Model order reduction for pattern formation in reaction-diffusion systems

Date

2017-09-22

Author

Karasözen, Bülent
Küçükseyhan, Tuğba
Mülayim, Gülden

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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 the Brusselator model with cross diusion [4]. DMD is an equation-free, data driven method which extracts dynamically relevant information content without explicitly knowing the dynamical operator. We use DMD as an alternative method to DEIM in order to approximate the nonlinear reaction terms. Application of the POD-DMD Galerkin projection gives rise to a linear system of equations. The high delity full order solutions (FOMs) are obtained by the discontinuous Galerkin discretization in space and semi-implicit Euler method in time. We compare the accuracy and CPU times of three reduced order model (ROM) solutions with the ones for FOM solutions. Numerical results show that POD is the most accurate whereas POD-DMD is the fastest.

Subject Keywords

Cross diffusion, FitzHugh-Nagumo model, Pattern formation, Reduced order modelling, Turing-Hopf bifurcation

URI

https://hdl.handle.net/11511/88164
https://acomen.ugent.be/BoA_ACOMEN2017.pdf

Conference Name

7th International Conference on Advanced Computational Methods in Engineering, ACOMEN 2017 18–22 September 2017

Collections

Department of Mathematics, Conference / Seminar

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Citation Formats

B. Karasözen, T. Küçükseyhan, and G. Mülayim, “ Model order reduction for pattern formation in reaction-diffusion systems,” Ghent, Belgium, 2017, p. 93, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/88164.