An adaptive wavelet collocation method for the optimal heat source problem

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.

Optimal Heat Distribution Using Asymptotic Analysis Techniques

In this chapter, we consider the optimization problem of a heat distribution on a bounded domain Ω containing a heat source at an unknown location ω⊂Ω. More precisely, we are interested in the best location of ω allowing a suitable thermal environment. For this propose, we consider the minimization of the maximum temperature and its L2 mean oscillations. We extend the notion of topological derivative to the case of local coated perturbation and we perform the asymptotic expansion of the considered shape functionals. In order to reconstruct the location of ω, we propose a one-shot algorithm based on the topological derivative. Finally, we present some numerical experiments in two dimensional case, showing the efficiency of the proposed method.