# abdeljalil nachaoui

## Université de Nantes

H-index: 18

Europe-France

## About abdeljalil nachaoui

abdeljalil nachaoui, With an exceptional h-index of 18 and a recent h-index of 15 (since 2020), a distinguished researcher at Université de Nantes, specializes in the field of Inverse Problems, Shap Optimization, Computing in Mathematics Natural Science Engineering and Medicine, Nonlinear Analysis, Scie.

His recent articles reflect a diverse array of research interests and contributions to the field:

On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition

An accelerated alternating iterative algorithm for data completion problems connected with Helmholtz equation

An hybrid finite element method for a quasi-variational inequality modeling a semiconductor

On the Optimization Problem of One Market Relation Containing the Delay Functional Differential Equation

An improved hybrid defuzzification method for fuzzy controllers

International Conference on Mathematics & Data Science International E-Conference on Differential Equations and Applications.

Polynomial Approximation of a Nonlinear Inverse Cauchy Problem

AN ITERATIVE METHOD FOR CAUCHY PROBLEMS SUBJECT TO THE CONVECTION-DIFFUSION EQUATION.

### abdeljalil nachaoui Information

University | Université de Nantes |
---|---|

Position | Laboratoire de Mathématiques Jean Leray |

Citations(all) | 1093 |

Citations(since 2020) | 681 |

Cited By | 567 |

hIndex(all) | 18 |

hIndex(since 2020) | 15 |

i10Index(all) | 38 |

i10Index(since 2020) | 26 |

University Profile Page | Université de Nantes |

#### abdeljalil nachaoui Skills & Research Interests

Inverse Problems

Shap Optimization

Computing in Mathematics Natural Science Engineering and Medicine

Nonlinear Analysis

Scie

## Top articles of abdeljalil nachaoui

### On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition

The analytic relation between solutions of the original Cauchy problem and a corresponding perturbed problem is established. In the representation formula of solution, the effects of the discontinuous initial condition and perturbation of the initial data are revealed.

Authors

Abdeljalil Nachaoui,Tea Shavadze,Tamaz Tadumadze

Journal

Georgian Mathematical Journal

Published Date

2024/1/11

### An accelerated alternating iterative algorithm for data completion problems connected with Helmholtz equation

This paper deals with an inverse problem governed by the Helmholtz equation. It consists in recovering lackingdata on a part of the boundary based on the Cauchy data on the other part. We propose an optimal choice of the relaxationparameter calculated dynamically at each iteration. This choice of relaxation parameter ensures convergence without priordetermination of the interval of the relaxation factor required in our previous work. The numerous numerical example showsthat the number of iterations is drastically reduced and thus, our new relaxed algorithm guarantees the convergence for allwavenumber k and gives an automatic acceleration without any intervention of the user.

Authors

Karzan Ahmad Berdawood,Abdeljalil Nachaoui,Mourad Nachaoui

Journal

Statistics, Optimization & Information Computing

Published Date

2023/1/9

### An hybrid finite element method for a quasi-variational inequality modeling a semiconductor

A problem of determining the characteristics of a semiconductor can be reduced to the study of the quasi-variational inequality, (J. Abouchabaka, R. Aboulaïch, A. Nachaoui and A. Souissi, COMPEL 18 (1999) 143–164.) where the obstacle M(u) is the solution of an elliptic problem depending on u. We present here an hybrid finite element method for the computation of obstacle M(u) and we discuss some numerical aspects appearing in its approximation.

