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408 Maatoug3. Numerical resultsHere, we limit ourselves to the two dimensional case. We consider a cavity with oneinlet Γ in and three outlets Γ i out, i = 1, 2, 3, having the same section. We assume that theflow satisfies the following boundary conditions:• On the inlet Γ in we define the normal component of the stress tensor : σ(u).n =φ on Γ in , where σ(u) = ν(∇u + ∇u T ) − pI and I is the 2 × 2 identity matrix.• On the outlets, we use a free surface boundary condition : σ(u).n = 0 on ∪ 3 i=1 Γi out.The cost function measuring the outflow rate is given by3∑∫J(u) = |u.n| ds.i=1Our implementation is based on the following optimization algorithm. We apply aniterative process to build a sequence of geometries (Ω k ) k≥0 with Ω 0 = Ω. At the k-thiteration, the topological gradient is denoted by g k , and the new geometry Ω k+1 is definedby a level set curve of g k .The algorithm :• Initialization: choose Ω 0 = Ω, and set k = 0.• Repeat until g k ≥ 0 in Ω k :− solve (2) and its associated adjoint problem in Ω k ,− compute the topological sensitivity g k ,− set Ω k+1 = {x ∈ Ω k , g k (x) ≥ c k }, where c k is chosen in such a way that the costfunction decreases as most as possible,− k ←− k + 1.This algorithm can be seen as a descent method where the descent direction is determinedby the topological sensitivity g k and the step length is given by the volume variationmeas(Ω k \Ω k+1 ).In the above algorithm, the direct and the adjoint problems are discretized by a finite elementmethod using a Reynold number Re = 100. The computation of the approximatesolution is achieved by Uzawa algorithm.The results are presented in figures 2 and 3. We illustrate the topological gradient and thegeometries obtained during the optimization process in figures 2. The topological gradientcorresponding to the initial geometry is shown in Figure 2-(a). The shape obtainedafter optimization is presented in figure 2-(d). In figure 3, we present the velocity fieldcomputed in the geometry during the optimization process. The optimal velocity is givenin figure 3-(d).Γ i outTAMTAM –Tunis– 2005
Shape optimization 409(a)(b)(c)(d)Figure 2. The topological gradient describing the geometry during optimization process.4. ReferencesG. Allaire, F. Jouve, A-M. Toader. Structural optimization using sensitivity analysis and a level-setmethod. J. Comput. Phys. 194 (2004), no. 1, 363-393.M. Bendsoe. Optimal topology design of continuum structure: an introduction. Technical report,Departement of mathematics, Technical University of Denmark, DK2800 Lyngby, Denmark,1996.G. Buttazzo and G. Dal Maso. Shape optimization for Dirichlet problems: Relaxed formulationand optimality conditions. Appl. Math. Optim. 23, 17-49, 1991.S. Garreau, Ph. Guillaume, M. Masmoudi. The topological asymptotic for pde systems: the elasticitycase, SIAM J. Control Optim., 39, no.4(2001), 1756-1778.Ph. Guillaume and K.Sid Idris. Topological sensitivity and shape optimization for the Stokes equations.SIAM J. Control Optim. 43(1), 1-31, 2004.TAMTAM –Tunis– 2005
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PréfaceOrganiser la seconde éditi
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Comité d’organisationMohamed Abd
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SOMMAIRE / CONTENTSI Conférences I
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Equilibre dans un système dynamiqu
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Arlequin method: Practical impacts
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Application de la méthode de Gauss
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Conférences InvitéesInvited Prese
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4 Amara et al.1. IntroductionWe are
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6 Amara et al.2.2. The nonlinear Na
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8 Amara et al.4. Numerical resultsW
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10 Auger et al.1. Introduction :Dan
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12 Auger et al.La condition de stab
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14 Auger et al.3.1. Taux de migrati
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16 Auger et al.L’équilibre rapid
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18 Auger et al.[7] BRAVO DE LA PARR
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Quelques aspects mathématiques etn
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22 El Alaoui Talibi M.- Modèle d
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24 El Alaoui Talibi M.[3] M. Chamba
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26 Habbal1. IntroductionAngiogenesi
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28 HabbalThe pressure drop denoted
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30 Habbaltheorem 1 There exists a N
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32 HabbalFigure 2. Second Nash loop
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34 Hauray et al.1. IntroductionWe a
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36 Hauray et al.minimal time interv
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38 Hauray et al.From this last theo
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Approximation de l’opérateur d
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42 LemrabetLorsque δ → 0, l’é
