Optimal Heat Distribution Using Asymptotic Analysis Techniques / / Zakaria Belhachmi [and three others].

• VerfasserIn: Belhachmi, Zakaria,
• Place / Publishing House: London : : IntechOpen,, 2021.
• Year of Publication: 2021
• Language: English
• Physical Description: 1 online resource (279 pages)

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.

Table of Contents

1. Introduction -- 2. The model problem -- 3. Topological derivatives -- 3.1 Application to the model problem -- 3.1.1 Variation of the bilinear form -- 3.1.2 Variation of the linear form -- 3.1.3 Variation of the cost function -- 4. Estimates of the remainders -- 4.1 Preliminary lemmas -- 4.2 Asymptotic behavior of the remainders -- 5. Numerical experiments -- 5.1 Example 1 -- 5.1 Example 1 -- 6. Conclusion -- References.