NIKODYM : Finite element modeling for ultrasonic tranducers, Medical Imaging'98 International Society for Optics and Photonics, pp.19-42, 1998. ,
STEGUN : Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1964. ,
Ray methods for waves in elastic solids, 1982. ,
Uniform Asymptotic Theory of Diffraction by the Edge of a Three-Dimensional Body, SIAM Journal on Applied Mathematics, vol.18, issue.2, pp.287-301, 1970. ,
DOI : 10.1137/0118024
A radial basis function partition of unity method for transport on the sphere, 2014. ,
On the far-field operator in elastic obstacle scattering, IMA Journal of Applied Mathematics, vol.67, issue.1, pp.1-21, 2002. ,
DOI : 10.1093/imamat/67.1.1
On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem, Applicable Analysis, vol.1980, issue.1-4, pp.75-84, 1990. ,
DOI : 10.1121/1.382498
General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients, Wave Motion, vol.1, issue.1, pp.3-10, 1979. ,
DOI : 10.1016/0165-2125(79)90020-9
Fiabilité et optimisation des calculs obtenus par des formulations en propagation d'ondes, Thèse de doctorat, 2016. ,
Boundary decomposition for helmholtz and maxwell equations 1 : disjoint sub-scatterers, asymptotic analysis, Asymptotic Analysis, vol.38, issue.1, pp.1-10, 2004. ,
Scattering from submerged objects by a hybrid asymptotic-boundary integral equation method, Wave Motion, vol.29, issue.2, pp.137-156, 1999. ,
DOI : 10.1016/S0165-2125(98)00027-4
Scattering by a hybrid asymptotic/finite element method, Computer Methods in Applied Mechanics and Engineering, vol.164, issue.1-2, pp.141-156, 1998. ,
DOI : 10.1016/S0045-7825(98)00051-6
SEN : Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations, Geophysics, vol.72, pp.81-95, 2007. ,
Modélisation de la propagation et de l'interaction d'une onde acoustique pour la télemétrie de structures complexes, Thèse de doctorat, 2011. ,
Équations intégrales et éléments finis de frontière. Applications en mécanique des solides et des fluides, CNRS Éditions/Eyrolles, 1995. ,
Efficient Numerical Methods for non-local Operators. H 2 -matrix compression, algorithms and analysis, 2010. ,
Méthodes asymptotiques en électromagnétisme, 1994. ,
The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems, Proc. Roy. Soc. London, volume Ser. A 323, pp.201-210, 1971. ,
DOI : 10.1098/rspa.1971.0097
A Fictitious Domain Method with Mixed Finite Elements for Elastodynamics, SIAM Journal on Scientific Computing, vol.29, issue.3, pp.1244-1267, 2007. ,
DOI : 10.1137/060655821
Comparison of the Born and the Rytov approximations for scattering on quasi-homogeneous media, Optics Communications, vol.74, issue.5, pp.284-289, 1990. ,
DOI : 10.1016/0030-4018(90)90384-6
Trends and Stakes of NDT Simulation, Journal of Nondestructive Evaluation, vol.38, issue.4, pp.339-341, 2012. ,
DOI : 10.1016/j.ndteint.2005.04.002
Two and Three Dimensional Partition of Unity Interpolation by Product-Type Functions, Applied Mathematics & Information Sciences, vol.9, issue.1, pp.1-8, 2015. ,
DOI : 10.12785/amis/090101
Seismic ray theory, 2000. ,
DOI : 10.1115/1.1508173
Méthode multipôle rapide pour les équations intégrales de frontière en élastodynamique 3D. Application à la propagation d'ondes sismiques, Thèse de doctorat, Ecole Nationale des Ponts et Chaussées, 2009. ,
A new Fast Multipole formulation for the elastodynamic half-space Green??s tensor, Journal of Computational Physics, vol.258, pp.787-808, 2014. ,
DOI : 10.1016/j.jcp.2013.11.010
