Topological sensitivity analysis for a three-dimensional parabolic type problem

Article type: Research Article

Authors: Ghezaiel, Emna^a | Abdelwahed, Mohamed^{b; *} | Chorfi, Nejmeddine^b | Hassine, Maatoug^c

Affiliations: [a] ESSTHS, Sousse University, Tunisia | [b] College of Sciences, King Saud University, Riyadh, Saudi Arabia | [c] FSM, Department of Mathematics, Monastir University, Tunisia

Correspondence: [*] Corresponding author. E-mail: mabdelwahed@ksu.edu.sa.

Abstract: This work focuses on the topological sensitivity analysis of a three-dimensional parabolic type problem. The considered application model is described by the heat equation. We derive a new topological asymptotic expansion valid for various shape functions and geometric perturbations of arbitrary form. The used approach is based on a rigorous mathematical framework describing and analyzing the asymptotic behavior of the perturbed temperature field.

Keywords: Geometric inverse problem, topological sensitivity analysis, asymptotic expansion, parabolic operator

DOI: 10.3233/ASY-191587

Journal: Asymptotic Analysis, vol. 120, no. 3-4, pp. 249-272, 2020