Authors

Abdeljalil Nachaoui,Mourad Nachaoui

Journal

RAIRO-Operations Research

Published Date

2023/7/1

### On the Optimization Problem of One Market Relation Containing the Delay Functional Differential Equation

Let market relation demand and supply for the good i1 are described by functions D1 (t, ω) and S1 (t, x1, x2, u) and for the good i2 are described by functions D2 (t, ϑ) and S2 (t, x1, x2, v). Let cost of the goods i1 and i2 at the moment t be u (t) and v (t), respectively. Suppose that at time t consumer demand will be satisfied on the good i1 which has been ordered at time t-ρ, where ρ> 0 is a fixed delay parameter and on the good i2 which has been ordered at time t-θ, where θ> 0, in general, is non fixed delay. The function

Authors

Phridon Dvalishvili,Adeljalil Nachaoui,Mourad Nachaoui,Tamaz Tadumadze

Journal

REPORTS OF QUALITDE

Published Date

2023/12/9

### An improved hybrid defuzzification method for fuzzy controllers

This paper deals with fuzzy logic controllers. Our interest is in studying different techniques of defuzzification methods. In particular, we propose a generalization of the WABL method to the multiple output system controller. We give a numerical realization, and we show the advantages of this method compared to other defuzzification methods (MOM, COG, WAF,\ldots) through an application for intelligent control of air conditioners.

Authors

Mourad Nachaoui,Abdeljalil Nachaoui,RY Shikhlinskaya,Abdelali Elmoufidi

Journal

Statistics, Optimization & Information Computing

Published Date

2023/1/9

### International Conference on Mathematics & Data Science International E-Conference on Differential Equations and Applications.

The article focuses on qualitative analysis and numerical simulation of mathematical models, covering topics such as mathematical analysis of differential equations, nonlinear Partial Differential Equations (PDE) problems, and numerical simulation methodologies. It mentions contributions from two international conferences, providing insights into various aspects of linear and nonlinear mathematical models within the context of advanced mathematical analysis and applications.

Authors

Abdeljalil Nachaoui

Journal

Advanced Mathematical Models & Applications

Published Date

2023/5/2

### Polynomial Approximation of a Nonlinear Inverse Cauchy Problem

In this paper, a class of nonlinear inverse boundary problem in the context of heat transfer is considered. We consider a class of nonlinear inverse boundary problems in the context of heat transfer. The problem involves determining the temperature distribution within a domain subject to a Cauchy boundary condition on a part of its boundary. We introduce a transformed variable, which allows us to reformulate the problem as a linear Cauchy problem followed by a series of nonlinear equations. We propose a polynomial expansion method to solve the linear Cauchy problem for the Laplace equation, and we employ the Newton method to solve the resulting nonlinear equations. Importantly, our approach does not rely on mesh-based discretization, allowing for parallel computation and preserving the mesh-free nature of the problem. We present numerical results obtained using our methodology and discuss the effectiveness of the proposed approach. The results show that the method provides a robust and efficient framework for solving nonlinear inverse boundary problems in heat transfer, with potential applications in various engineering and scientific fields.

Authors

Sudad Rasheed,Abdeljalil Nachaoui

Journal

Academic Science Journal

Published Date

2023/11/15

### AN ITERATIVE METHOD FOR CAUCHY PROBLEMS SUBJECT TO THE CONVECTION-DIFFUSION EQUATION.

In this text, we presented the Nachaoui’s iterative alternating method for solving the Cauchy problem governed by the convection-diffusion equation. The method is an iterative algorithm that alternates between solving two subproblems of the same type with boundary conditions of the Dirichlet and Neuman type on the inaccessible part of the boundary. The algorithm continues iterating until a convergence criterion is met. We discussed the convergence and computational efficiency of the method. The numerical results show that the method is computationally efficient and that the relaxation parameter can greatly reduce the number of iterations.

Authors

Abdeljalil Nachaoui

Journal

Advanced Mathematical Models & Applications

Published Date

2023/5/2

### Meshless methods to noninvasively calculate neurocortical potentials from potentials measured at the scalp surface

Noninvasive measurement of neurocortical potentials using electroencephalography (EEG) is a valuable tool in neuroscience research and clinical practice. However, accurate estimation of neurocortical potentials from scalp potentials is a challenging problem, due to the complex and ill-posed nature of the forward and inverse problems. In this paper, we present an approach based on the annular model and polynomial expansion method to solve the Cauchy problem associated with noninvasive calculation of neurocortical potentials. We derive the mathematical formulas and discuss the numerical implementation of the method, and demonstrate its effectiveness using numerical simulations.

Authors

Abdeljalil Nachaoui,Mourad Nachaoui,Tamaz Tadumadze

Published Date

2022/5/19

### An effective relaxed alternating procedure for cauchy problem connected with helmholtz equation

This paper is concerned with the Cauchy problem for the Helmholtz equation. Recently, some new works asked the convergence of the well‐known alternating iterative method. Our main result is to propose a new alternating algorithm based on relaxation technique. In contrast to the existing results, the proposed algorithm is simple to implement, converges for all choice of wave number, and it can be used as an acceleration of convergence in the case where the classical alternating algorithm converges. We present theoretical results of the convergence of our algorithm. The numerical results obtained using our relaxed algorithm and the finite element approximation show the numerical stability, consistency and convergence of this algorithm. This confirms the efficiency of the proposed method.

Authors

Karzan A Berdawood,Abdeljalil Nachaoui,Mourad Nachaoui,Fatima Aboud

Journal

Numerical Methods for Partial Differential Equations

Published Date

2023/5

### A mesh free wavelet method to solve the cauchy problem for the helmholtz equation

In this paper, we present a numerical based on Haar wavelets to solve an inverse Cauchy problem governed by the Helmholtz equation. The problem involves reconstructing the boundary condition on an inaccessible boundary from the given Cauchy data on another part of the boundary. We discuss the formulation of the problem and the use of Haar wavelets. The proposed method involves approximating the solution using a finite sum of Haar wavelets and solving the resulting linear system of equations using a least-squares method. The effectiveness of the proposed method is demonstrated through numerical experiments. From these results, we demonstrate that the Haar wavelet method can be used to obtain an accurate solution to the problem.

Authors

Abdeljalil Nachaoui,Sudad Musa Rashid

Published Date

2023/7/16

### A Haar wavelets-based direct reconstruction method for the Cauchy problem of the Poisson equation

In this paper, we develop a Haar wavelet-based reconstruction method to recover missing data on an inaccessible part of the boundary from measured data on another accessible part. The technique is developed to solve inverse Cauchy problems governed by the Poisson equation which is severely ill-posed. The new method is mathematically simple to implement and can be easily applied to Cauchy problems governed by other partial differential equations appearing in various fields of natural science, engineering, and economics. To take into account the ill-conditioning of the obtained linear system due to the ill-posedness of the Cauchy problem, a preconditioning strategy combined with a regularization has been developed. Comparing the numerical results produced by a meshless method based on the polynomial expansion with those produced by the proposed technique illustrates the superiority of the latter …

Authors

Sudad Musa Rashid,Abdeljalil Nachaoui

Journal

Discrete and Continuous Dynamical Systems-S

Published Date

2023/4/7

### Solving geometric inverse problems with a polynomial based meshless method

In this paper, we present a novel method for solving an inverse problem that involves determining an unknown defect D compactly contained in a simply-connected bounded domain , given the Dirichlet temperature data u, the Neumann heat flux data on the boundary , and a Dirichlet boundary condition on the boundary . We assume that the temperature u satisfies the modified Helmholtz equation governing the conduction of heat in a fin. The proposed method involves dividing the problem into two subproblems: first, solving a Cauchy problem governed by the modified Helmholtz equation to determine the temperature u, followed by solving a series of nonlinear scalar equations to determine the coordinates of the points defining the boundary . Our numerical experiments demonstrate the effectiveness and accuracy of the proposed method in solving this challenging inverse problem.

Authors

Abdeljalil Nachaoui,Fatima Aboud

Published Date

2023/7/16

### On the numerical approximation of some inverse problems governed by nonlinear delay differential equation

The paper deals with the approximate solving of an inverse problem for the nonlinear delay differential equation, which consists of finding the initial moment and delay parameter based on some observed data. The inverse problem is considered as a nonlinear optimal control problem for which the necessary conditions of optimality are formulated and proved. The obtained optimal control problem is solved by a method based on an improved parallel evolutionary algorithm. The efficiency of the proposed approach is demonstrated through various numerical experiments.

