Reduced order optimal control of the convective FitzHugh-Nagumo equations

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2020-02-15

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Karasözen, Bülent
KÜÇÜKSEYHAN, TUĞBA

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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 most commonly used method in reduced optimal control is POD. We use DEIM and DMD to approximate efficiently the nonlinear terms in reduced order models. We compare the accuracy and computational times of three reduced-order optimal control solutions with the full order discontinuous Galerkin finite element solution of the convection dominated FHN equations with terminal controls. Numerical results show that POD is the most accurate whereas POD-DMD is the fastest.

Subject Keywords

FitzHugh-Nagumo equation, Optimal control, Discontinuous Galerkin method, Proper orthogonal decomposition, Discrete empirical interpolation, Dynamic mode decomposition

URI

https://hdl.handle.net/11511/31649

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS

DOI

https://doi.org/10.1016/j.camwa.2019.08.009

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Karasözen and T. KÜÇÜKSEYHAN, “Reduced order optimal control of the convective FitzHugh-Nagumo equations,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 982–995, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31649.