Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
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
195
views
113
downloads
Cite This
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
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.