Optimal control of convective FitzHugh-Nagumo equation

Download

index.pdf

Date

2017-05-01

Author

Uzunca, Murat
Kucukseyhan, Tugba
Yücel, Hamdullah
Karasözen, Bülent

Metadata

Show full item record

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

Item Usage Stats

133
views

70
downloads

We investigate smooth and sparse optimal control problems for convective FitzHugh Nagumo equation with traveling wave solutions in moving excitable media. The cost function includes distributed space time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) method and by backward Euler method in time. Several numerical results are presented for the control of the traveling waves. We also show numerically the validity of the second order optimality conditions for the local solutions of the sparse optimal control problem for vanishing Tikhonov regularization parameter. Further, we estimate the distance between the discrete control and associated local optima numerically by the help of the perturbation method and the smallest eigenvalue of the reduced Hessian.

Subject Keywords

FitzHugh-Nagumo equation, Traveling waves, Sparse controls, Second order optimality conditions, Discontinuous Galerkin method

URI

https://hdl.handle.net/11511/32645

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS

DOI

https://doi.org/10.1016/j.camwa.2017.02.028

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Moving mesh discontinuous Galerkin methods for PDEs with traveling waves UZUNCA, MURAT; Karasözen, Bülent; Kucukseyhan, T. (2017-01-01) In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning approach which decouples the solution of the PDE from the moving mesh equation. We show that the dG moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal, arc-length and curvature monitor functions. Numerical results reveal the effi...
Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation UZUNCA, MURAT; Karasözen, Bülent; Sariaydin-Filibelioglu, Ayse (2015-09-18) We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization for the advective Allen-Cahn equation with nondivergence-free velocity fields. Numerical simulations for convection dominated problems demonstrate the accuracy and efficiency of the adaptive algorithm for resolving the sharp layers occurring in interface problems with small surface tension.
Optimal Control of convective FitzHugh Nagumo model Karasözen, Bülent; Güney , Tuğba (2015-06-29) In this talk we investigate optimal control of wave propagation in excitable media described by two-dimensional FitzHugh-Nagumo model. The model consists of two coupled reaction-diffusionconvection equations describing the flow in blood coagulation and in bioreactors [2] ∂u ∂t = du∆u − V (y) ∂u ∂x + αu(u − β)(1 − u) − v, ∂v ∂t = dv∆v − V (y) ∂v ∂x + (γu − v), where u and v are activator and inhibitor, respectively and V (y) is the velocity profile. The flow plays an important role by the regularization of ...
Spatial behavior estimates for the wave equation under nonlinear boundary conditions Celebi, AO; Kalantarov, VK (2001-09-01) Our aim is to establish a spatial decay and growth estimates for solutions of the initial-boundary value problem for the linear wave equation with the damping term under nonlinear boundary conditions.
Multiscale Modeling of Thin-Wire Coupling Problems Using Hybridization of Finite Element and Dipole Moment Methods and GPU Acceleration ÖZGÜN, ÖZLEM; Mittra, Raj; Kuzuoğlu, Mustafa (2020-01-01) In this article, a hybrid numerical method, called finite element method (FEM) + dipole moment (DM), is presented for efficient solution of multiscale electromagnetic radiation and scattering problems that involve structures with fine features, such as thin-wire antennas or objects. In this method, the FEM is hybridized with the DM approach to help ease certain computational burdens, such as mesh refinement, ill-conditioning, memory overload, and long computation times, when solving multiscale problems with...

Citation Formats

M. Uzunca, T. Kucukseyhan, H. Yücel, and B. Karasözen, “Optimal control of convective FitzHugh-Nagumo equation,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 2151–2169, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32645.