Computation of singular and hypersingular boundary integrals by Green identity and application to boundary value problems

Engineering Analysis with Boundary Elements

Volumn 33, Issue 8-9, 2009, Pages 1124-1131

  Seydou, F ^a   Duraiswami, R ^b   Seppanen T ^a   Gumerov, N A ^b  

^a UNIVERSITY OF OULU   (Finland)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

Bounday integral method; Green identity; Hypersingular integrals; Nystr m method; Singular integrals

Indexed keywords

BOUNDARY INTEGRALS; BOUNDAY INTEGRAL METHOD; DIAGONAL ELEMENTS; DISCRETIZATION METHOD; GREEN IDENTITY; GREEN'S THEOREM; HYPERSINGULAR; HYPERSINGULAR INTEGRAL; HYPERSINGULAR INTEGRALS; LARGE CLASS; MATRIX; SINGULAR INTEGRALS;

BOUNDARY VALUE PROBLEMS;

EID: 65749111476     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2009.02.004     Document Type: Article

References (21)

1. Burton A.J., and Miller G.F. The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc R Soc London A 323 (1971) 201-210
2. Chen Ke. Efficient iterative solution of linear systems from discretizing singular integral equations. Electron Trans Numer Anal 2 (1994) 76-91
3. Colton D., and Kress R. Integral equation methods in scattering theory (1983), Wiley, New York
4. Colton D., and Kress R. Inverse acoustic and electromagnetic scattering theory. second ed (1997), Springer, Berlin
5. Cohen D., Lepore N., and Heller E.J. Consolidating boundary methods for finding the eigenstates of billiards. J Phys A Math Gen 37 (2004) 2139-2161 PII: S0305-4470(04)69126-8
6. Duduchava R., and Prössdorf S. On the approximation of singular integral equations by equations with smooth kernels. Integral Equations and Operator Theory 21 (1995) 223-237
7. Felbacq D., Tayeb G., and Maystre D. Scattering by a random set of parallel cylinders. J Opt Soc Am A 11 9 (1994) 2526-2538
8. N.A. Gumerov, R. Duraiswami, A broadband fast multipole accelerated boundary element method for the 3D Helmholtz equation. J Acoust Soc Am 2009;125(1):191-205.
9. Gutkin B. Can billiard eigenstates be approximated by superpositions of plane waves?. J Phys A Math Gen 36 (2003) 8603-8622
10. Heller EJ. In: Giannoni M-J, Voros A, Zinn-Justin J, editors. Chaos and quantum systems. Amsterdam: Elsevier; 1991. p. 548.
11. Kaufman D.L., Kosztin I., and Schulten K. Expansion method for stationary states of quantum billiards. Am J Phys 67 (1999)
12. Kirsch A., and Monk P. Convergence analysis of a coupled finite element and spectral method in acoustic scattering. IMA J Numer Anal 9 (1990) 425-447
13. Kleinman R.E., and Martin P.A. On single integral equations for the transmission problem of acoustics. SIAM J Appl Math 48 (1988) 307-325
14. Kress R. Linear integral equations (1989), Springer, New York
15. Kress R. On the numerical solution of a hypersingular integral equation in scattering theory. J Comput Appl Math 61 (1995) 345-360
16. Leis R. Zur Dirichletschen randwertaufabe des auenraumes der schwingungsgleichung. Math Zeit 90 (1965) 205-211 English Translation
17. Panich I.O. On the question of solvability of the exterior boundary value problem for the wave equation and Maxwell's equation. Uspekhi Mat Nauk (Russian Math Surv) 20 1 (1965) 221-226
18. Singh KM, Tanaka M. Analytical evaluation of weakly singular integrals for Helmholtz equation. Trans Jpn Soc Comput Eng Sci 1999;1:161-6.
19. Song JM, Chew WC. FMM and MLFMA in 3D and fast Illinois solver code. In: Chew WC, Jin JM, Michielssen E, Song JMM, editors. In: Fast and efficient algorithms in computational electromagnetics. Norwood, MA: Artech House; 2001.
20. Zaman SI. A comprehensive review of boundary integral formulations of acoustic scattering problems. Sci Technol Special Rev 2000:281-310.
21. Zhang C, JL, Raizen MG, Niu Q. Quantum chaos of bogoliubov waves for a Bose-Einstein condensate in stadium billiards, Phys Rev Lett 2004;93:074101.