Authors

Mourad Nachaoui,Abdeljalil Nachaoui,Tamaz Tadumadze

Journal

RAIRO-Operations Research

Published Date

2022/5/1

### On numerical approaches for solving an inverse cauchy stokes problem

In this paper, we are interested in the study of an inverse Cauchy problem governed by Stokes equation. It consists in determining the fluid velocity and the flux over a part of the boundary, by introducing given measurements on the remaining part. As it’s known, it is one of highly ill-posed problems in the Hadamard’s sense (Phys Today 6:18, 1953), it is then an interesting challenge to carry out a numerical procedure for approximating their solutions, in particular, in the presence of noisy data. To solve this problem, we propose here a regularizing approach based on a Tikhonov regularization method. We show the existence of the regularization optimization problem and prove the convergence of subsequence of optimal solutions of Tikhonov regularization formulations to the solution of the Cauchy problem, when the noise level goes to zero. Then, we suggest the numerical approximation of this problem using the finite …

Authors

Hamid Ouaissa,Abdelkrim Chakib,Abdeljalil Nachaoui,Mourad Nachaoui

Journal

Applied Mathematics & Optimization

Published Date

2022/2

### An efficient DN alternating algorithm for solving an inverse problem for Helmholtz equation.

Data completion known as Cauchy problem is one most investigated inverse problems. In this work we consider a Cauchy problem associated with Helmholtz equation. Our concerned is the convergence of the well-known alternating iterative method [25]. Our main result is to restore the convergence for the classical iterative algorithm (KMF) when the wave numbers are considerable. This is achieved by, some simple modification for the Neumann condition on the under-specified boundary and replacement by relaxed Neumann ones. Moreover, for the small wave number kk, when the convergence of KMF algorithm's [25] is ensured, our algorithm can be used as an acceleration of convergence. In this case, we present theoretical results of the convergence of this relaxed algorithm. Meanwhile it, we can deduce the convergence intervals related to the relaxation parameters in different situations. In contrast to the …

Authors

Karzan Berdawood,Abdeljalil Nachaoui,Rostam Saeed,Mourad Nachaoui,Fatima Aboud

Journal

Discrete & Continuous Dynamical Systems-Series S

Published Date

2022/1/1

### Polynomial approximation of an inverse Cauchy problem for Helmholtz type equations

The objective of this paper is to solve numerically a Cauchy problem defined on a two-dimensional domain occupied by a material satisfying the Helmholtz type equations and verifying additional Cauchy-type boundary conditions on the accessible part of the boundary. A meshless numerical method using an approximation of the solution based on the polynomial expansion is applied. To confirm the efficiency of the proposed method, different examples were considered and the obtained linear system was solved using the well-known CG and CGLS algorithms.

Authors

Fatima Aboud,Ibtihal Th. Jameel,Athraa F. Hasan,Baydaa Kh. Mostafa,Abdeljalil Nachaoui

Journal

Advanced Mathematical Models & Applications (ISSN : 2519-4445)

Published Date

2022/12/17

### On the coefficient of sensitivity of a controlled differential model of the immune response

A form of the system of differential equations is established, which satisfies the sensitivity coefficients of a controlled differential model of the immune response considering perturbations of the delay parameter, the initial and control functions.

Authors

Tamaz Tadumadze,Abdeljalil Nachaoui,Tea Shavadze

Journal

Semin. I. Vekua Inst. Appl. Math. Rep.

Published Date

2022

### Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity

In this paper, we are interested in solving a Cauchy inverse problem in linear elasticity. For this, we propose a new method based on Robin conditions on the inaccessible boundary, then we study the convergence and regularizing property of the proposed algorithm. We use the finite element method for the discretization of our problem. Further, we treat the spectrum analysis of the discrete problem in order to study the convergence behavior of the proposed method in the discrete case. Finally, we present numerical results which show the efficiency and stability of the proposed approach in the presence of perturbed data. The robustness of the proposed algorithm is also performed for the anisotropic and heterogeneous cases.

Authors

Abdellatif Ellabib,Abdeljalil Nachaoui,Abdessamad Ousaadane

Journal

Inverse Problems

Published Date

2022/6/6

### Some novel numerical techniques for an inverse Cauchy problem

In this paper, we are interested in solving an elliptic inverse Cauchy problem. As it is well known this problem is one of highly ill posed problem in Hadamard’s sense (Hadamard, 1953). We first establish formally a relationship between the Cauchy problem and an interface problem illustrated in a rectangular structure divided into two domains. This relationship allows us to use classical methods of non-overlapping domain decomposition to develop some regularizing and stable algorithms for solving elliptic inverse Cauchy problem. Taking advantage of this relationship we reformulate this inverse problem into a fixed point one, based on Steklov–Poincaré operator. Thus, using the topological degree of Leray–Schauder we show an existence result. Finally, the efficiency and the accuracy of the developed algorithms are discussed.

Authors

Abdeljalil Nachaoui,Mourad Nachaoui,Abdelkrim Chakib,MA Hilal

Journal

Journal of Computational and Applied Mathematics

Published Date

2021/1/1

### On the stability of a mathematical model for HIV (AIDS)—cancer dynamics

In this work, we study an impulsive mathematical model proposed by Chavez et al.[1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

Authors

HW Salih,A Nachaoui

Journal

Mathematical modeling and computing

Published Date

2021

### Mathematical analysis and simulation of fixed point formulation of Cauchy problem in linear elasticity

In this work, an inverse problem in linear elasticity is considered, it is about reconstructing the unknown boundary conditions on a part of the boundary based on the other boundaries. A methodology based on the domain decomposition operating mode is opted by constructing a Steklov–Poincaré kind’s operator. This allows us to reformulate our inverse problem into a fixed point one involving a Steklov kind’s operator, the existence of the fixed point problem is shown using the topological degree of Leray–Schauder. The proposed approach offers the opportunity to exploit domain decomposition methods for solving this inverse problem. Finally, a numerical study of this problem using the boundary element method is presented. The obtained numerical results show the efficiency of the proposed approach.

Authors

Abdellatif Ellabib,Abdeljalil Nachaoui,Abdessamad Ousaadane

Journal

Mathematics and Computers in Simulation

Published Date

2021/9/1

### Mathematical control and numerical applications

This book contains a collection of selected papers presented at the Numerical Analysis and Optimization Days (JANO13), held in Khouribga, Morocco, from 22 to 24 February 2021. The book focuses on topics related to mathematical control and numerical applications. This volume covers new trends and advances in several very important fields of mathematical modelling and recent developments in new numerical approximation methods. The relevance of these topics is particularly related to the study of approximation parameters, sources separation and partial differential equations (PDEs) approximations related to image processing applications. All contributing authors are eminent researchers and scholars in their respective fields, hailing from around the world. The information given in this book will be of value to the work of researchers, scientists and engineers in the fields of both academia and industry.

Authors

Abdeljalil Nachaoui,A Laghrib,M Hakim

Published Date

2021

### PARALLEL NUMERICAL COMPUTATION OF AN ANALYTICAL METHOD FOR SOLVING AN INVERSE PROBLEM.

We solve the inverse Cauchy problems for the Laplace and Poisson equations using a closed-form regularization analytical solution. The formula is written in the form of series whose terms are integrals. The discretization is done using a Gaussian quadrature and the finite sum thus obtained is implemented on distributed memory using the Message Passing Interface (MPI). A detailed study of the parallelization procedure is presented.

Authors

Nachaoui Abdeljalil,Nachaoui Mourad,Bayram Gasimov

Journal

Advanced Mathematical Models & Applications

Published Date

2021/5/1

### On the approximation of a Cauchy problem in a non-homogeneous medium

This paper deals with an inverse Cauchy problem governed by an elliptical equation defined in non-homogeneous domain. We propose two approaches based on alternating algorithm [11] combined with a domain decomposition method [14]. We use the finite elements method to approximate the associate direct problems. Finally, we show the numerical convergence of both proposed algorithms and we discuss there efficiency trough some numerical experiments.