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44 Lemrabetavec[∆ ∗ (δ)c = [I
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46 Lemrabet6. Bibliographie[1] N. B
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48 Jaafar-Belaid et al.1. Introduct
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50 Jaafar-Belaid et al.where f(ρ)
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52 Jaafar-Belaid et al.202040406060
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IIContrôleControl55
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58 Arfaoui1. IntroductionCe travail
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60 ArfaouiLe système adjoint assoc
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62 Arfaoui[3] H. ARFAOUI , « Comma
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64 Benzekri et al.1. Global control
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66 Benzekri et al.ẏ = ∂H∂x =
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0 1 2 3 4 5 668 Benzekri et al.32.5
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70 Akian et al.1. IntroductionWe co
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72 Akian et al.We prove that v t+δ
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.74 Akian et al.0.0−1.0Exact solu
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76 Bokanowski et al.1. General fram
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78 Bokanowski et al.One interesting
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80 Bokanowski et al.4. Numerical ex
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Sur les problèmes de contrôle opt
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84 Metouileur lorsque u est dans L
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86 MetouiThéorème 2 Soit ū ε le
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88 Metoui[5] L.S. HOU, S.S. RAVINDR
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Système d’information intégré
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Gestion et modélisation des ressou
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Random perturbations of reduced gra
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Global Optimization of Water Resour
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Global Optimization of Water Resour
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IVEquations DifférentiellesDiffere
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114 B. Abdelkader1. IntroductionTel
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116 B. AbdelkaderNotons que les con
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118 B. AbdelkaderAlors pour tout X
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120 Bouzahir1. IntroductionWe consi
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122 Bouzahirwhere the linear operat
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Goursat boundary value problem forh
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126 A. Guezane-Lakoud et al.3. Func
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128 A. Guezane-Lakoud et al.5. Exis
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ACP neuronale : application à l’
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132 Chitroubl’approximation de la
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134 Chitroubcompression égal à 3.
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136 Chitroub[4] J. P. Nougier, Mét
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138 Ferchichi et al.1. Introduction
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140 Ferchichi et al.soit T −1 = (
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142 Ferchichi et al.[4] G.I. BISCHI
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144 Hafidi1. IntroductionOn étudie
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146 Hafidia ) ∫ Ωpdx → +∞ qu
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148 HafidiLEMME 3.2. On a lim R(θ
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150 Lefebvre1. IntroductionSoit (X
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152 LefebvreOn peut aussi écrire q
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154 Lefebvre5. BibliographieD.R. Co
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156 Meskine1. IntroductionDans le p
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158 Meskinefaibles σ( ∏ L M ,
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160 Meskine[12] E. YA. KHRUSLOV, L.
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162 K. Saoudi1. IntroductionL’ét
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164 K. Saoudice qui montre que la s
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166 K. Saoudieton aboutit au résul
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168 K. Saoudietc 1 + c 2 = 1 ∫(u
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170 K. SaoudiRemarque 3.1. Du lemme
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172 K. Saoudiet∫v(t, x) dxΩest c
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VEstimation d’ErreursError Estima
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178 Achchab et al.1. IntroductionDu
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180 Achchab et al.such that}Xh 2 ={
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182 Achchab et al.[2] B.ACHCHAB, M.
