Reduced order optimal control of the convective FitzHugh-Nagumo equations

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KARASÖZEN B., UZUNCA M., KÜÇÜKSEYHAN T.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.79, no.4, pp.982-995, 2020 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 79 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1016/j.camwa.2019.08.009
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, MLA - Modern Language Association Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.982-995
  • Keywords: FitzHugh-Nagumo equation, Optimal control, Discontinuous Galerkin method, Proper orthogonal decomposition, Discrete empirical interpolation, Dynamic mode decomposition, PROPER ORTHOGONAL DECOMPOSITION, SPARSE OPTIMAL-CONTROL, GALERKIN SIPG METHOD, BLOOD-COAGULATION, DIFFUSION, SYSTEM, POD, DISCRETIZATION, PROPAGATION, REDUCTION
  • Open Archive Collection: AVESIS Open Access Collection
  • Middle East Technical University Affiliated: Yes

Abstract

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. (C) 2019 Elsevier Ltd. All rights reserved.