Authors

F Aboud,Abdeljalil Nachaoui,M Nachaoui

Journal

Journal of Physics: Conference Series

Published Date

2021

### REGULARIZED AND PRECONDITIONED CONJUGATE GRADIENT LIKE-METHODS METHODS FOR POLYNOMIAL APPROXIMATION OF AN INVERSE CAUCHY PROBLEM.

In this paper, regularization combined with a preconditioning strategy is used to solve the illconditioned linear system obtained from the approximation of the inverse Cauchy problem for the Poisson equation in an arbitrary bounded domain. This approximation is based on the polynomial expansion (Liu & Kuo, 2016).

Authors

Sudad M Rasheed,Abdeljalil Nachaoui,Mudhafar F Hama,Adil K Jabbar

Journal

Advanced Mathematical Models & Applications

Published Date

2021/5/1

### Numerical simulation of a nonlinear problem modeling the cooling of a metal

In this work, the finite difference method was used to calculate the heat distribution during cooling by the boundary part of a cylindrical material subjected to high temperature. A mathematical model of the process was formulated using cylindrical coordinates. The heat transfer coefficient occurring in the Robin condition at the cooled boundary is nonlinear. We use quasi-Newton techniques combined with gradient-like methods to solve the discrete nonlinear problem.

Authors

Fatima Aboud,Abdeljalil Nachaoui

Journal

Journal of Physics: Conference Series

Published Date

2021

### Acceleration of the KMF Algorithm Convergence to Solve the Cauchy Problem for Poisson’s Equation

In this article we propose a new demonstration of the convergence of the relaxed iterative JN algorithm for solving the inverse Cauchy problem. We give in particular the convergence interval as well as the interval of the convergence acceleration of KMF algorithm.

Authors

Abdeljalil Nachaoui,Fatima Aboud,Mourad Nachaoui

Published Date

2021/2/22

### On a regularization approach for solving the inverse Cauchy Stokes problem

In this paper, we are interested to an inverse Cauchy problem governed by the Stokes equation, called the data completion problem. It consists in determining the unspecified fluid velocity, or one of its components over a part of its boundary, by introducing given measurements on its remaining part. As it's known, this problem is one of the highly ill-posed problems in the Hadamard's sense \cite{had}, it is then an interesting challenge to carry out a numerical procedure for approximating their solutions, mostly in the particular case of noisy data. To solve this problem, we propose here a regularizing approach based on a coupled complex boundary method, originally proposed in \cite{source}, for solving an inverse source problem. We show the existence of the regularization optimization problem and prove the convergence of the subsequence of optimal solutions of Tikhonov regularization formulations to the solution of the Cauchy problem. Then we suggest the numerical approximation of this problem using the adjoint gradient technic and the finite element method of type. Finally, we provide some numerical results showing the accuracy, effectiveness, and robustness of the proposed approach.

Authors

Abdelkrim Chakib,Abdeljalil Nachaoui,Mourad Nachaoui,Hamid Ouaissa

Journal

arXiv preprint arXiv:2112.14141

Published Date

2021/12/28

### Study of the stability for Drug Delivery Models

In this work, mathematical models of drug delivery are presented. We are particularly interested in studying the stability of these models to release the drug in a polymer matrix and detect its transfer to the overall biological tissue. These results are illustrated on two models. In order to gain protocol treatment, instead of using the optimal control theory, Lyapunov's stability theorem is used to study the stability of the first nonlinear system. For the second, we proceed by establishing the properties of the equilibrium point (which is strongly related to the stability of the nonlinear system) by modifying the system into a canonical equation and studying the spectrum of its Jacobian matrix to show that the system is stable.

Authors

Hero W Salih,Abdeljalil Nachaoui

Journal

Journal of Physics: Conference Series

Published Date

2021

### On the existence of an optimal element for the neutral optimal problem with delay in controls

Under conditions of compactness and convexity we show the existence of an optimal element for optimal control problems involving a neutral differential equations with delays in the controls.

Authors

A Nachaoui,T Shavadze

Journal

Semin. I. Vekua Inst. Appl. Math. Rep.

Published Date

2021

### AN ANALYTICAL SOLUTION FOR THE NONLINEAR INVERSE CAUCHY PROBLEM

This paper discusses the recovering of both Dirichlet and Neumann data on some part of the domain boundary, starting from the knowledge of these data on another part of the boundary for a family of quasi-linear inverse problems. The nonlinear problem is reduced to a linear Cauchy problem for the Laplace equation coupled with a sequence of nonlinear scalar equations. We solve the linear problem using a closed-form regularization analytical solution. Various numerical examples and effects of added small perturbations into the input data are investigated. The numerical results show that the method produces a stable reasonably approximate solution.

Authors

Abdeljalil Nachaoui,Hero W. Salih

Journal

Advanced Mathematical Models & Applications

Published Date

2021/12/27

### An efficient evolutionary algorithm for a shape optimization problem

A shape optimization formulation connected with a free boundary heat transfer welding problem is considered. Based on piecewise finite elements discretization, the associated nonlinear problem is presented. To solve this problem, some reliable and robust methods are developed. Namely, a gradient-based method, which is the classical approach for this kind of problems, and an efficient evolutionary algorithm are presented. The comparative results demonstrate that both algorithms converge reliably to the same optimum. However, depending on the nature of the problem, the number of design variables, and the degree of convergence, the evolutionary algorithm requires from 5 to 40 times as many expansive objective function evaluations as the gradient-based algorithm. To reduce the time complexity of the evolutionary algorithm a variant enhanced by fuzzy logic controllers and performed with a parallel solver …

Authors

M Nachaoui,A Chakib,A Nachaoui

Journal

Applied and Computational Mathematics

Published Date

2020/1/1

### An alternating procedure with dynamic relaxation for Cauchy problems governed by the modified Helmholtz equation

In this paper, two relaxation algorithms on the Dirichlet Neumann boundary condition, for solving the Cauchy problem governed to the Modified Helmholtz equation are presented and compared to the classical alternating iterative algorithm. The numerical results obtained using our relaxed algorithm and the finite element approximation show the numerical stability, consistency and convergence of these algorithms. This confirms the efficiency of the proposed methods.

Authors

Karzan A Berdawood,Abdeljalil Nachaoui,Rostam Saeed,Mourad Nachaoui,Fatima Aboud

Journal

Advanced Mathematical Models & Applications

Published Date

2020/1/1

### On a numerical shape optimization approach for a class of free boundary problems

This paper is devoted to a numerical method for the approximation of a class of free boundary problems of Bernoulli’s type, reformulated as optimal shape design problems with appropriate shape functionals. We show the existence of the shape derivative of the cost functional on a class of admissible domains and compute its shape derivative by using the formula proposed in Boulkhemair (SIAM J Control Optim 55(1):156–171, 2017) and Boulkhemair and Chakib (J Convex Anal 21(1):67–87, 2014), that is, by means of support functions. On the numerical level, this allows us to avoid the tedious computations of the method based on vector fields. A gradient method combined with a boundary element method is performed for the approximation of this problem, in order to overcome the re-meshing task required by the finite element method. Finally, we present some numerical results and simulations concerning …

Authors

Abdesslem Boulkhemair,Abdelkrim Chakib,Abdeljalil Nachaoui,Agaddin A Niftiyev,Azeddine Sadik

Journal

Computational Optimization and Applications

Published Date

2020/11

### Computing general form of the focal value and Lyapunov function for the lopsiderd system in degree eight

In this paper, Concerned with planer autonomous system lopsided system of degree eight. We find the general form of all the focal values ηk (k is even and k≥ 2) and the Lyapunov function V (x, y) for the lopsided system degree eight. As the type for find the maximum number of limit cycles which can be bifurcate out of the origin and the necessary and sufficient conditions for the existence of center we need to compute the focal values η2k+ 2, the Lyapunov quantities L (k) and Lyapunov function V (x, y).

Authors

Hero W Salih,Abdeljalil Nachaoui

Journal

Advanced Mathematical Models & Applications

Published Date

2020/1/1

### The local representation formula of solution for the perturbed controlled differential equation with delay and discontinuous initial condition

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the delay parameter, the initial vector, the initial and control functions are detected.

Authors

Abdeljalil Nachaoui,T Shavadze,T Tadumadze

Journal

Mathematics

Published Date

2020/10/20

### Single-rank quasi-Newton methods for the solution of nonlinear semiconductor equations

This paper presents some of the author’s experimental results in applying a family of iterative methods, the family of EN-like methods Eirola & Nevanlinna (1989), to equations obtained from the discretization of the nonlinear two dimentional Poisson equation occuring in semiconductor device modelling. It is shown that these iterative methods are efficient both in computation times and in storage requirements in comparison with other known methods.

Authors

Fatima Aboud,Abdeljalil Nachaoui

Journal

Adv. Math. Models Appl

Published Date

2020/1/1

### Multiscale computational method for nonlinear heat transmission problem in periodic porous media

This paper deals with multiscale analysis, by using the correctors, of a nonlinear heat transmission problem in a periodic microscopic structure with multiple components. The occurring nonlinearity is related to the flux condition at the interface between the two parts of the medium. In this work, we present first the multiscale asymptotic expansion of the solution for this kind of problems and the strong convergence of the asymptotic expansion to the solution of the multiscale model. Then, we introduce a numerical algorithm based on the multiscale method for solving this problem. Finally, in order to confirm the efficiency of the proposed algorithm, some numerical results obtained through finite element approximations are presented.

Authors

A Chakib,A Hadri,A Nachaoui,M Nachaoui

Journal

Applied Numerical Mathematics

Published Date

2020/4/1

### Effects of the initial moment and several delays perturbations in the variation formulas for a solution of a functional differential equation with the continuous initial condition

For the nonlinear functional differential equation with several constant delays, the variation formulas for its solution are proved, in which the effects of perturbations of delays and the initial moment are detected.

Authors

Phridon Dvalishvili,Abdeljalil Nachaoui,Tamaz Tadumadze

Journal

Georgian Mathematical Journal

Published Date

2020/3/1

## abdeljalil nachaoui FAQs

### What is abdeljalil nachaoui's h-index at Université de Nantes?

The h-index of abdeljalil nachaoui has been 15 since 2020 and 18 in total.

### What are abdeljalil nachaoui's top articles?

The articles with the titles of

On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition

An accelerated alternating iterative algorithm for data completion problems connected with Helmholtz equation

An hybrid finite element method for a quasi-variational inequality modeling a semiconductor

On the Optimization Problem of One Market Relation Containing the Delay Functional Differential Equation

An improved hybrid defuzzification method for fuzzy controllers

International Conference on Mathematics & Data Science International E-Conference on Differential Equations and Applications.

Polynomial Approximation of a Nonlinear Inverse Cauchy Problem

AN ITERATIVE METHOD FOR CAUCHY PROBLEMS SUBJECT TO THE CONVECTION-DIFFUSION EQUATION.

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are the top articles of abdeljalil nachaoui at Université de Nantes.

### What are abdeljalil nachaoui's research interests?

The research interests of abdeljalil nachaoui are: Inverse Problems, Shap Optimization, Computing in Mathematics Natural Science Engineering and Medicine, Nonlinear Analysis, Scie

### What is abdeljalil nachaoui's total number of citations?

abdeljalil nachaoui has 1,093 citations in total.

### What are the co-authors of abdeljalil nachaoui?

The co-authors of abdeljalil nachaoui are Tamaz Tadumadze, Nabil Nassif, Pridon Dvalishvili, Mudhafar Fattah Hama.