Youness El Yazidi
@fst.ac.ma
Department of Mathematics, Faculty of Sciences
Abdelmalek Essaadi University
RESEARCH INTERESTS
inverse problems
Shape optimization
Parameter identification
Image processing
denoising Algorithms
Image segmentation
Scopus Publications
Scopus Publications
Youness El Yazidi and Abdellatif Ellabib
EDP Sciences
In this study, we focus on a specific class of bilateral free boundaries problems. We approach this problem by formulating it as a shape optimization problem using a defined cost functional. The existence of an optimal solution for the optimization problem is proved. To tackle this problem, we propose an iterative approach that combines the particle swarm optimization and fuzzy logic methods. Additionally, we employ the finite element method as a discretization technique for the state equation. To validate our approaches, we investigate various types of domains. Furthermore, we compare the performance of these approaches in two scenarios: one with exact measurements used for identification and another with noisy measurements.
Y Ouakrim, I Boutaayamou, Y El Yazidi, and A Zafrar
IOP Publishing
Abstract The paper presents a numerical method for identifying discontinuous conductivities in elliptic equations from boundary observations. The solutions to this inverse problem are obtained through a constrained optimization problem, where the cost functional is a combination of the Kohn–Vogelius and Total Variation functionals. Instead of regularizing the Total Variation stabilization functional, which is commonly used in the literature, we introduce an Alternating Direction Method of Multipliers to preserve the favorable properties of non-smoothness and convexity. The discretization is carried out using a mixed finite element/volume method, while the numerical solutions are iteratively computed using a variant of the Uzawa algorithm. We show the surjectivity of the derivatives of the constraints related to the discrete optimization problem and derive a source condition for the discrete inverse problem. We then investigate the convergence analysis and establish the convergence rate. Finally, we conclude with some numerical experiments to illustrate the efficiency of the proposed method.
Abderrahim Charkaoui and Youness El Yazidi
World Scientific Pub Co Pte Ltd
In this paper, we address the identification of an unknown inclusion in an elliptic equation, which arises in the context of electrical impedance tomography and multiphase problems. We present a novel approach by formulating the overdetermined system as an optimal design problem based on the unknown inclusion and two state solutions, which is derived from by introducing a least square functional. We establish the existence results and first optimality conditions, and employ the finite element method to discretize the involved variational equations. Furthermore, we update the unknown inclusion using the level-set method. To demonstrate the effectiveness and validity of our proposed algorithm, we investigate simple and complex geometries numerically. Our results showcase the efficiency and accuracy of the method, making it a promising tool for solving similar inverse problems in various engineering applications.
Youness El Yazidi and Abdellatif ELLABIB
American Institute of Mathematical Sciences (AIMS)
<p style='text-indent:20px;'>The aim of this work is to reconstruct the depletion region in pn junction. Starting with famous drift diffusion model, we establish the simplified equation for the considered semiconductor. There we call the shape optimization technique to formulate a minimization problem from the inverse problem at hand. The existence of an optimal solution of the optimization problem is proved. The proposed numerical algorithm is a combined Domain Decomposition method with an efficient hybrid conjugate gradient guided by differential evolution heuristic algorithm, the finite element method is used to discretize the state equation. At the end we establish several numerical examples, to prove the validity of theoretical results using the proposed algorithm, in addition we show some simulation of the depletion region approximation under two different functioning modes.</p>
Youness El Yazidi and Abdellatif Ellabib
Springer Science and Business Media LLC
Youness El Yazidi and Abdellatif Ellabib
Wiley
In this paper, a bilateral free boundaries problem is considered. This kind of inverse problems appears in the theory of semiconductors and multi‐phase problems. Using a shape functional and some regularization terms, an optimal control problem is formulated. In addition, we prove its solution existence. The first optimality conditions and the shape gradient are computed. With the finite element method, we write the discrete version of the optimal control problem. To design our proposed scheme, we based on the conjugate gradient, where we use the genetic algorithm to find the best initial guess for the gradient method. At each mesh regeneration, we perform a mesh refinement in order to avoid any domain singularities. Some numerical examples are shown to demonstrate the validity of the theoretical results and to prove the robustness and efficiency of the proposed scheme, especially to identify free boundaries with jump points.
Youness El Yazidi, Abdellatif Ellabib, and Youssef Ouakrim
Elsevier BV
El Yazidi Youness, , Ellabib Abdellatif, and
Lviv Polytechnic National University