152 6.2.1 Résultats numériques pour la méthode numérique associée au premier modèle approché, p.153 ,
Topics in computational wave propagation : direct and inverse problems. Lecture notes in computational science and engineering, 2003. ,
DOI : 10.1007/978-3-642-55483-4
Analyse numérique et optimisation : une introduction à la modélisation mathématique et à la simulation numérique, 2005. ,
Direct Elastic Imaging of a Small Inclusion, SIAM Journal on Imaging Sciences, vol.1, issue.2, pp.169-187, 2008. ,
DOI : 10.1137/070696076
URL : https://hal.archives-ouvertes.fr/hal-00654620
Polarization tensors and their applications, Journal of Physics: Conference Series, vol.12, issue.1, p.13, 2005. ,
DOI : 10.1088/1742-6596/12/1/002
Non-conforming high order approximations of the elastodynamics equation, Computer Methods in Applied Mechanics and Engineering, vol.209, issue.212, pp.209-212212, 2012. ,
DOI : 10.1016/j.cma.2011.11.004
Discretization by finite elements of a model parameter dependent problem, Numerische Mathematik, vol.5, issue.41, pp.405-421, 1981. ,
DOI : 10.1007/BF01400318
Numerical solution to the time-dependent Maxwell equations in axisymmetric singular domains: the singular complement method, Journal of Computational Physics, vol.191, issue.1, pp.147-176, 2003. ,
DOI : 10.1016/S0021-9991(03)00309-7
URL : https://hal.archives-ouvertes.fr/hal-00989621
On compact embedding theorems in weighted Sobolev spaces, Czechoslovak Math. J, vol.29, issue.1044, pp.635-648, 1979. ,
Locking effects in the finite element approximation of elasticity problems, Numerische Mathematik, vol.7, issue.1, pp.439-463, 1992. ,
DOI : 10.1007/BF01396238
On Locking and Robustness in the Finite Element Method, SIAM Journal on Numerical Analysis, vol.29, issue.5, pp.1261-1293, 1992. ,
DOI : 10.1137/0729075
cost functionals, Inverse Problems, vol.29, issue.7, p.75012, 2013. ,
DOI : 10.1088/0266-5611/29/7/075012
URL : https://hal.archives-ouvertes.fr/hal-01323305
Scattering of a scalar time-harmonic wave by N small spheres by the method of matched asymptotic expansions, Numerical Analysis and Applications, vol.5, issue.2, pp.116-123, 2012. ,
DOI : 10.1134/S1995423912020036
URL : https://hal.archives-ouvertes.fr/hal-00760457
Approximation by Multipoles of the Multiple Acoustic Scattering by Small Obstacles in Three Dimensions and Application to the Foldy Theory of Isotropic Scattering, Archive for Rational Mechanics and Analysis, vol.55, issue.12, 2014. ,
DOI : 10.1007/s00205-015-0915-5
URL : https://hal.archives-ouvertes.fr/hal-01258966
The effect of a thin coating on the scattering of a timeharmonicwave for the helmholtz equation, SIAM Journal of Applied Mathematics, vol.6, issue.5, pp.1664-1693, 1996. ,
Asymptotic analysis of the scattering of a timeharmonicwave by a perfectly conductingmetal coated with a thin dielectric shell, Asymptotic Analysis, vol.57, pp.199-227, 2008. ,
A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, vol.114, issue.2, pp.185-200, 1994. ,
DOI : 10.1006/jcph.1994.1159
INTERACTIONS BETWEEN MODERATELY CLOSE INCLUSIONS FOR THE LAPLACE EQUATION, Mathematical Models and Methods in Applied Sciences, vol.19, issue.10, 2009. ,
DOI : 10.1142/S021820250900398X
URL : https://hal.archives-ouvertes.fr/hal-00455312
On moderately close inclusions for the Laplace equation, Comptes Rendus Mathematique, vol.345, issue.11, pp.345609-614, 2007. ,
DOI : 10.1016/j.crma.2007.10.037
Convex Optimization, 2004. ,
Analyse fonctionnelle. Théorie et applications, 1983. ,
On the analysis of B??renger's Perfectly Matched Layers for Maxwell's equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.1, pp.87-119 ,
DOI : 10.1051/m2an:2002004
Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition, ESAIM : M2AN, pp.377-398, 2009. ,
DOI : 10.1051/m2an:2008047
Perfectly matched layers in negative index metamaterials and plasmas, ESAIM: Proceedings and Surveys, vol.50, pp.113-132, 2015. ,
DOI : 10.1051/proc/201550006
Numerical computation of approximate generalized polarization tensors, Applicable Analysis, vol.144, issue.6, pp.1189-1203, 2012. ,
DOI : 10.1017/CBO9780511613357
URL : https://hal.archives-ouvertes.fr/hal-00770191
Multiple scattering of acoustic waves by small sound-soft obstacles in two dimensions: Mathematical justification of the Foldy???Lax model, Wave Motion, vol.50, issue.1, pp.18-28, 2013. ,
DOI : 10.1016/j.wavemoti.2012.06.001
URL : https://hal.archives-ouvertes.fr/hal-00849557
Introduction and study of fourth order theta schemes for linear wave equations, Journal of Computational and Applied Mathematics, vol.245, pp.194-212, 2013. ,
DOI : 10.1016/j.cam.2012.12.023
URL : https://hal.archives-ouvertes.fr/hal-01051803
Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth, Computer Methods in Applied Mechanics and Engineering, vol.209, issue.212, pp.250-265, 2012. ,
DOI : 10.1016/j.cma.2011.08.013
Numerical solution of Maxwell's equations in axisymmetric domains with the Fourier singular complement method, Differ. Equ. Appl, vol.3, issue.1, pp.113-155, 2011. ,
The finite element method for elliptic problems, Studies in Mathematics and its Applications, 1978. ,
Analyse asymptotique et numérique de la diffraction d'ondes par des fils minces, 2008. ,
Augmented Galerkin schemes for the numerical solution of scattering by small obstacles, Numerische Mathematik, vol.17, issue.12, pp.243-268, 2010. ,
DOI : 10.1007/s00211-010-0301-z
URL : https://hal.archives-ouvertes.fr/hal-00976812
Higher-order numerical methods for transient wave equations, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-01166961
Higher-Order Numerical Methods for Transient Wave Equations. Lecture Notes in Economic and Mathematical Systems, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-01166961
MIXED FINITE ELEMENTS WITH MASS-LUMPING FOR THE TRANSIENT WAVE EQUATION, Journal of Computational Acoustics, vol.08, issue.01, pp.171-188, 2000. ,
DOI : 10.1142/S0218396X0000011X
Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation, SIAM Journal on Numerical Analysis, vol.38, issue.6, pp.2047-2078, 2001. ,
DOI : 10.1137/S0036142997329554
URL : https://hal.archives-ouvertes.fr/hal-01010373
A conservative space-time mesh refinement method for the 1-d wave equation. part i : Construction, Numerische Mathematik, vol.95, issue.2, pp.197-221, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00989055
Inverse Acoustic and Electromagnetic Scattering Theory, Number 93 in Series of Applied Mathematics, 1992. ,
ON THE WELL-POSEDNESS, STABILITY AND ACCURACY OF AN ASYMPTOTIC MODEL FOR THIN PERIODIC INTERFACES IN ELECTROMAGNETIC SCATTERING PROBLEMS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.13, pp.12-2013 ,
DOI : 10.1142/S021820251350036X
URL : https://hal.archives-ouvertes.fr/hal-00682357
Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.1985-2014, 2009. ,
DOI : 10.1137/070709414
URL : https://hal.archives-ouvertes.fr/inria-00193160
Green's Functions with Applications, Applied Mathematics, vol.38, 2001. ,
DOI : 10.1201/9781420034790
Partial Differential Equations. Graduate studies in mathematics, 2010. ,
Mellin transforms and asymptotics: Harmonic sums, Theoretical Computer Science, vol.144, issue.1-2, pp.3-58, 1995. ,
DOI : 10.1016/0304-3975(95)00002-E
URL : https://hal.archives-ouvertes.fr/inria-00074307
The Multiple Scattering of Waves. I. General Theory of Isotropic Scattering by Randomly Distributed Scatterers, Physical Review, vol.67, issue.3-4, pp.107-119, 1945. ,
DOI : 10.1103/PhysRev.67.107
Adaptive quadrature?revisited, Bit Numerical Mathematics, vol.40, issue.1, pp.84-101, 2000. ,
DOI : 10.1023/A:1022318402393
On the application of mixed finite element methods to the wave equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.22, issue.2, pp.243-250, 1988. ,
DOI : 10.1051/m2an/1988220202431
Finite element methods for Navier-Stokes equations Theory and algorithms, of Springer Series in Computational Mathematics, 1986. ,
Etude de quelques problèmes aux limites extérieurs et résolution par équations intégrales, Thèse de doctorat dirigée par Raviart, Pierre- Arnaud Sciences, 1987. ,
A fictitious domain method for Dirichlet problem and applications, Computer Methods in Applied Mechanics and Engineering, vol.111, issue.3-4, pp.283-303, 1994. ,
DOI : 10.1016/0045-7825(94)90135-X
Polarization tensors and effective properties of anisotropic composite materials, Journal of Differential Equations, vol.215, issue.2, pp.401-428, 2005. ,
DOI : 10.1016/j.jde.2004.09.010
Sur les problèmes aux dérivés partielles et leur signification physique, Princeton University Bulletin, vol.13, pp.49-52, 1902. ,
A finite element method enriched for wave propagation problems, Computers & Structures, vol.94, issue.95, pp.94-951, 2012. ,
DOI : 10.1016/j.compstruc.2012.01.001
URL : https://hal.archives-ouvertes.fr/hal-01403646
On L2-estimates for discrete-time galerkin approximation to second order hyperbolic equations, Mathematics and Computers in Simulation, vol.23, issue.2, pp.127-132, 1981. ,
DOI : 10.1016/0378-4754(81)90049-5
Generalized Foldy-Lax formulation, Journal of Computational Physics, vol.229, issue.12, pp.4544-4553, 2010. ,
DOI : 10.1016/j.jcp.2010.02.021
Modélisation mathématique et numérique de capteurs piézoélectriques, p.2012 ,
Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section, Applied Numerical Mathematics, vol.79, 2013. ,
DOI : 10.1016/j.apnum.2013.03.011
URL : https://hal.archives-ouvertes.fr/hal-00875811
A complete FE simulation tools for NDT inspections with piezoelectric transducers, Acoustics 2012, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00811151
Transformation de mellin et développements asymptotiques, Enseignement Mathématique, vol.25, p.285, 1979. ,
Analyse et approximation de modèles de propagation d'ondes, partie 1, 2001. ,
Construction and analysis of improved Kirchoff conditions for acoustic
wave propagation in a junction of thin slots, ESAIM: Proceedings, vol.25, issue.12, pp.44-67, 2008. ,
DOI : 10.1051/proc:082504
URL : https://hal.archives-ouvertes.fr/hal-00976404
Matching of asymptotic expansions for wave propagation in media with thin slots i : The asymptotic expansion. Multiscale Modeling and Simulation : A, SIAM Interdisciplinary Journal, vol.5, issue.1, pp.304-336, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00527588
Abstract, Advances in Applied Mathematics and Mechanics, vol.22, issue.01, pp.181-203, 2011. ,
DOI : 10.4208/aamm.10-m1018
Removing Small Features from Computational Domains, Journal of Computational Physics, vol.113, issue.1, pp.148-150, 1994. ,
DOI : 10.1006/jcph.1994.1124
Elliptic Boundary Value Problems in Domains with Point Singularities, Mathematical Surveys and Monographs . AMS, vol.52, 1997. ,
DOI : 10.1090/surv/052
Some applications of weighted Sobolev spaces, 1987. ,
Stability of <mml:math altimg="si44.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>??</mml:mi></mml:math>-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments, Applied Mathematics Letters, vol.23, issue.2, pp.198-206, 2010. ,
DOI : 10.1016/j.aml.2009.09.012
Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, 2000. ,
Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, 2000. ,
Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Volume I, volume 111 of Operator theory, advances and applications, 2000. ,
Cramming More Components Onto Integrated Circuits, Proceedings of the IEEE, vol.86, issue.1, 1938. ,
DOI : 10.1109/JPROC.1998.658762
Asymptotic conditions at a point, selfadjoint extensions of operators, and the method of matched asymptotic expansions, Proceedings of the St, pp.77-125, 1999. ,
DOI : 10.1090/trans2/193/05
Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol.44, 1983. ,
DOI : 10.1007/978-1-4612-5561-1
Numerical Characterization of Concrete Heterogeneity, Materials Research, vol.5, issue.3, pp.309-314, 2002. ,
DOI : 10.1590/S1516-14392002000300015
Evaluation of the Perfectly Matched Layer for Computational Acoustics, Journal of Computational Physics, vol.139, issue.1, pp.166-183, 1998. ,
DOI : 10.1006/jcph.1997.5868
Introduction à l'analyse numérique des équations aux dérivées partielles, 2004. ,
An introduction to acoustics, p.19, 2003. ,
Functional Analysis. International series in pure and applied mathematics, 1991. ,
A Unified Analysis of Transmission Conditions for Thin Conducting Sheets in the Time-Harmonic Eddy Current Model, SIAM Journal on Applied Mathematics, vol.73, issue.6, pp.731980-2003, 2013. ,
DOI : 10.1137/120901398
Asymptotic boundary element methods for thin conducting sheets, Discrete Contin. Dyn. Syst. Ser. S, vol.8, issue.3, pp.619-647, 2015. ,
The treatment of the locking phenomenon for a general class of variational inequalities, Journal of Computational and Applied Mathematics, vol.170, issue.1, pp.121-143, 2004. ,
DOI : 10.1016/j.cam.2003.12.044
URL : https://hal.archives-ouvertes.fr/hal-00690589
Basic Linear Partial Differential Equations, 1975. ,
Topological vector spaces, distributions and kernels, 2006. ,
Analyse multi-échelle et conditions aux limites approchées pour un prolème avec couche mince dans un domaine à coin, 2003. ,
Principles of Multiscale Modeling, 2011. ,