Multiple scattering and modified Green's functions

Journal of Mathematical Analysis and Applications

Volumn 275, Issue 2, 2002, Pages 642-656

  Martin, P A ^a  

^a Department of Geology and Geological Engineering   (United States)

Author keywords

Acoustics; Boundary integral equations; Modified fundamental solutions

Indexed keywords

EID: 0037113603     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00318-9     Document Type: Article

References (19)

1. M.G. Andreasen, Scattering from parallel metallic cylinders with arbitrary cross sections, IEEE Trans. Antennas and Propagation AP-12 (1964) 746-754.
2. D. Colton, R. Kress, Integral Equation Methods in Scattering Theory, Wiley, New York, 1983.
3. R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience, New York, 1953.
4. R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. II, Interscience, New York, 1962.
5. M. Danos, L.C. Maximon, Multipole matrix elements of the translation operator, J. Math. Phys. 6 (1965) 766-778.
6. M. de St.Q. Isaacson, Vertical cylinders of arbitrary section in waves, J. Waterway, Port, Coastal and Ocean Div., Proc. ASCE 104 (1978) 309-324.
7. D.S. Jones, Integral equations for the exterior acoustic problem, Quart. J. Mech. Appl. Math. 27 (1974) 129-142.
8. R.E. Kleinman, G.F. Roach, Boundary integral equations for the three-dimensional Helmholtz equation, SIAM Rev. 16 (1974) 214-236.
9. R.E. Kleinman, G.F. Roach, On modified Green functions in exterior problems for the Helmholtz equation, Proc. Roy. Soc. London Ser. A 383 (1982) 313-332.
10. RE. Kleinman, G.F. Roach, Operators of minimal norm via modified Green's functions, Proc. Roy. Soc. Edinburgh Sect. A 94 (1983) 163-178.
11. P.A. Martin, Integral-equation methods for multiple-scattering problems I. Acoustics, Quart. J. Mech. Appl. Math. 38 (1985) 105-118.
12. P.A. Martin, Multiple scattering and the Rehr-Albers-Fritzsche formula for the propagator matrix, J. Phys. A 31 (1998) 8923-8932.
13. R.F. Millar, The scattering of a plane wave by a row of small cylinders, Canad. J. Phys. 38 (1960) 272-289.
14. A.F. Peterson, The "interior resonance" problem associated with surface integral equations of electromagnetics: numerical consequences and a survey of remedies, Electromagnetics 10 (1990) 293-312.
15. R.P. Radlinski, Comments on "Multi-obstacle acoustic scattering in the simple source formulation with accuracy checks" [J. Acoust. Soc. Am. 66, 1536-1541 (1979)] (Ref. [17] below), J. Acoust. Soc. Amer. 68 (1980) 989-992.
16. A.F. Seybert, B. Soenarko, F.J. Rizzo, D.J. Shippy, A special integral equation formulation for acoustic radiation and scattering for axisymmetric bodies and boundary conditions, J. Acoust. Soc. Amer. 80 (1986) 1241-1247.
17. L. Sorensen, Multi-obstacle acoustic scattering in the simple source formulation with accuracy checks, J. Acoust. Soc. Amer. 66 (1979) 1536-1541.
18. F. Ursell, On the exterior problems of acoustics, Proc. Cambridge Philos. Soc. 74 (1973) 117-125.
19. F. Ursell, On the exterior problems of acoustics. II, Math. Proc. Cambridge Philos. Soc. 84 (1978) 545-548.