Scattering by infinite one-dimensional rough surfaces

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 455, Issue 1990, 1999, Pages 3767-3787

  Chandler Wilde, Simon N ^a   Ross, Chris R ^a   Zhang, B O ^a  

^a BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

Helmholtz equation; Integral equations; Radiation conditions; Rough surface scattering

Indexed keywords

EID: 0001144682     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1999.0476     Document Type: Article

References (46)

1. Anselone, P. M. & Sloan, I. II. 1985 Integral equations on the half-line. J. Integral Eqns 9, 3-23.
2. Bao, G., Dobson, D. C. & Cox, J. A. 1995 Mathematical studies in rigorous grating theory. J. Opt. Soc. Am. A12, 1029-1042.
3. Bishop, G. C. & Smith, J. 1992 A scattering model for nondifferentiable periodic surface-roughness. J. Acoust. Soc. Am. 91, 744-770.
4. Buck, R. C. 1958 Bounded continuous functions on a locally compact space. Michigan Math. 31 5, 95-104.
5. Chandler-Wilde, S. N. 1995 Boundary value problems for the Helmholtz equation in a half-plane. In Proc. 3rd Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation (ed. G. Cohen, P. Joly, E. Becache & J. E. Roberts), pp. 188-197. Philadelphia, PA: SIAM.
6. Chandler-Wilde, S. N. 1997 The impedance boundary value problem for the Helmholtz equation in a half-plane. Math. Methods Appl. Sci. 20, 813-840.
7. Chandler-Wilde, S. N. & Hothersall, D. C. 1995 Efficient calculation of the Green function for acoustic propagation above a homogeneous impedance plane. J. Sound Vib. 180, 705-724.
8. Chandler-Wilde, S. N. & Ross, C. R. 1995 Uniqueness results for direct and inverse scattering by infinite surfaces in a lossy medium. Inverse Problems 10, 1063-1067.
9. Chandler-Wilde, S. N. & Ross, C. R. 1996 Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane. Math. Methods Appl. Sci. 19, 959-976.
10. Chandler-Wilde, S. N. & Zhang, B. 1997 On the solvability of a class of second kind integral equations on unbounded domains. J. Math. Analysis Appl. 214, 482-502.
11. Chandler-Wilde, S. N. & Zhang, B. 1998a A uniqueness result for scattering by infinite rough surfaces. SIAM Jl Appl. Math. 58, 1774-1790.
12. Chandler-Wilde, S. N. & Zhang, B. 1998& Electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate. Proc. R. Soc. Lond. A 454, 519-542.
13. Chandler-Wilde, S. N. & Zhang, B. 1999 Scattering of electromagnetic waves by rough interfaces and inhomogencous layers. SIAM Jl Math. Analysis 30, 559-583.
14. Chandler-Wilde, S. N., Zhang, B. & Ross, C. R. 1999 On the solvability of second kind integral equations on the real line. (Submitted.)
15. Chen, X. & Priedman, A. 1991 Maxwell's equations in a periodic structure. Trans. Am. Math. Soc. 323, 465-507.
16. Colton, D. & Kress, R. 1983 Integral equation methods in scattering theory. New York: Wiley.
17. Colton, D. & Kress, R. 1998 Inverse acoustic and electromagnetic scattering theory, 2nd edn. Berlin: Springer.
18. DeSanto, J. A. & Brown, G. S. 1986 Analytical techniques for multiple scattering from rough surfaces. In Progress in optics (ed. E. Wolf), vol. XXIII, pp. 1-62. Amsterdam: Elsevier.
19. DeSanto, J. A. & Martin, P. A. 1997 On the derivation of boundary integral equations for scattering by an infinite one-dimensional rough surface. J. Acoust. Soc. Am. 102, 67-77.
20. DeSanto, J. A., Erdmann, G., Hereman, W. & Misa, M. 1998 Theoretical and computational aspects of scattering from rough surfaces: one-dimensional perfectly reflecting surfaces. Waves Random Media 8, 385-414.