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184 Alla et al.1. IntroductionLes e
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186 Alla et al.3. Position du probl
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IsoValue-0.00070533-0.000604452-0.0
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190 Achchab et al.1. IntroductionLe
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192 Achchab et al.où T hi/2 est le
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IsoValue0.000933570.002800710.00840
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196 El Dabaghi et al.1. Motivation
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198 El Dabaghi et al.0 ≤ λ i ≤
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200 El Dabaghi et al.Figure 4. Mail
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Residual error estimators for the t
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204 Kharrat et al.The step (3) need
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206 Kharrat et al.following estimat
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VIMécanique des FluidesFluid Mecha
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212 Abdelwahed et al.1. Introductio
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214 Abdelwahed et al.Ainsi, suivre
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216 Abdelwahed et al.Figure 3. Isov
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Procédure spectrale avec diagonali
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220 El Guarmah et al.où Ra et P r
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222 El Guarmah et al.M 10 20 25 35
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Simulation de l’onde de crue via
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226 El Dabaghi et al.de R 2 , de fr
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228 El Dabaghi et al.INRIA-MODULEFm
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INRIA-MODULEF230 El Dabaghi et al.I
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232 Amoura et al.1. IntroductionFor
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234 Amoura et al.where u = rot r ψ
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236 Amoura et al.CURRENT FUNCTION5
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238 Frih et al.1. IntroductionLa mo
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240 Frih et al.et dans la fracture,
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242 Frih et al.6. Bibliographie[1]
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244 Hasnaoui et al.1. IntroductionL
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246 Hasnaoui et al.On obtient alors
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248 Hasnaoui et al.5. Conclusion et
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250 Hernane-Boukari1. IntroductionW
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252 Hernane-Boukarianda 3 =−11 +
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254 Kloucha et al.1. Motivation et
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256 Kloucha et al.Si le domaine Λ
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INRIA-MODULEF0INRIA-MODULEF.250INRI
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Dimensions fractales : attracteurs
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262 Lamrini Uahabi et al.4. Attract
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264 Lamrini Uahabi et al.l 0 = λ
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266 Lamrini Uahabi et al.En conséq
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Numerical analysis for the problem
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270 El-Kyal et al.d(u) = 1 2(∇u +
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272 El-Kyal et al.Theorem 3.1 There
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274 Marchand et al.1. IntroductionD
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276 Marchand et al.On remarque en p
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278 Marchand et al.dans la formulat
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280 Mezali et al.1. Motivation et m
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282 Mezali et al.s’annulant sur c
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284 Mezali et al.Temps CPUTemps Ela
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R. Touihri & S. Ghnimi *Méthode de
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288 Touihri et al.Les équations go
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290 Touihri et al.Tol N It (Newt) t
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292 Touihri et al.5. Bibliographie[
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Décomposition de domaine pour un m
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DDM pour les fractures 297et−→
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DDM pour les fractures 299dont l’
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Arlequin method: Practical impacts
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Arlequin method 303of the Arlequin
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Arlequin method 3052.2. Penalized A
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Arlequin method 307refinements of t
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Reduction methods and uncertaintypr
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Reduction methods and uncertainty p
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Reduction methods and uncertainty p
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0.00e+00 1.00e−11 2.00e−11 3.00
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Homogénéisation d’un problème
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Problème de conduction-rayonnement
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Problème de conduction-rayonnement
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Equation d’Hamilton-Jacobi 3231.
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Equation d’Hamilton-Jacobi 325qui
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0Equation d’Hamilton-Jacobi 3272
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Détermination du nombre de région
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Simulation des courants de Foucault
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Une méthode d’accélération de
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Schéma SRNHS 3491. IntroductionUn
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Schéma SRNHS 3513. Application du
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Schéma SRNHS 3535. ConclusionLes r
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Smoothing and compressing surfaces
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Page 387 and 388: Condensation de masse 369Le terme h
Page 389 and 390: Condensation de masse 371Aet Qile f
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Page 394 and 395: 376 Ben Abdallah et al.1. Introduct
Page 396 and 397: 378 Ben Abdallah et al.where B ∓
Page 398 and 399: 380 Ben Abdallah et al.ture that th
Page 400 and 401: 382 Degond et al.1. IntroductionOn
Page 402 and 403: 384 Degond et al.q φ s (x, t)/(|q|
Page 404 and 405: 386 Degond et al.Enfin l’opérate
Page 407 and 408: Les métaheuristiques : application
Page 409 and 410: Les métaheuristiques 391simulé fu
Page 411 and 412: Les métaheuristiques 393Fig. 1 Dia
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Page 415 and 416: Prices after capacity addition in m
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Page 425: Shape optimization 4072.1. Variatio
Page 429 and 430: Problèmes d’optimisation en éco
Page 431 and 432: Problèmes d’optimisation en éco
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Page 437 and 438: Assimilation de données pour l’e
Page 443 and 444: Écart à la Réciprocité et ident
Page 445 and 446: Identification de fissures planes 4
Page 451 and 452: Algorithme de Kohn et Vogelius 4331
Page 453 and 454: Algorithme de Kohn et Vogelius 435l
Page 455 and 456: Algorithme de Kohn et Vogelius 4375
Page 457 and 458: Résolution d’un problème de Cau
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Page 473 and 474: Application de l’algorithme deNeu
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Complétion de données en élastic
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Analytic extensions on an annulus:a
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Analytic extensions on an annulus 4
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Analytic extensions on an annulus 4
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−1 −0.8 −0.6 −0.4 −0.2 0
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Cauchy problem for Laplace’s equa
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Modélisation asymptotique des onde
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Ondes de relief 479 uuuv 1 1 pu v
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Ondes de relief 481( )ˆeiZw( C e D
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Ondes de relief 4836. Bibliographie
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Régularisation pour l’aéroacous
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Miroir à retournement temporel 491
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Vibro-acoustique instationnaire 497
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Vibro-acoustique instationnaire 499
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Ondes dans les milieux poroélastiq
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The implicitly restarted Arnoldi me
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¨§¨ §IRAM method 509To overcome
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IRAM method 511The application of t
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XIIScience du VivantLife Science513
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516 Achchab1. IntroductionDans la m
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518 AchchabNous montrons dans le pa
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520 Achchab5. Bibliographie[1 ] AIE
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522 Derbel et al.1. IntroductionLa
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524 Derbel et al.On se propose de d
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A Stochastic partial differential e
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528 El Saadidiffusion process to a
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530 El Saadiwhere δ Xi(t) is the D
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532 El Saadi5. References[1] A. L.
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534 Ben Miled et al.1. Introduction
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536 Ben Miled et al.nature de l’e
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538 Ben Miled et al.Ensuite on étu
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Optimal spatial distribution of a b
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542 Mchich et al.at time t. The com
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544 Mchich et al.3∑where r = r i
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XIIIStructureStructure547
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550 Ayadi1. IntroductionConsider a
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552 AyadiFor all 0 ≤ p ≤ i, P p
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554 AyadiFigure 3. The curves above
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Analyse mathématique et numérique
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558 Chamekh et al.2. Modèle de tig
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560 Chamekh et al.Γ sr(s)r(σ)Figu
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Modélisation de l’effet dynamiqu
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564 RahmaniI 2 étant l’identité
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566 Rahmani• ( u 1δ1∫+ ,0u 1δ
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Résolution d’un systéme d’ela
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570 Saidoù u vérifie :n∑n∑j=1
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572 SaidEn effet :∣ u(y, s) 1+α
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Régularisation d’un problème d
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576 Achchab et al.On définit : F +
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578 Achchab et al.3. Estimation a p
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Modélisation d’un pieuR. Aboulai
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582 Aboulaich et al.Figure 1. Struc
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584 Aboulaich et al.5. Résultats n
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XIVThéorie des GraphesGraph Theory
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590 Hlaoui1. IntroductionMore and m
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592 Hlaoui3. The New Graph Represen
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594 Hlaoui1 1 2 3 4 1 1 3 411 421 4
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596 M. Nekri et al.1. IntroductionL
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598 M. Nekri et al.proposés. Ces m
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600 M. Nekri et al.cycle de longueu
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TAMTAM -Tunis- 2005 602
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El Guarmah, M., 218El Kacimi, A., 2
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