Optimizing ultrasonic transducers based on piezoelectric composites using a finite-element method, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.37, issue.3, pp.135-140, 1990. ,
DOI : 10.1109/58.55302
Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering, Acta Numerica, vol.21, pp.89-305, 2012. ,
DOI : 10.1017/S0962492912000037
Fundamentals of seismic wave propagation, 2004. ,
DOI : 10.1017/CBO9780511616877
Optimal Discontinuous Galerkin Methods for Wave Propagation, SIAM Journal on Numerical Analysis, vol.44, issue.5, pp.2131-2158, 2006. ,
DOI : 10.1137/050641193
URL : http://authors.library.caltech.edu/6854/1/CHUsiamjna06.pdf
A single trace integral formulation of the second kind for acoustic scattering. research report, 2011. ,
Multi-Trace Boundary Integral Formulation for Acoustic Scattering by Composite Structures, Communications on Pure and Applied Mathematics, vol.11, issue.no. 2, pp.1163-1201, 2013. ,
DOI : 10.1515/9781400877577
Higer-order numerical methods for transient wave equations, 2013. ,
Numerical microlocal anaysis in time domain, 2011. ,
Integral Equation Methods in Scattering Theory, 1983. ,
DOI : 10.1137/1.9781611973167
Inverse acoustic and electromagnetoc scattering theory, 1992. ,
DOI : 10.1007/978-1-4614-4942-3
Main Features of a Complete Ultrasonic Measurement Model: Formal Aspects of Modeling of Both Transducers Radiation and Ultrasonic Flaws Responses, Open Journal of Acoustics : Conference Series, pp.43-53, 2013. ,
DOI : 10.4236/oja.2013.33A008
Recent advances in semi-analytical scattering models for NDT simulation, Journal of Physics : Conference Series, 2013. ,
DOI : 10.1088/1742-6596/269/1/012013
Modeling of scattering of ultrasounds by flaws, Springer Proceedings in Physics, 2009. ,
On the Reconstruction of a Rigid Body in the Theory of Elasticity, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.44, issue.12, pp.911-923, 1997. ,
DOI : 10.1007/978-3-642-87722-3
Solveur rapide pour modéliser la propagation des ondes visco-élastiques 3D dans des milieux complexes, Thèse de doctorat, 2017. ,
Ray-based Simulation of Defect Echoes for Ultrasonic Non Destructive Testing, Physics Procedia, 2015. ,
DOI : 10.1016/j.phpro.2015.08.063
The approximation of one matrix by another of lower rank, Psychometrika, vol.1, issue.3, pp.211-218, 1936. ,
DOI : 10.1007/BF02288367
Computational high frequency wave propagation, Acta Numerica, vol.1, pp.1-86, 2003. ,
DOI : 10.1017/cbo9780511550157.003
Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations, SIAM Journal on Scientific Computing, vol.16, issue.4, pp.865-897, 1995. ,
DOI : 10.1137/0916051
Modélisation du champ ultrasonore rayonné dans un solide anisotrope et hétérogène par un traducteur immergé, Thèse de doctorat, 1999. ,
LHÉMERY : Pencil method in elastodynamics : application to ultrasonic field computation, Ultrasonics, vol.38, issue.1, 2000. ,
SCHUMM : A semi-analytic-FEM hybrid model for simulating UT configurations involving complicated interactions of waves with defects, AIP Conference Proceedings, numéro A, pp.74-80, 2003. ,
The Far-Field Equations in Linear Elasticity ??? an Inversion Scheme, ZAMM, vol.81, issue.5, pp.305-316, 2001. ,
DOI : 10.1002/1521-4001(200105)81:5<305::AID-ZAMM305>3.0.CO;2-T
Application of the Inhomogeneous Lippmann--Schwinger Equation to Inverse Scattering Problems, SIAM Journal on Applied Mathematics, vol.73, issue.1, pp.212-231, 2013. ,
DOI : 10.1137/120869584
Accelerating fast multipole methods for the Helmholtz equation at low frequencies, IEEE Computational Science and Engineering, vol.5, issue.3, pp.32-38, 1998. ,
DOI : 10.1109/99.714591
Approximation of bi-variate functions: singular value decomposition versus sparse grids, IMA Journal of Numerical Analysis, vol.34, issue.1, pp.28-54, 2014. ,
DOI : 10.1093/imanum/drs047
Hybrid numerical-asymptotic approximation for high-frequency scattering by penetrable convex polygons, IMA Journal of Applied Mathematics, vol.80, issue.2, pp.1-30, 2013. ,
DOI : 10.1093/imamat/hxt040
Hybrid numerical?asymptotic approximation for highfrequency scattering by penetrable convex polygons, Journal of Applied Mathematics, vol.21, pp.1-30, 2013. ,
Elastodynamic Green's functions for a smoothly heterogeneous half-space, International Journal of Solids and Structures, vol.33, issue.7, pp.1005-1021, 1996. ,
DOI : 10.1016/0020-7683(95)00081-X
On the analysis of wave motions in a multi-layered solid, The Quarterly Journal of Mechanics and Applied Mathematics, vol.54, issue.1, p.1337, 2001. ,
DOI : 10.1093/qjmam/54.1.13
SARKAR : Fully coupled hybrid-method FEM/high-frequency technique for the analysis of 3D scattering and radiation problems. Microwave and optical technology letters, pp.104-107, 2005. ,
On retarded potential boundary integral equations and their discretisation Topics in computational wave propagation, pp.301-336, 2003. ,
UT simulation of embedded parametric defects using a hybrid model based upon spectral finite element and domain decomposition methods, 19th World Conference on Non-Destructive Testing, 2016. ,
Mathematical and numerical modelling of piezoelectric sensors, ESAIM: Mathematical Modelling and Numerical Analysis, vol.46, issue.4, pp.875-909, 2012. ,
DOI : 10.1051/m2an/2011070
URL : https://hal.archives-ouvertes.fr/hal-00869631
Time domain integral equation methods in computational electromagnetism . Lecture notes in mathematics, Computational Electromagnetism, vol.2148, pp.111-189, 2014. ,
Hierarchical matrices and the high-frequency fast multipole method for the Helmholtz equation with decay, Max-Plank Institut fur Mathematik in den Naturwissenschaften Leipzig, 2014. ,
Fundamental solutions in elastodynamics : A compendium, 2006. ,
DOI : 10.1017/CBO9780511546112
Asymptotic Methods for Partial Differential Equations: The Reduced Wave Equation and Maxwell???s Equations, Surveys in applied mathematics, pp.1-82, 1995. ,
DOI : 10.1007/978-1-4899-0436-2_1
Seismic wave propagation in stratified media, 1983. ,
DOI : 10.26530/OAPEN_459524
An $\cal O(N)$ Level Set Method for Eikonal Equations, SIAM Journal on Scientific Computing, vol.22, issue.6, pp.2178-2193, 2000. ,
DOI : 10.1137/S1064827500367130
The application of reciprocity theory to scattering of acoustic waves by flaws, Journal of Applied Physics, vol.12, issue.6, pp.3190-3199, 1978. ,
DOI : 10.1016/0020-7683(76)90044-5
Introduction to the spectral element method for three-dimensional seismic wave propagation, Geophysical Journal International, vol.139, issue.3, pp.806-822, 1999. ,
DOI : 10.1046/j.1365-246x.1999.00967.x
A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface, Proceedings of the IEEE, pp.1448-1461, 1974. ,
DOI : 10.1109/PROC.1974.9651
ORLOV : Geometrical optics of Inhomogeneous Media, 1990. ,
MINIMIZING THE CONDITION NUMBER OF BOUNDARY INTEGRAL OPERATORS IN ACOUSTIC AND ELECTROMAGNETIC SCATTERING, The Quarterly Journal of Mechanics and Applied Mathematics, vol.38, issue.2, pp.323-421, 1985. ,
DOI : 10.1093/qjmam/38.2.323
Linear Integral Equations, 1989. ,
On the condition number of boundary integral operators for the exterior Dirichlet problem for the Helmholtz equation, Numerische Mathematik, vol.20, issue.1, pp.77-95, 1983. ,
DOI : 10.1007/978-3-322-92139-0
A Numerical Method for the exterior neumann problem for the reduced wave equation, Computing, vol.55, issue.1, pp.246-273, 1969. ,
DOI : 10.1007/BF02234773
A uniform asymptotic theory of edge diffraction, IEEE Transactions on antennas propagation, vol.25, issue.1, pp.25-34, 1976. ,
Coupling high-frequency methods and boundary element techniques for scattering problems with several obstacles, 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2017. ,
Uniform Asymptotic Theory of Edge Diffraction, Journal of Mathematical Physics, vol.7, issue.12, pp.2291-2305, 1969. ,
DOI : 10.1002/cpa.3160170203
SCHUMM : Semi-analitycal-FEM hybrid modeling of ultrasonic defect responses, ECNDT, 2006. ,
A Half-Space Boundary Element Method for Acoustic Problems With a Reflecting Plane of Arbitrary Impedance, Journal of Sound and Vibration, vol.171, issue.2, pp.173-184, 1992. ,
DOI : 10.1006/jsvi.1994.1112
Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions, Computer Methods in Applied Mechanics and Engineering, vol.107, issue.1-2, pp.131-144, 1993. ,
DOI : 10.1016/0045-7825(93)90171-S
SEDOV : Measurement models and scattering models for predicting the ultrasonic pulse-echo response from side-drilled holes, Journal of Nondestructive Evaluation : Conference Series, vol.24, issue.3, 2005. ,
Simulation of complex ultrasonic NDT cases using coupled analytical-numerical method : the MOHYCAN Project, 10th European Conference of NDT, 2010. ,
??ber eine Methode zum r??umlichen Neumannschen Problem mit einer Anwendung f??r torusartige Berandungen, Acta Mathematica, vol.109, issue.0, pp.75-135, 1963. ,
DOI : 10.1007/BF02391810
URL : http://doi.org/10.1007/bf02391810
Hybrid methods for analysis of complex scatterers, Proceeding of the IEEE, pp.770-779, 1989. ,
DOI : 10.1109/5.32067
The Finite-Difference Time-Domain Method for Modeling of Seismic Wave Propagation, Advances in Geophysics, vol.48, pp.421-516, 2007. ,
DOI : 10.1016/S0065-2687(06)48008-0
Interpolation by fast Fourier and Chebyshev transforms, International Journal for Numerical Methods in Engineering, vol.20, issue.11, pp.1679-1692, 1979. ,
DOI : 10.2307/2346986
Seismic Surface Waves. Lecture Notes for post-graduate studies, 1999. ,
Acoustic and Electromagnetic Equations Integral representations for harmonic problems, 2001. ,
Some efficient boundary integral strategies for time-harmonic wave problems in an elastic halfspace, Computer Methods in Applied Mechanics and Engineering, vol.164, issue.1-2, pp.207-221, 1998. ,
DOI : 10.1016/S0045-7825(98)00055-3
Solving two-point seismic ray-tracing problems in a heterogeneous medium, pp.79-99, 1980. ,
Mathematical aspects of Discontinuous Galerkin Method, 2010. ,
Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools, Geophysical Journal International, vol.105, issue.1, pp.271-284, 1991. ,
DOI : 10.1111/j.1365-246X.1991.tb03461.x
A comparison between the Born and Rytov approximations for the inverse backscattering problem, GEOPHYSICS, vol.54, issue.7, pp.864-871, 1989. ,
DOI : 10.1190/1.1442715
Waves Propagation and Scattering ? 12 lectures of 24 ? Part III, 2012. ,
Hyperbolic partial differential equations and geometric optics, 2012. ,
DOI : 10.1090/gsm/133
REZAYAT : A boundary integral equation method for time-harmonic radiation and scattering in an elastic half-space. Advance Topics in Boundary Element Analysis, ASME, pp.83-90, 1995. ,
Rapid solution of integral equations of scattering theory in two dimensions, Journal of Computational Physics, vol.86, issue.2, pp.414-439, 1990. ,
DOI : 10.1016/0021-9991(90)90107-C
YARVIN : Generalized gaussian quadratures and singular value decompositions of integral operators, 1996. ,
TATARSKII : Principle of statistical radiophysics 4 : Wave propagation through random media, 1989. ,
Transport equations for elastic and other waves in random media, Wave Motion, vol.24, issue.4, pp.327-370, 1996. ,
DOI : 10.1016/S0165-2125(96)00021-2
URL : http://math.stanford.edu/~papanico/pubftp/TRANSPORT.pdf
Ultrasonic nondestructive evaluation systems : Models and measurements, 2007. ,
Adaptive bivariate Chebyshev approximation, Numerical Algorithms, vol.8, issue.1-3, pp.79-94, 2007. ,
DOI : 10.1007/BF02810617
URL : http://www.math.unipd.it/~marcov/pdf/bivchebfin.pdf
A new frequency-uniform coercive boundary integral equation for acoustic scattering, Communications on Pure and Applied Mathematics, vol.59, issue.3, pp.1384-1415, 2011. ,
DOI : 10.1016/0022-1236(84)90066-1
Conservative numerical schemes for high-frequency wave propagation in heterogeneous media, Thèse de doctorat, 2013. ,
URL : https://hal.archives-ouvertes.fr/tel-01005143
La Méthode Multipôle Rapide en Electromagnétisme : Performances, Parallélisation, Applications, Thèse de doctorat, CERMICS/INRIA, 2002. ,
Analyse et Simulations Numériques du Retournement Temporel et de la Diffraction Multiple, Thèse de doctorat, 2011. ,
Using physical models of the testing process in the determination of probability of detection, Materials evaluation, vol.59, issue.7, pp.861-865, 2001. ,
A model relating ultrasonic scattering measurements through liquid???solid interfaces to unbounded medium scattering amplitudes, The Journal of the Acoustical Society of America, vol.74, issue.4, pp.1279-1290, 1989. ,
DOI : 10.1121/1.390045
SYMES : Upwind finite-difference calculation of traveltimes, Geophysics, vol.56, issue.6, pp.812-821, 1991. ,
Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations, SIAM Journal on Numerical Analysis, vol.41, issue.2, pp.673-694, 2003. ,
DOI : 10.1137/S0036142901396533
THURBER : A fast algorithm for two-point seismic ray tracing, Bulletin of the Seismological Society of America, vol.77, issue.3, pp.972-986, 1980. ,
Stability, Accuracy, and Robustness of the Time Domain Integral Equation Method for Radar Scattering Analysis, Thèse de doctorat, 2013. ,
Finite-difference calculation of travel times, Bulletin of the Seismological Society of America, vol.78, issue.6, pp.2062-2076, 1988. ,
Traveltime and amplitude estimation using wavefront construction, GEOPHYSICS, vol.58, issue.8, pp.1157-1166, 1993. ,
DOI : 10.1190/1.1443499
wave propagation in heterogeneous media: Velocity???stress finite???difference method, GEOPHYSICS, vol.51, issue.4, pp.889-901, 1986. ,
DOI : 10.1190/1.1442147
A treatize on the theory of Bessel functions, 1966. ,
Die numerische Approximation von Randintegraloperatoren für die Helmholtzgleichung im R 3, Thèse de doctorat, 1990. ,
Wave???equation tomography, GEOPHYSICS, vol.57, issue.1, pp.15-26, 1992. ,
DOI : 10.1190/1.1443179