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10 results on '"Boulkhemair, Abdesslam"'

5. On numerical study of constrained coupled shape optimization problems based on a new shape derivative method.

Author

Boulkhemair, Abdesslam, Chakib, Abdelkrim, and Sadik, Azeddine

Subjects
*STRUCTURAL optimization, *NEUMANN boundary conditions, *BOUNDARY value problems, *CONVEX domains, *BOUNDARY element methods, *CONSTRAINED optimization
Abstract

In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions, using a new formula of shape derivative on a family of convex domains. This allows us to avoid the disadvantages related to the classical shape derivative method using vectors field. Then the numerical discretization is performed using the dual reciprocity boundary element method in order to avert the remeshing task required for the finite element method. Finally, we give some numerical results, based on the gradient method, showing the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Published
2023
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7. Existence et effet régularisant pour des équations de Schrödinger non linéaires généralisées : le cas de l'intéraction quadratique

Author

Bienaimé, Pierre-Yves, Boulkhemair, Abdesslam, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)

Subjects
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract

We improve the result obtained by C. E. Kenig, G. Ponce and L. Vega, 1998, Inventionnes Math., on generalized nonlinear Schrödinger equations in the case where the interactions are quadratic. We establish the well-posedness of the Cauchy problem for such equations in weighted Sobolev spaces H s,σ (R n) for s > n/2 + 2 and σ > 1.; Nous améliorons le resultat obtenu par C. E. Kenig, G. Ponce and L. Vega, 1998, Inventionnes Math., sur les équations de Schrödinger non linéaires généralisées dans le cas où les interactions sont quadratiques. Nous démontrons le caractère bien posé de telles équations dans des espaces de Sobolev à poids H s,σ (R n) avec s > n/2 + 2 et σ > 1.

Published
2019

8. GEOMETRICAL VARIATIONS OF A STATE-CONSTRAINED FUNCTIONAL ON STAR-SHAPED DOMAINS.

Author

Boulkhemair, Abdesslam, Chakib, Abdelkrim, and Sadik, Azeddine

Subjects
NUMERICAL solutions to boundary value problems, GEOMETRY, DERIVATIVES (Mathematics), BOUNDARY value problems, MATHEMATICAL functions
Abstract

The aim of this paper is to compute the shape derivative of a volume cost functional subject to a Dirich- let boundary value state constraint problem using the shape derivative formula introduced in (Boulkhemair et al., 2020), which concerns star-shaped domains. This allows us to express the shape derivative by means of support functions of convex domains. Then we give a simple algorithm for the numerical resolution of this problem. [ABSTRACT FROM AUTHOR]

Published
2021

10. On the Feffermann-Phong inequality

Author

Boulkhemair, Abdesslam, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)

Subjects
MSC : 35, t-quantization, Feffermann-Phong inequality, Mathematics::Classical Analysis and ODEs, Garding inequality, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], pseudodifferential operators, Weyl quantization, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
Abstract

We show that the number of derivatives of the symbol needed to establish the Fefferman-Phong inequality is bounded by $n+4+\epsilon$ improving thus the bound $2n+4+\epsilon$ obtained by N. Lerner and Y. Morimoto. We also give an abstract result. We even show that in the case of classical symbols, that is $S^2_{1,0}$, the number of needed derivatives is bounded by ${n\over2}+4+\epsilon$.

Published
2008

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