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Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems Cover

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

By: A. Aimi,  M. Diligenti and  C. Guardasoni  
Open Access
|Jul 2017

References

  1. 1. M. P.M. and I. K.U., Theoretical Acoustic. McGraw-Hill, 1968.
  2. 2. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory. Springer, 2012.10.1007/978-1-4614-4942-3
  3. 3. L. Tsang, J. A. Kong, K.-H. Ding, and C. O. Ao, Scattering of Electro- magnetic waves, Numerical Simulations. John Wiley & Sons., 2004.
  4. 4. P. Banerjee and P. Butter field, Boundary Element Methods in Engineering. McGraw-Hill U.K. Ltd., 1981.
  5. 5. F. Hartmann, Introduction to Boundary Element Theory Method in En- gineering. McGraw-Hill, U.K. Ltd., 1981.
  6. 6. A. Aimi, M. Diligenti, C. Guardasoni, and S. Panizzi, Energetic BEMFEM coupling for wave propagation in layered media, Commun. Appl. Ind. Math., vol. DOI: 10.1685/journal.caim.438, 2013.
  7. 7. A. Aimi, L. Desiderio, M. Diligenti, and C. Guardasoni, A numerical study of energetic BEM-FEM applied to wave propagation in 2D multidomains, Publications de l'Institut Mathématique - Beograd, vol. 96, no. 110, pp. 5-22, 2014.10.2298/PIM1410005A
  8. 8. A. Aimi, M. Diligenti, A. Frangi, and C. Guardasoni, Energetic BEMFEM coupling for wave propagation in 3D multidomains, Int. J. Num. Meth. Engng., vol. 97, pp. 377-394, 2014.10.1002/nme.4602
  9. 9. H. Antes, G. Beer, and W. Moser, Soil-structure interaction and wave propagation problems in 2D by a Duhamel integral based approach and the convolution quadrature method, Comput. Mech., vol. 36, no. 6, pp. 431-443, 2005.10.1007/s00466-005-0679-0
  10. 10. A. Bachelot, L. Bounhoure, and A. Pijols, Couplage éléments finis- potentiels retardés pour la diffraction électromagnétique par un obstacle hétérogène, Numer. Math., vol. 89, pp. 257-306, 2001.10.1007/PL00005468
  11. 11. T. Cruse and F. Rizzo, A direct formulation and numerical solution of the general transient elastodynamic problem-I, J. Math. Anal. Appl., vol. 22, pp. 244-259, 1968.10.1016/0022-247X(68)90171-6
  12. 12. A. Frangi and G. Novati, On the numerical stability of time-domain elastodynamic analyses by BEM, Comput. Methods Appl. Mech. Engrg., vol. 173, pp. 403-417, 1999.10.1016/S0045-7825(98)00294-1
  13. 13. M. Schanz, Application of 3D boundary element formulation to wave propagation in poroelastic solids, Eng. Anal. Boundary Elem., vol. 25, pp. 363-376, 2001.10.1016/S0955-7997(01)00022-4
  14. 14. A.Münch and A. F. Pazoto, Uniform stabilization of a viscous numerical approximation for a locally damped wave equation, ESAIM Control Optim. Calc. Var., vol. 13, no. 2, pp. 265-293, 2007.10.1051/cocv:2007009
  15. 15. L. R. Tcheugoué Tébou and E. Zuazua, Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity, Numer. Math., vol. 95, no. 3, pp. 563-598, 2003.10.1007/s00211-002-0442-9
  16. 16. E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods, SIAM Rev., vol. 47, no. 2, pp. 197-243, 2005.10.1137/S0036144503432862
  17. 17. A. Aimi, M. Diligenti, and C. Guardasoni, Energetic BEM-FEM coupling for the numerical solution of the damped wave equation, Adv. Comput. Math., pp. 1-25, 2016.10.1063/1.4912432
  18. 18. A. Aimi and S. Panizzi, BEM-FEM coupling for the 1D Klein-Gordon equation, Numer. Methods Partial Di_erential Equations, vol. 30, no. 6, pp. 2042-2082, 2014.
  19. 19. A. Bamberger and T. H. Duong, Formulation variationnelle espacetemps pour le calcul par potentiel retard_e de la diffraction d'une onde acoustique. I, Math. Methods Appl. Sci., vol. 8, no. 3, pp. 405-435, 1986.10.1002/mma.1670080127
  20. 20. A. Bamberger and T. H. Duong, Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide, Math. Methods Appl. Sci., vol. 8, no. 4, pp. 598-608, 1986.10.1002/mma.1670080139
  21. 21. C. Lubich, Convolution quadrature and discretized operational calculus I, Numer. Math., vol. 52, pp. 129-145, 1988.10.1007/BF01398686
  22. 22. C. Lubich, Convolution quadrature and discretized operational calculus II, Numer. Math., vol. 52, pp. 413-425, 1988.10.1007/BF01462237
  23. 23. T. Ha Duong, On retarded potential boundary integral equations and their discretization, in Topics in computational wave propagation. Direct and inverse problems (P. D. et al., ed.), pp. 301-336, Springer-Verlag, 2003.10.1007/978-3-642-55483-4_8
  24. 24. G. Maier, M. Diligenti, and A. Carini, A variational approach to boundary element elasto-dynamic analysis and extension to multidomain problems, Comput. Methods Appl. Mech. Engrg., vol. 92, pp. 193-213, 1991.10.1016/0045-7825(91)90239-3
  25. 25. A. Vick and R. West, Analysis of Damped Wave Using the Boundary Element Method, Transaction on Modelling and Simulation, vol. 15, pp. 265-278, 1997.
  26. 26. M. Costabel, Time-dependent problems with the boundary integral equation method, in Encyclopedia of Computational Mechanics (E. S. et al., ed.), pp. 1-28, John Wiley and Sons, 2004.10.1002/0470091355.ecm022
  27. 27. A. Aimi, M. Diligenti, and C. Guardasoni, Comparison between numerical methods applied to the damped wave equation, J. Integral Equations Appl., vol. 29, no. 1, pp. 5-40, 2017.10.1216/JIE-2017-29-1-5
  28. 28. A. Aimi and M. Diligenti, A new space-time energetic formulation for wave propagation analysis in layered media by BEMs, Int. J. Numer. Meth. Engng., vol. 75, pp. 1102-1132, 2008.
  29. 29. A. Aimi, M. Diligenti, C. Guardasoni, I. Mazzieri, and S. Panizzi, An energy approach to space-time Galerkin BEM for wave propagation problems, Int. J. Numer. Meth. Engng., vol. 80, no. 9, pp. 1196-1240, 2009.
  30. 30. A. Aimi, M. Diligenti, A. Frangi, and C. Guardasoni, Neumann exterior wave propagation problems: Computational aspects of 3D energetic galerkin BEM, Comput. Mech., vol. 51, no. 4, pp. 475-493, 2013.10.1007/s00466-012-0796-5
  31. 31. P. Shearer, Introduction to Seismology. Cambridge University Press, 2009.10.1017/CBO9780511841552
  32. 32. J. Chevangen, N. Remacle, and X. Gallez, Discontinuous galerkin implementation of the extended helmhotz resonator impedence model in time domain, in Proceedings of the 12th AIAAA/CEAS Aeroacoustics Conference-Cambridge, AIAAA 2006-2569, 2006.10.2514/6.2006-2569
  33. 33. B. Kennett, Seismic wave propagation in stratified media. ANU-The Australian National University, 2009.10.22459/SWPSM.05.2009
  34. 34. J. Achenbach, Wave propagation in Elastic Solids. North-Holland, 1973.
  35. 35. C. Lubich, On the multistep time discretization of linear initialboundary value problems and their boundary integral equations, Numer. Math., vol. 67, no. 3, pp. 365-389, 1994.10.1007/s002110050033
  36. 36. G. Monegato and L. Scuderi, Numerical integration of functions with boundary singularities, J. Comput. Appl. Math., vol. 112, no. 1-2, pp. 201-214, 1999. Numerical evaluation of integrals.10.1016/S0377-0427(99)00230-7
Language: English
Page range: 103 - 127
Submitted on: Nov 7, 2016
Accepted on: May 2, 2017
Published on: Jul 20, 2017
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2017 A. Aimi, M. Diligenti, C. Guardasoni, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.