An adaptive wavelet collocation method for the optimal heat source problem
Mahmood Khaksar-e Oshagh, Mostafa Abbaszadeh, Esmail Babolian, Hossein Pourbashash · International Journal of Numerical Methods for Heat & Fluid Flow · 2021
Purpose This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP). Design/methodology/approach The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction. Findings This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution. Originality/value The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.