Model Order Reduction for Pattern Formation of FitzHugh-Nagumo Equation

Küçükseyhan, Tuğba
Karasözen, Bülent
Uzunca, Murat
MME2017 International Workshop on Mathematical Models in Engineering (2017)


Model Order Reduction for Pattern Formation inFitzHugh Nagumo Equation
Karasözen, Bülent (null; 2015-10-12)
Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equations
Karasözen, Bülent; Kucukseyhan, Tugba (2015-09-18)
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) equation. The FHN equation is discretized in space by the discontinuous Galerkin (dG) method and in time by the backward Euler method. Applying POD-DEIM (discrete empirical interpolation method) to the full order model (FOM) for different values of the parameter in the bistable nonlinearity, we show that using few POD and DEIM modes...
Model order reduction for pattern formation in reaction-diffusion systems
Karasözen, Bülent; Küçükseyhan, Tuğba; Mülayim, Gülden (null; 2017-09-22)
We compare three reduced order modelling (ROM) techniques: the proper orthogonal decomposition (POD), discrete empirical interpolation (DEIM) [2], and dynamical mode decomposition (DMD) [1] to reaction diusion equations in biology. The formation of patterns in reaction-diusion equations require highly accurate solutions in space and time and therefore require large computational time to reach the steady states. The three reduced order methods are applied to the diusive FitzHugh-Nagumo equation [3] and th...
Model order reduction for nonlinear Schrodinger equation
Karasözen, Bülent; Uzunca, Murat (2015-05-01)
We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reprodu...
Model Order Reduction on Control Problems of Navier-Stokes Equations
Evcin, Cansu; Uğur, Ömür (null; 2017-09-18)
Citation Formats
T. Küçükseyhan, B. Karasözen, and M. Uzunca, “Model Order Reduction for Pattern Formation of FitzHugh-Nagumo Equation,” Ankara, Türkiye, 2017, p. 95, Accessed: 00, 2021. [Online]. Available: