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312 Boutahar et al.g(x). x are the initial concentrations and the appropriate forcing parameters (for instancetemperature). HDMR expresses g(x) as an exact expansion through:g(x) = f 0 + ∑ i=ni=1 f i(x i ) + ∑ 1≤i
Reduction methods and uncertainty propagation 313f 0 can be calculated from N sets of input vector x s = (x s 1, x s 2..., x s n), randomly generated:f 0 ≈ 1 ∑ NN s=1 g(Xs ). The φ k (x i ) are orthogonal polynomial functions with zero meanand unit norm over K i =[0,1 ]. They can be easily computed. In most cases ([9]), takinginto account the third-order development (φ 1 , φ 2 , φ 3 ) provides a satisfactory descriptionof g(x). The coefficients c i kand cijklare constants and can be computed by a minimizationprocedure.Implementation of FEOM model: We have implemented the HDMR method ina chemical kinetics model. The resulting model, FEOM (Fully Equivalent OperationalModel) replaces the initial chemical solver. FEOM can be used with a time step δt thatcan be much higher than the standard stiff integration time step (of the initial model).The use of FEOM starts with the definition of the input variables (initial concentrations,boundary conditions, temperature, pressure....) and of the output variables (species concentrationsto be computed at time t + δt). Finally the evaluation is done by a simplereading of the tables (once at the beginning of the integration) and a summation of thevarious component functions of HDMR according to Equation (4).We have used this approach by replacing the initial stiff solver (a Rosenbrock method,[13]) by FEOM. The chemical mechanism was CBM IV. The results are shown in figure2 are prove the accuracy of the method. The speed-up is about 3.4. Deterministic equivalent modeling method (DEMM)The DEMM method is used in order to reduce the number of simulations neededfor computing the PDF (Probability Density Function) of the output g(x) on the basisof the PDF of the inputs x. It is based on the representation of the uncertain outputg(x) as a development in series of orthogonal polynomials of random variables ξ (after atransformation of input parameters x to standardized random variables ξ) in the followingform ([5]):g(x) = Y 0 + ∑ n+ ∑ n−1i=1+ ∑ n−1i=1+ ∑ n−2i=1i=1 Y (1)iH 1 (ξ i ) + ∑ ni=1 Y (2)i H 2 (ξ i )∑ nj=i+1 Y (1)ij H 1 (ξ i )H 1 (ξ j ) + ∑ ni=1 Y (3)∑ nj=i+1 Y (2)iji H 3 (ξ i )H 1 (ξ i )H 2 (ξ j ) + ∑ n−1 ∑ ni=1 j=i+1 Y (3)ij H 2 (ξ i )H 2 (ξ j )∑ n−1 ∑ nj=i+1 k=j+1 Y (1)ijk H 1(ξ i )H 1 (ξ j )H 1 (ξ k ) + ... (10)where ξ i is a standard random variable (typically a gaussian variable), H m (ξ i ) are theseries of orthogonal polynomials of Hermit of degree m. The coefficients Y 0 , Y (1)i , y (2)i ,y (3)i , Y (1)ij , y (2)ij , y(3) ij , Y (1)ijk,... are computed by running the model with a limited numberof appropriate input values. The choice of these input values is therefore crucial ([6]). Inour case, we have used the SRSM method (Stochastic Response Surface Method, ([6]).The idea is to choose these points according to the PDF of the input parameters. TheTAMTAM –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
Page 280 and 281: 262 Lamrini Uahabi et al.4. Attract
Page 282 and 283: 264 Lamrini Uahabi et al.l 0 = λ
Page 284 and 285: 266 Lamrini Uahabi et al.En conséq
Page 286 and 287: Numerical analysis for the problem
Page 288 and 289: 270 El-Kyal et al.d(u) = 1 2(∇u +
Page 290 and 291: 272 El-Kyal et al.Theorem 3.1 There
Page 292 and 293: 274 Marchand et al.1. IntroductionD
Page 294 and 295: 276 Marchand et al.On remarque en p
Page 296 and 297: 278 Marchand et al.dans la formulat
Page 298 and 299: 280 Mezali et al.1. Motivation et m
Page 300 and 301: 282 Mezali et al.s’annulant sur c
Page 302 and 303: 284 Mezali et al.Temps CPUTemps Ela
Page 304 and 305: R. Touihri & S. Ghnimi *Méthode de
Page 306 and 307: 288 Touihri et al.Les équations go
Page 308 and 309: 290 Touihri et al.Tol N It (Newt) t
Page 310 and 311: 292 Touihri et al.5. Bibliographie[
Page 313 and 314: Décomposition de domaine pour un m
Page 315 and 316: DDM pour les fractures 297et−→
Page 317 and 318: DDM pour les fractures 299dont l’
Page 319 and 320: Arlequin method: Practical impacts
Page 321 and 322: Arlequin method 303of the Arlequin
Page 323 and 324: Arlequin method 3052.2. Penalized A
Page 325 and 326: Arlequin method 307refinements of t
Page 327 and 328: Reduction methods and uncertaintypr
Page 329: Reduction methods and uncertainty p
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Page 335 and 336: Homogénéisation d’un problème
Page 337 and 338: Problème de conduction-rayonnement
Page 339 and 340: Problème de conduction-rayonnement
Page 341 and 342: Equation d’Hamilton-Jacobi 3231.
Page 343 and 344: Equation d’Hamilton-Jacobi 325qui
Page 345 and 346: 0Equation d’Hamilton-Jacobi 3272
Page 347 and 348: Détermination du nombre de région
Page 353 and 354: Simulation des courants de Foucault
Page 359 and 360: Une méthode d’accélération de
Page 367 and 368: Schéma SRNHS 3491. IntroductionUn
Page 369 and 370: Schéma SRNHS 3513. Application du
Page 371 and 372: Schéma SRNHS 3535. ConclusionLes r
Page 373 and 374: Smoothing and compressing surfaces
Page 379 and 380: Problème de convection en milieu p
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0
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Condensation de masse pour la méth
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Condensation de masse 367montre que
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Condensation de masse 369Le terme h
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Condensation de masse 371Aet Qile f
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VIIIModèles CinétiquesKinetic Mod
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376 Ben Abdallah et al.1. Introduct
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378 Ben Abdallah et al.where B ∓
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380 Ben Abdallah et al.ture that th
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382 Degond et al.1. IntroductionOn
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384 Degond et al.q φ s (x, t)/(|q|
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386 Degond et al.Enfin l’opérate
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Les métaheuristiques : application
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Les métaheuristiques 391simulé fu
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Les métaheuristiques 393Fig. 1 Dia
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Les métaheuristiques 395Fig.4 : R
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Prices after capacity addition in m
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Multi-user elastic demand communica
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Shape optimization 4051. Introducti
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Shape optimization 4072.1. Variatio
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Shape optimization 409(a)(b)(c)(d)F
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Problèmes d’optimisation en éco
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Assimilation de données pour l’e
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Écart à la Réciprocité et ident
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Identification de fissures planes 4
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Algorithme de Kohn et Vogelius 4331
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Algorithme de Kohn et Vogelius 435l
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Algorithme de Kohn et Vogelius 4375
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Résolution d’un problème de Cau
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Problème inverse géométrique 445
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Identification de fissures 4511. In
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−0.5 −0.4 −0.3 −0.2 −0.1
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Application de l’algorithme deNeu
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Complétion de données en élastic
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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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