21. Dobson, D. 1993 Optimal design of periodic antireflective structures for the Helmholtz equation. Eur. Jl Appl. Math. 4, 321-340.
22. Dobson, D. & Priedman, A. 1992 The time-harmonic Maxwell equations in a doubly periodic structure. J. Math. Analysis Appl. 166, 507-528.
23. Eidus, D. M. & Vinnik, A. A. 1974 On radiation conditions for domains with infinite boundaries. Sov. Math. Dokl. 15, 12-15.
24. Gilbarg, D. & Trudinger, N. S. 1983 Elliptic partial differential equations of second order, 2nd edn. Berlin: Springer.
25. Günter, N. M. 1967 Potential theory. New York: Frederick Ungar.
26. Jörgens, K. 1982 Linear integral operators. London: Pitman.
27. Kapp, D. A. & Brown, G. S. 1996 A new numerical method for rough surface scattering calculations. IEEE Trans. Antenn. Propag. 44, 711-721.
28. Kim, M. J., Berenyi, H. M. & Bürge, R. E. 1994 Scattering of scalar waves by two-dimensional gratings of arbitrary shape: application to rough surfaces at near-grazing incidence. Proc. R. Soc. Lond. A 446, 289-308.
29. Kirsch, A. 1993 Diffraction by periodic structures. In Inverse problems in mathematical physics (ed. L. Paivarinta & E. Somersalo), pp. 87-102. Berlin: Springer.
30. Macaskill, C. & Cao, P. 1996 A new treatment of rough surface scattering. Proc. R. Soc. Lond. A 452, 2593-2612.
31. Maystre, D., Saillard, M. & Ingers, J. 1991 Scattering by one- or two-dimensional randomly rough surfaces. Waves Random Media 3, s143-s155.
32. Milder, D. M. 1996 Role of the admittance operator in rough-surface scattering. J. Acoust. Soc. Am. 100, 759-768.
33. Minskii, V. 1983 Sommerfeld radiation conditions for second-order differential operator in a domain with infinite border. J. Diff. Equal. 48, 157-176.
34. Nedelec, J. C. & Starling, F. 1991 Integral equation methods in a quasi-periodic diffraction problem for the time-harmonic Maxwell's equations. SIAM Jl Math. Analysis 22, 1679-1701.
35. Ogilvy, J. A. 1991 Theory of wave scattering from random rough surfaces. Bristol: Adam Hilger. Petit, R. 1980 Electromagnetic theory of gratings. Berlin: Springer.
36. Ross, C. R. 1996 Direct and inverse scattering by rough surfaces. PhD thesis, Brunei University, UK.
37. Spivack, M. 1990 A numerical approach to rough-surface scattering by the parabolic equation method. J. Acoust. Soc. Am. 87, 1999-2004.
38. Thorsos, E. I. & Jackson, D. R. 1989 The validity of the perturbation approximation for rough surface scattering using a Gaussian roughness spectrum. J. Acoust. Soc. Am. 86, 261-277.
39. Tsang, L., Chan, C. H., Pak, K. & Sangani, H. 1995 Monte Carlo simulations of large-scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method. IEEE Tmns. Antenn. Propag. 43, 851-859.
40. Ursell, F. 1973 On the exterior problems of acoustics. Proc. Camb. Phil. Soc. 74, 117-125.
41. Vogelsang, V. 1975 Das Ausstrahlungsproblem für elliptische Differentialgleichungen in Gebieten mit Unbeschränktem Rand. Math. Z. 144, 101-124.
42. Voronovich, A. G. 1994 Wave scattering from rough surfaces. Berlin: Springer.
43. Voronovich, A. G. 1996 Non-local small-slope approximation for wave scattering from rough surfaces. Waves Random Media 6, 151-167.
44. Wagner, R. L., Song, J. M. & Chew, W. C. 1997 Monte Carlo simulation of electromagnetic scattering from two-dimensional random rough surfaces. IEEE Trans. Antenn. Propag. 45, 235-246.
45. Willers, A. 1987 The Helmholtz equation in disturbed half-spaces. Math. Meth. Appl. Sci. 9, 312-323.
46. Zhang, B. & Chandler-Wilde, S. N. 1998 Acoustic scattering by an inhoinogeneous layer on a rigid plate. SIAM Jl Appl. Math. 58, 1931-1950.