Approximation and numerical realization of an optimal design welding problem

Chakib, Abdelkrim; Nachaoui, Abdeljalil; Nachaoui, Mourad

doi:10.1002/num.21767

Cited by 6 publications

(2 citation statements)

References 9 publications

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“…It is essentially a searching method based on the Darwinian principles of biological evolution that explains the adaptive change of species by the principle of natural selection, which favors those species for survival and further evolution that are best adapted to their environmental conditions. It has been successfully applied to various optimization problems [6][7][8]19].…”

Section: Numerical Algorithmmentioning

confidence: 99%

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

Nachaoui

Tadumadze

2022

RAIRO-Oper. Res.

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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.

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Section: Numerical Algorithmmentioning

confidence: 99%

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

Nachaoui

Tadumadze

2022

RAIRO-Oper. Res.

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“…For details concerning the differentiation with respect to the domain( see [30,28,29] and the book [23]). We can also use the techniques developed in [13,14,15] .…”

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confidence: 99%

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

Afraites¹

2022

DCDS-S

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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 contained in a larger bounded domain Ω via boundary measurements on ∂Ω. In order to solve this problem, we use the coupled complex boundary method (CCBM), originaly proposed in [16]. The new method transforms our inverse problem to a complex boundary problem with a complex Robin boundary condition coupling the Dirichlet and Neumann boundary data. Then, we optimize the shape cost function constructed by the imaginary part of the solution in the whole domain in order to determine the inclusion ω. Thanks to the tools of shape optimization, we prove the existence of the shape derivative of the complex state with respect to the domain ω. We characterize the gradient of the cost functional in order to make a numerical resolution. We then investigate the stability of the optimization problem and explain why this inverse problem is severely ill-posed by proving compactness of the Hessian of cost functional at the critical shape. Finally, some numerical results are presented and compared with classical methods.

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