University of Tabriz Computational Methods for Differential Equations 2345-3982 14 2 2026 04 01 An heuristic method for solving an inverse problem in semiconductors governed by a nonlinear coupled system 606 615 19198 10.22034/cmde.2025.62043.2708 EN Youness El Yazidi Research Laboratory in Numerical Analysis and Nonlinear Analysis (LaR2A) Department of Mathematics, Faculty of Sciences, University Abdelmalek Essaadi, BP 2121 M'Hannech II 93030 Tetouan, Morocco. Abdellatif Ellabib Laboratory of Applied Mathematics and Computer Science, Faculty of Science and Technology, Cady Ayyad University, Marrakesh, Morocco. Journal Article 2024 06 10 In this work, we utilize a coupled system to describe the carrier density in the Metal-Semiconductor Field-Effect Transistor (MESFET) device. To identify the depletion layer in this semiconductor, we define a cost functional $J$, and then use it to derive the shape optimization problem, for which we prove the existence of a solution. We develop an approach to solve this optimization problem using the finite element method combined with particle swarm optimization. Finally, we present several numerical examples to demonstrate the robustness of our proposed algorithm in identifying the depletion layer in the MESFET device. https://cmde.tabrizu.ac.ir/article_19198_15b6710a02c8f64ecb7c03166a73ef13.pdf