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Volumn 459, Issue 2036, 2003, Pages 1891-1924

Spurious and true eigensolutions of Helmholtz BIEs and BEMs for a multiply connected problem

Author keywords

Boundary integral equation; Degenerate kernel; Fourier series; Helmholtz equation; Multiply connected domain; Spurious eigenvalue

Indexed keywords

ARTICLE; DECOMPOSITION; FOURIER ANALYSIS; GEOMETRY; MATHEMATICAL COMPUTING; STATISTICAL ANALYSIS;

EID: 1542616907     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2002.1084     Document Type: Article
Times cited : (68)

References (38)
  • 2
    • 0032624581 scopus 로고    scopus 로고
    • Matrices, vector spaces, and information retrieval
    • Berry, M. W., Drmac, Z. & Jessup, E. R. 1999 Matrices, vector spaces, and information retrieval. SIAM Rev. 41, 335-362.
    • (1999) SIAM Rev. , vol.41 , pp. 335-362
    • Berry, M.W.1    Drmac, Z.2    Jessup, E.R.3
  • 3
    • 0000181954 scopus 로고
    • The application of integral equation methods to numerical solution of some exterior boundary value problems
    • Burton, A. J. & Miller, G. F. 1971 The application of integral equation methods to numerical solution of some exterior boundary value problems. Proc. R. Soc. Lond. A 323, 201-210.
    • (1971) Proc. R. Soc. Lond. A , vol.323 , pp. 201-210
    • Burton, A.J.1    Miller, G.F.2
  • 4
    • 0032154169 scopus 로고    scopus 로고
    • On the fictitious frequencies using dual series representation
    • Cheri, J. T. 1998 On the fictitious frequencies using dual series representation. Mech. Res. Commun. 25, 529-534.
    • (1998) Mech. Res. Commun. , vol.25 , pp. 529-534
    • Cheri, J.T.1
  • 5
    • 0032022002 scopus 로고    scopus 로고
    • Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary
    • Chen, J. T. & Chen, K. H. 1998 Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary. Engng Analysis Bound. Elem. 21, 105-116.
    • (1998) Engng Analysis Bound. Elem. , vol.21 , pp. 105-116
    • Chen, J.T.1    Chen, K.H.2
  • 6
    • 0001799089 scopus 로고    scopus 로고
    • Review of dual boundary element methods with emphasis on hypersingular integral and divergent series
    • Chen, J. T. & Hong, H.-K. 1999 Review of dual boundary element methods with emphasis on hypersingular integral and divergent series. Appl. Mech. Rev. 52, 17-33.
    • (1999) Appl. Mech. Rev. , vol.52 , pp. 17-33
    • Chen, J.T.1    Hong, H.-K.2
  • 7
    • 0033890489 scopus 로고    scopus 로고
    • On fictitious frequencies using circulants for radiation problems of a cylinder
    • Chen, J. T. & Kuo, S. R. 2000 On fictitious frequencies using circulants for radiation problems of a cylinder. Mech. Res. Commun. 27, 49-58.
    • (2000) Mech. Res. Commun. , vol.27 , pp. 49-58
    • Chen, J.T.1    Kuo, S.R.2
  • 9
    • 0033734398 scopus 로고    scopus 로고
    • Determination of spurious eigenvalues and multiplicities of true eigenvalues in the dual multiple reciprocity method using the singular value decomposition technique
    • Chen, J. T., Huang, C. X. & Wong, F. C. 2000a Determination of spurious eigenvalues and multiplicities of true eigenvalues in the dual multiple reciprocity method using the singular value decomposition technique. J. Sound Vib. 230, 219-230.
    • (2000) J. Sound Vib. , vol.230 , pp. 219-230
    • Chen, J.T.1    Huang, C.X.2    Wong, F.C.3
  • 11
    • 0035103213 scopus 로고    scopus 로고
    • A new method for true and spurious eigensolutions of arbitrary cavities using the CHEEF method
    • Chen, I. L., Chen, J. T., Kuo, S. R. & Liang, M. T. 2001a A new method for true and spurious eigensolutions of arbitrary cavities using the CHEEF method. J. Acoust. Soc. Am. 109, 982-999.
    • (2001) J. Acoust. Soc. Am. , vol.109 , pp. 982-999
    • Chen, I.L.1    Chen, J.T.2    Kuo, S.R.3    Liang, M.T.4
  • 12
    • 0035856935 scopus 로고    scopus 로고
    • Analytical study and numerical experiments for radiation and scattering problems using the CHIEF method
    • Chen, I. L., Chen, J. T. & Liang, M. T. 2001 & Analytical study and numerical experiments for radiation and scattering problems using the CHIEF method. J. Sound Vib. 248, 809-828.
    • (2001) J. Sound Vib. , vol.248 , pp. 809-828
    • Chen, I.L.1    Chen, J.T.2    Liang, M.T.3
  • 13
    • 57249083923 scopus 로고    scopus 로고
    • Boundary element analysis for the Helmholtz eigenvalue problems with a multiply connected domain
    • Chen, J. T., Lin, J. H., Kuo, S. R. & Chyuan, S. W. 2001c Boundary element analysis for the Helmholtz eigenvalue problems with a multiply connected domain. Proc. R. Soc. Lond. A 457, 2521-2546.
    • (2001) Proc. R. Soc. Lond. A , vol.457 , pp. 2521-2546
    • Chen, J.T.1    Lin, J.H.2    Kuo, S.R.3    Chyuan, S.W.4
  • 14
    • 0016873983 scopus 로고
    • Calculation of the Helmholtz equation by an integral equation
    • De Mey, G. 1976 Calculation of the Helmholtz equation by an integral equation. Int. J. Numer. Meth. Engng 10, 59-66.
