Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equations

Download

index.pdf

Date

2015-09-18

Author

Karasözen, Bülent
Kucukseyhan, Tugba

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

206
views

117
downloads

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, the patterns can be computed accurately. Due to the local nature of the dG discretization, the PODDEIM requires less number of connected nodes than continuous finite element for the nonlinear terms, which leads to a significant reduction of the computational cost for dG POD-DEIM.

Subject Keywords

Empirical interpolation method

URI

https://hdl.handle.net/11511/30926

DOI

https://doi.org/10.1007/978-3-319-39929-4_35

Conference Name

European Conference on Numerical Mathematics and Advanced Applications (ENUMATH)

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Reduced order optimal control of the convective FitzHugh-Nagumo equations Karasözen, Bülent; KÜÇÜKSEYHAN, TUĞBA (2020-02-15) In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposition (DMD) for the optimal control of the convective FitzHugh-Nagumo (FHN) equations. The convective FHN equations consist of the semi-linear activator and the linear inhibitor equations, modeling blood coagulation in moving excitable media. The semilinear activator equation leads to a non-convex optimal control problem (OCP). The ...
Symbolic polynomial interpolation using Mathematica Yazıcı, Adnan; Ergenc, T (2004-01-01) This paper discusses teaching polynomial interpolation with the help of Mathematica. The symbolic power of Mathematica is utilized to prove a theorem for the error term in Lagrange interpolating formula. Derivation of the Lagrange formula is provided symbolically and numerically. Runge phenomenon is also illustrated. A simple and efficient symbolic derivation of cubic splines is also provided.
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...
2d polynomial interpolation: A symbolic approach with mathematica Yazıcı, Adnan; Ergenc, T (2005-01-01) This paper extends a previous work done by the same authors on teaching 1d polynomial interpolation using Mathematica [1] to higher dimensions. In this work, it is intended to simplify the the theoretical discussions in presenting multidimensional interpolation in a classroom environment by employing Mathematica's symbolic properties. In addition to symbolic derivations, some numerical tests are provided to show the interesting properties of the higher dimensional interpolation problem. Runge's phenomenon w...

Citation Formats

B. Karasözen and T. Kucukseyhan, “Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equations,” Middle E Tech Univ, Inst Appl Math, Ankara, TURKEY, 2015, vol. 112, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30926.