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

M Nachaoui, A Nachaoui, T Tadumadze - RAIRO-Operations Research, 2022 - rairo-ro.org
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 the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems

JFT Rabago - arXiv preprint arXiv:2205.12620, 2022 - arxiv.org
We expose here a novel application of the so-called coupled complex boundary method--
first put forward by Cheng et al.(2014) to deal with inverse source problems--in the …

A new coupled complex boundary method (CCBM) for an inverse obstacle problem.

L Afraites - … & Continuous Dynamical Systems-Series S, 2022 - search.ebscohost.com
In the present work we introduce and study a new method for solving the inverse obstacle
problem. It consists in identifying a perfectly conducting inclusion ω ω contained in a larger …

Shape optimization methods for detecting an unknown boundary with the robin condition by a single boundary measurement

L Afraites, JFT Rabago - Discrete and Continuous Dynamical …, 2025 - aimsciences.org
We consider the problem of identifying an unknown portion Γ of the boundary of a d-
dimensional (d= 2, 3) body Ω by a pair of Cauchy data (f, g) on the accessible part Σ of the …

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

A Nachaoui, M Nachaoui, T Tadumadze - The International Conference …, 2022 - Springer
Noninvasive measurement of neurocortical potentials using electroencephalography (EEG)
is a valuable tool in neuroscience research and clinical practice. However, accurate …

Solving geometric inverse problems with a polynomial based meshless method

A Nachaoui, F Aboud - The International Conference on New Trends in …, 2022 - Springer
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 …

Coupled complex boundary method for a geometric inverse source problem

L Afraites, C Masnaoui, M Nachaoui - RAIRO-Operations Research, 2022 - rairo-ro.org
This work deals with a geometric inverse source problem. It consists in recovering the
characteristic function of an unknown inclusion based on boundary measurements. We …

Shape reconstruction for advection-diffusion problems by shape optimization techniques: The case of constant velocity

E Cherrat, L Afraites, JFT Rabago - Discrete and Continuous …, 2025 - aimsciences.org
We consider the inverse problem of identifying an unknown portion of the boundary of a two-
dimensional body Ω by using a pair of Cauchy data (f, g) on the accessible portion Σ …

Boundary shape reconstruction with Robin condition: existence result, stability analysis, and inversion via multiple measurements

L Afraites, JFT Rabago - Computational and Applied Mathematics, 2024 - Springer
This study revisits the problem of identifying the unknown interior Robin boundary of a
connected domain using Cauchy data from the exterior region of a harmonic function. It …

Detecting immersed obstacle in Stokes fluid flow using the coupled complex boundary method

JFT Rabago, L Afraites, H Notsu - arXiv preprint arXiv:2403.11819, 2024 - arxiv.org
A non-conventional shape optimization approach is introduced to address the identification
of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded …