preserves the gradient dissipative structure. The coupled system of reaction-diffusion equations are discretized in space by the symmetric interior penalty discontinuous...
Structure preserving model order reduction of shallow water equations
Karasözen, Bülent; 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 the SWE. After integration in time by the fully implicit average vector field method, ROMs are constructed with proper orthogonal decomposition(POD)/discrete empirical interpolation method that preserves the Hamiltonian structure. In the second approach, the SWE as a partial differential eq...
Shape preserving quadratic spline interpolation.
Gürson, Nursun; Department of Mathematics (1985)
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 by finite differences. The resulting system of ordinary differential equations is integrated in time by the energy preserving average vector field (AVF) method. The Poisson structure of the discretized NTSWE exhibits a skew-symmetric matrix depending on the state variables. An energy- pres...
Citation Formats
B. Karasözen and T. Küçükseyhan, “Structure Preserving Integration and Model Order Reduction of Skew Gradient Reaction Diffusion Systems,” 2015, Accessed: 00, 2021. [Online]. Available: