High-frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions

Asymptotic Analysis

Volumn 26, Issue 3-4, 2001, Pages 257-283

  Antoine, X ^a   Barucq, H ^b   Vernhet, L ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

Author keywords

Acoustics; Approximate boundary condition; Asymptotic expansion; Dissipation; Helmholtz equation; Pseudodifferential operators

Indexed keywords

EID: 0035368186     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, 9th printing, 1972.
2. X. Antoine, Fast approximate computation of a time-harmonic scattered field using the on-surface radiation condition method, IMA J. Appl. Math. 66 (2001), 83-110.
3. X. Antoine, H. Barucq and A. Bendali, Bayliss-and-Turkel-like radiation conditions on surfaces of arbitrary shape, J. Math. Anal. Appl. 229 (1999), 184-211.
4. X. Antoine, H. Barucq and L. Vernhet, Approximate numerical solution of the acoustic scattering by a penetrable object using impedance boundary conditions, in: Mathematical and Numerical Aspects of Wave Propagation, A. Bermudez, D. Gomez, C. Hazard, P. Joly and J.E. Roberts, eds, SIAM, Philadelphia, 2000, pp. 709-713.
5. X. Antoine, H. Barucq and L. Vernhet, Approximate solution for the scattering of a time-harmonic wave by a homogeneous dissipative obstacle, Research Report No. 00-18, Laboratoire de Mathématiques pour l'Industrie et la Physique, Université P. Sabatier, Toulouse III, France, 2000.
6. A. Bendali and K. Lemrabet, The effect of a thin coating on the scattering of a time-harmonic wave for the Helmholtz equation, SIAM J. Appl. Math. 56(6) (1996), 1664-1693.
7. A. Bendali and M. Souilah, Consistency estimates for a double-layer potential and application to the numerical analysis of the boundary-element approximation of acoustic scattering by a penetrable object, Math. Comp. 62(205) (1994), 65-91.
8. J. Chazarain and A. Piriou, Introduction to the Theory of Linear Partial Differential Equations, North-Holland, Amsterdam, 1982.
9. M. Costabel and E. Stephan, A direct boundary integral equation method for transmission problems, J. Math. Anal. Appl. 106 (1985), 367-413.
10. B. Engquist and J.C. Nédélec, Effective boundary conditions for acoustic and electromagnetic scattering in thin layers, Research Report CMAP, Ecole Polytechnique, Palaiseau, France, 1993.
11. L. Hörmander, The Analysis of Linear Partial Differential Operators III, Pseudodifferential Operators, Springer, 1985.
12. L. Hörmander, Lectures on Nonlinear Hyperbolic Equations, Collection Mathématiques et Applications, Vol. 26, Springer, 1997.
13. D.S. Jones, An improved surface radiation condition, IMA J. Appl, Math. 48 (1992), 163-193.
14. O. Lafitte, Diffraction in the high frequency regime by a thin layer of dielectric material I: The equivalent impedance boundary condition, SIAM J. Appl. Math. 59(3) (1999), 1028-1052.
15. R.S. Phillips, On the exterior problem for the reduced wave equation, in: Partial Differential Equations, D.C. Spencer, ed., Proc. Sympos. Pure Math., Vol. 23, Amer. Math. Soc., Providence, RI, 1973, pp. 153-160.
16. J. Rauch, Lectures on Geometric Optics, 1995.
17. F. Rellich, Über das asymptotische Verhalten der Lösungen von Δu+λu = 0 in unendlichen Gebieten, Jahresber. Deutsch. Math. Verein. 53 (1943), 57-65.
18. S.M. Rytov, Calcul du skin-effect par la méthode des perturbations, J. Phys. USSR 2 (1940), 233-242.
19. T.B.A. Senior, Impedance boundary conditions for imperfectly conducting surface, Appl. Sci. Res. B. 8 (1960), 418-436.
20. T.B.A. Senior, Approximate boundary conditions for homogeneous dielectric bodies, J. Electromagn. Waves Applicat. 9 (1995), 1227-1239.
21. T.B.A. Senior, Generalized boundary conditions for scalar fields, J. Acoust. Soc. Amer. 97(6) (1995), 3473-3477.
22. T.B.A. Senior and J.L. Volakis, Approximate Boundary Conditions in Electromagnetics, IEE Electromagnetic Waves, Serie 41, London, 1995.
23. T.B.A. Senior, J.L. Volakis and S.R. Legault, Higher order impedance and absorbing boundary conditions, IEEE Trans. Antennas Propagation 45(1) (1997), 107-114.
24. A. Taflove, G.A. Kriegsmann and K.R. Umashankar, A new formulation of electromagnetic wave scattering using the on-surface radiation condition approach, IEEE Trans. Antennas and Propagation 35 (1987), 153-161.
25. M.E. Taylor, Pseudodifferential Operators, Princeton University Press, NJ, 1981.
26. M.E. Taylor, Partial Differential Equations II, Qualitative Study of Linear Equations, Applied Math. Sciences, Vol. 116, Springer, 1996.
27. M. Teymur, A note on higher-order surface radiation conditions, IMA J. Appl. Math. 57(2) (1996), 137-163.
28. F. Treves, Introduction to Pseudodifferential Operators and Fourier Integral Operators, Plenum Press, New York, 1980.
29. L. Vernhet, Boundary element solution of a scattering problem involving a generalized impedance boundary condition, Math. Methods Appl. Sci. 22 (1999), 587-603.
30. D.S. Wang, Limits and validity of the impedance boundary conditions on penetrable surfaces, IEEE Trans. Antennas Propagation 35 (1987), 453-457.