arXiv subjects

Youssef Ouakrim

Publications and source records attributed to Youssef Ouakrim.

4 recordsLinked to original sources

arXiv2026

A Dual ADMM Framework for Inverse Parameter Identification in Elliptic Variational Inequalities

This paper is concerned with an inverse parameter identification problem governed by a second-kind elliptic variational inequality involving a non-differentiable boundary functional. The objective is to reconstruct an unknown Robin-type coefficient from boundary measurements while preserving the intrinsic nonsmooth structure of the underlying model. The inverse problem is formulated as a constrained optimization problem, where the cost functional measures the discrepancy between the computed and observed data and is stabilized by Tikhonov regularization. To overcome the difficulties associated with the nonsmooth variational inequality, we reformulate the state problem as a constrained minimization problem and employ an augmented Lagrangian framework combined with the alternating direction method of multipliers (ADMM). Fenchel duality is used to treat the non-differentiable boundary term without introducing smoothing approximations. We establish identifiability of the unknown coefficient and prove existence and convergence results for the proposed approximation scheme. Numerical experiments performed on a classical benchmark problem confirm the theoretical analysis and demonstrate that accurate parameter reconstruction can be achieved with reduced computational effort. The proposed methodology provides a robust framework for inverse problems arising in applications such as heat transfer, frictional contact, and corrosion detection.

math.OC↗

arXiv2024

Effect of energy dissipation on radiofrequency ablation model in cardiac tissue: modelling, analysis and numerical simulation

This paper deals with the mathematical analysis and numerical simulation of a new nonlinear ablation system modeling radiofrequency ablation phenomena in cardiac tissue, {which incorporates the effects of blood flow on the heat generated when ablation by radiofrequency. The model also considers the effects of viscous energy dissipation. It consists of a coupled thermistor problem and the incompressible Navier--Stokes equations that describe the evolution of temperature, velocity and potential in cardiac tissue.} In addition to Faedo--Galerkin method, we use Schauder's fixed-point theory to prove the existence of the weak solutions in two- and three-dimensional space. Moreover, we prove the uniqueness of the solution under some additional conditions on the data and the solution. Finally, we discuss some numerical results for the validation of the proposed model using the finite element method.

math.AP↗

arXiv2024

Mathematical study of a new coupled electro-thermo radiofrequency model of cardiac tissue

This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo-Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.

math.NA↗

arXiv2018

Posture recognition using an RGB-D camera : exploring 3D body modeling and deep learning approaches

The emergence of RGB-D sensors offered new possibilities for addressing complex artificial vision problems efficiently. Human posture recognition is among these computer vision problems, with a wide range of applications such as ambient assisted living and intelligent health care systems. In this context, our paper presents novel methods and ideas to design automatic posture recognition systems using an RGB-D camera. More specifically, we introduce two supervised methods to learn and recognize human postures using the main types of visual data provided by an RGB-D camera. The first method is based on convolutional features extracted from 2D images. Convolutional Neural Networks (CNNs) are trained to recognize human postures using transfer learning on RGB and depth images. Secondly, we propose to model the posture using the body joint configuration in the 3D space. Posture recognition is then performed through SVM classification of 3D skeleton-based features. To evaluate the proposed methods, we created a challenging posture recognition dataset with a considerable variability regarding the acquisition conditions. The experimental results demonstrated comparable performances and high precision for both methods in recognizing human postures, with a slight superiority for the CNN-based method when applied on depth images. Moreover, the two approaches demonstrated a high robustness to several perturbation factors, such as scale and orientation change.

cs.CV↗