Optimal control solution for Pennes' equation using strongly continuous semigroup

Malek, Alaeddin; Abbasi, Ghasem

doi:10.14736/kyb-2014-4-0530

Cited by 1 publication

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References 12 publications

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“…Ganzler used sequential quadratic programming for parameter identification problems in hyperthermia (Gänzler et al, 2006). In the year 2014, a direct solution for the Pennes equation is presented in the literature (Malek and Abbasi, 2014). Malek and Abbasi used strongly continuous semigroup for solving optimal control subject to PBE (Malek and Abbasi, 2015, 2016).…”

Section: Introductionmentioning

confidence: 99%

Solving two-dimensional bioheat optimal control problem in solid and vessel domain by pseudospectral discretization

Dastyar

Malek

Yousefi

2022

Transactions of the Institute of Measurement and Control

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In this paper, an optimal control problem subject to an energy transfer equation in thermally significant blood vessel coupled with the Pennes governing equation is solved. The proposed dynamical system is modeled by a system of conduction-reaction and convection-conduction equations. Chebyshev–Gauss–Lobatto (CGL) and Legendre–Gauss–Lobatto (LGL) points are applied to discretize optimal control problem. Then, the problem transferred into a quadratic programming problem using domain decomposition and matching the solution and its first derivative across the related interfaces. The Tikhonov regularization method is used to compute the optimal regularization parameter for the objective function. Some theories have been discussed to prove that the discrete problem has a solution and it is also consistent with the continuous problem. Numerical results are compared and numerical convergent is shown. Optimal and non-optimal external heat source is compared and it is shown that the mathematical modeling is effective in saving the external heat energy. Numerical results show that by this process of heating at the final time, the temperature is very close to the desired temperature without damaging the vessel domain. Numerical results and corresponding graphs are depicted.

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