Open Access
Issue
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Page(s) S705 - S731
DOI https://doi.org/10.1051/m2an/2020047
Published online 26 February 2021
  1. S. Acosta, High order surface radiation conditions for time-harmonic waves in exterior domains. Comput. Methods Appl. Mech. Eng. 322 (2017) 296–310. [Google Scholar]
  2. M. Ainsworth, P. Monk and W. Muniz, Dispersive and dissipative properties of discontinuous galerkin finite element methods for the second-order wave equation. J. Sci. Comput. 27 (2006) 5–40. [Google Scholar]
  3. H. Alzubaidi, X. Antoine and C. Chniti, Formulation and accuracy of on-surface radiation conditions for acoustic multiple scattering problems. Appl. Math. Comput. 277 (2016) 82–100. [Google Scholar]
  4. C. Baldassari, H. Barucq, H. Calandra and J. Diaz, Numerical performances of a hybrid local-time stepping strategy applied to the reverse time migration. Geophys. Prospect. 59 (2011) 907–919. [Google Scholar]
  5. C. Baldassari, H. Barucq, H. Calandra, B. Denel and J. Diaz, Performance analysis of a high-order discontinuous galerkin method application to the reverse time migration. Commun. Comput. Phys. 11 (2012) 660–673. [Google Scholar]
  6. H. Barucq, R. Djellouli and E. Estecahandy, Efficient dg-like formulation equipped with curved boundary edges for solving elasto-acoustic scattering problems. Int. J. Numer. Methods Eng. 98 (2014) 747–780. [Google Scholar]
  7. H. Barucq, V. Mattesi and S. Tordeux, The mellin transform. Technical Report RR-8743, INRIA Bordeaux Sud Ouest (2015). [Google Scholar]
  8. H. Barucq, F. Faucher and H. Pham, Localization of small obstacles from back-scattered data at limited incident angles with full-waveform inversion. J. Comput. Phys. 370 (2018) 1–24. [Google Scholar]
  9. A. Bendali, P.-H. Cocquet and S. Tordeux, Approximation by multipoles of the multiple acoustic scattering by small obstacles in three dimensions and application to the foldy theory of isotropic scattering. Arch. Ration. Mech. Anal. 219 (2016) 1017–1059. [Google Scholar]
  10. N. Burk and G. Lebeau, Annales Scientifiques de I’École Normale Supérieure – Injections de Sobolev Probabilistes et Applications 4 (2013). [Google Scholar]
  11. M. Cassier and C. Hazard, Multiple scattering of acoustic waves by small sound-soft obstacles in two dimensions: mathematical justification of the foldy–lax model. Wave Motion 50 (2013) 18–28. [Google Scholar]
  12. D.P. Challa and M. Sini, On the justification of the foldy–lax approximation for the acoustic scattering by small rigid bodies of arbitrary shapes. Multiscale Model. Simul. 12 (2014) 55–108. [Google Scholar]
  13. X. Claeys, Analyse asymptotique et numérique de la diffraction d’ondes par des fils minces. Ph.D. thesis, Université de Versailles Saint-Quentin-en-Yvelines (2008). [Google Scholar]
  14. M. Costabel and M. Dauge, Les problèmes à coins en 10 leçons. [Google Scholar]
  15. J.D. De Basabe, M.K. Sen and M.F. Wheeler, The interior penalty discontinuous galerkin method for elastic wave propagation: grid dispersion. Geophys. J. Int. 175 (2008) 83–93. [Google Scholar]
  16. J. Diaz and M.J. Grote, Multi-level explicit local time-stepping methods for second-order wave equations. Comput. Methods Appl. Mech. Eng. 291 (2015) 240–265. [Google Scholar]
  17. V.M. Dikasov, An inverse problem for the wave equation in a ball. Funct. Anal. App. 25 (1991) 56–58. [CrossRef] [Google Scholar]
  18. L.L. Foldy, The multiple scattering of waves. I. General theory of isotropic scattering by randomly distributed scatterers. Phys. Rev. 67 (1945) 107. [Google Scholar]
  19. R.F.B. Frank, W.J. Olver, D.W. Lozier and C.W. Clark, NIST Handbook of Mathematical Functions. NIST and Cambridge University Press (2010). [Google Scholar]
  20. M.J. Grote, A. Schneebeli and D. Schötzau, Discontinuous galerkin finite element method for the wave equation. SIAM J. Numer. Anal. 44 (2006) 2408–2431. [Google Scholar]
  21. A. Gumerov and R. Duraiswami, Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. Elsevier (2004). [Google Scholar]
  22. C. Gundlach, J. Martin-Garcia and D. Garfinkle, Summation by parts methods for spherical harmonic decompositions of the wave equation in any dimensions. Class. Quantum Grav. 30 (2013) 145003. [CrossRef] [Google Scholar]
  23. A.M. Il’in, Matching of Asymptotic Expansions of Solutions of Boundary Value Problems. American Mathematical Society (1991). [Google Scholar]
  24. V.A. Kondratiev, Boundary value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16 (1967) 209–292. [Google Scholar]
  25. J. Labat, Modélisation multi-échelle de la diffraction des ondes électromagnétiques par de petits obstacles. Ph.D. thesis, Pau (2019). [Google Scholar]
  26. J. Labat, V. Péron and S. Tordeux, Equivalent multipolar point-source modeling of small spheres for fast and accurate electromagnetic wave scattering computations. Wave Motion 92 (2019) 102409. [Google Scholar]
  27. N.N. Lebedev, Spherical Functions & Their Applications. Dover Publication (1975). [Google Scholar]
  28. J. Li, H. Liu, Z. Shang and H. Sun, Two single-shot methods for locating multiple electromagnetic scatterers. SIAM J. Appl. Math. 73 (2013) 1721–1746. [Google Scholar]
  29. J. Li, H. Liu and Q. Wang, Locating multiple multiscale electromagnetic scatterers by a single far-field measurement. SIAM J. Imaging Sci. 6 (2013) 2285–2309. [Google Scholar]
  30. J. Li, H. Liu and J. Zou, Locating multiple multiscale acoustic scatterers. Multiscale Model. Simul. 12 (2014) 927–952. [Google Scholar]
  31. P.A. Martin, Multiple Scattering: Interaction of Time-harmonic Waves with N Obstacles. In Vol. 107 of Cambridge University Press (2006). [Google Scholar]
  32. V. Mattesi, Propagation des ondes dans un milieu comportant des petites hétérogénéités: analyse asymptotique et calcul numérique. Ph.D. thesis, Université de Pau et des Pays de l’Adour (2014). [Google Scholar]
  33. V. Mattesi and S. Tordeux, Equivalent source modelling of small heterogeneities in the context of 3D time-domain wave propagation equation. In: Waves 2013. Gammarth, Tunisia (2013). [Google Scholar]
  34. M. N’Diaye, Étude et développement de méthodes numériques d’ordre élevé pour la résolution des équations différentielles ordinaires (EDO): Applications à la résolution des équations d’ondes acoustiques et électromagnétiques. Ph.D. thesis, 2017. Thèse de doctorat dirigée par Barucq, Hélène et Duruflé, Marc Mathématiques appliquées Pau (2017). [Google Scholar]
  35. J.-C. Nédélec, Acoustic and electromagnetic equations. In: Vol. 144 of Applied Mathematical Sciences. Integral Representations for Harmonic Problems. Springer-Verlag, New York (2001). [Google Scholar]
  36. J. Novak, J.-L. Cornou and N. Vasset, A spectral method for the wave equation of divergence-free vectors and symmetric tensors inside a sphere. J. Comput. Phys. 229 (2010) 399–414. [Google Scholar]
  37. A.D. Poularikas, Transforms and Applications Handbook. CRC Press, 2010. [Google Scholar]
  38. M. Rietmann, M. Grote, D. Peter and O. Schenk, Newmark local time stepping on high-performance computing architectures. J. Comput. Phys. 334 (2017) 308–326. [Google Scholar]
  39. M.E. Taylor, Partial differential equations I. Basic theory, 2nd edition. In: Vol. 115 of Applied Mathematical Sciences. Springer, New York (2011). [Google Scholar]
  40. S. Tordeux, Méthodes asymptotiques pour la propagation des ondes dans les milieux comportant des fentes. Ph.D. thesis, Université de Versailles Saint-Quentin-en-Yvelines (2004). [Google Scholar]
  41. V. Villamizar, S. Acosta and B. Dastrup, High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions. J. Comput. Phys. 333 (2017) 331–351. [Google Scholar]
  42. S.N. Vladimir Maz’ya and B.1 Plamenevskij, Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Birkhäuser (2000). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you