    • (1976) Int. J. Numer. Meth. Engng , vol.10 , pp. 59-66
    • De Mey, G.1
  • 15
    • 84985331000 scopus 로고
    • A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation
    • De Mey, G. 1977 A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation. Int. J. Numer. Meth. Engng 11, 1340-1342.
    • (1977) Int. J. Numer. Meth. Engng , vol.11 , pp. 1340-1342
    • De Mey, G.1
  • 17
    • 31744434224 scopus 로고
    • Derivations of integral equations of elasticity
    • Hong, H.-K. & Chen, J. T. 1988 Derivations of integral equations of elasticity. J. Engng Mech. ASME 114, 1028-1044.
    • (1988) J. Engng Mech. ASME , vol.114 , pp. 1028-1044
    • Hong, H.-K.1    Chen, J.T.2
  • 18
    • 0033715103 scopus 로고    scopus 로고
    • Boundary integral methods in low frequency acoustics
    • Hsiao, G. C. & Wendland, W. L. 2000 Boundary integral methods in low frequency acoustics. J. Chin. Inst. Engrs 23, 369-375.
    • (2000) J. Chin. Inst. Engrs , vol.23 , pp. 369-375
    • Hsiao, G.C.1    Wendland, W.L.2
  • 19
    • 0000080532 scopus 로고
    • An alternative BEM formulation applied to membrane vibrations
    • (ed. C. A. Brebbia & G. Maier). Springer
    • Hutchinson, J. R. 1985 An alternative BEM formulation applied to membrane vibrations. In Boundary elements VII (ed. C. A. Brebbia & G. Maier). Springer.
    • (1985) Boundary Elements VII
    • Hutchinson, J.R.1
  • 21
    • 0005077083 scopus 로고
    • Analysis of plates and shells by boundary collocation
    • ed. D. E. Beskos. Springer
    • Hutchinson, J. R. 1991 Analysis of plates and shells by boundary collocation. In Boundary elements analysis of plates and shells (ed. D. E. Beskos), pp. 314-368. Springer.
    • (1991) Boundary Elements Analysis of Plates and Shells , pp. 314-368
    • Hutchinson, J.R.1
  • 22
    • 0025740414 scopus 로고
    • A retracted boundary integral equation for exterior acoustic problem with unique solution for all wavenumbers
    • Hwang, J. Y. & Chang, S. C. 1991 A retracted boundary integral equation for exterior acoustic problem with unique solution for all wavenumbers. J. Acoust. Soc. Am. 90, 1167-1180.
    • (1991) J. Acoust. Soc. Am. , vol.90 , pp. 1167-1180
    • Hwang, J.Y.1    Chang, S.C.2
  • 24
    • 0043087148 scopus 로고
    • Application of the multiple reciprocity boundary element method to neutron diffusion problems
    • Southampton: Computational Mechanics Publications
    • Itagaki, M. & Brebbia, C. A. 1994 Application of the multiple reciprocity boundary element method to neutron diffusion problems. In The multiple reciprocity boundary element method. Southampton: Computational Mechanics Publications.
    • (1994) The Multiple Reciprocity Boundary Element Method
    • Itagaki, M.1    Brebbia, C.A.2
  • 25
    • 0031222621 scopus 로고    scopus 로고
    • Power iterative multiple reciprocity boundary element method for solving three-dimensional Helmholtz equation
    • Itagaki, M., Nishiyama, S., Tomioka, S., Enoto, T. & Sahashi, N. 1997 Power iterative multiple reciprocity boundary element method for solving three-dimensional Helmholtz equation Engng Analysis Bound. Elem. 20, 113-121.
    • (1997) Engng Analysis Bound. Elem. , vol.20 , pp. 113-121
    • Itagaki, M.1    Nishiyama, S.2    Tomioka, S.3    Enoto, T.4    Sahashi, N.5
  • 26
    • 0027303559 scopus 로고
    • A note on multiple reciprocity integral formulation for Helmholtz equation
    • Kamiya, N. & Andoh, E. 1993 A note on multiple reciprocity integral formulation for Helmholtz equation. Commun. Numer. Meth. Engng 9, 9-13.
    • (1993) Commun. Numer. Meth. Engng , vol.9 , pp. 9-13
    • Kamiya, N.1    Andoh, E.2
  • 27
    • 0030214179 scopus 로고    scopus 로고
    • A new complex-valued formulation and eigenvalue analysis of the Helmholtz equation by boundary element method
    • Kamiya, N., Andoh, E. & Nogae, K. 1996 A new complex-valued formulation and eigenvalue analysis of the Helmholtz equation by boundary element method. Adv. Engng Software 26, 219-227.
    • (1996) Adv. Engng Software , vol.26 , pp. 219-227
    • Kamiya, N.1    Andoh, E.2    Nogae, K.3
  • 29
    • 0034229431 scopus 로고    scopus 로고
    • Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM
    • Kuo, S. R., Chen, J. T. & Huang, C. X. 2000a Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM. Int. J. Numer. Meth. Engng 48, 1404-1422.
    • (2000) Int. J. Numer. Meth. Engng , vol.48 , pp. 1404-1422
    • Kuo, S.R.1    Chen, J.T.2    Huang, C.X.3
  • 30
    • 0034247389 scopus 로고    scopus 로고
    • Applications of the generalized singular-value decomposition method on the eigenproblem using the incomplete boundary element formulation
    • Kuo, S. R., Yeih, W. & Wu, Y. C. 2000b Applications of the generalized singular-value decomposition method on the eigenproblem using the incomplete boundary element formulation. J. Sound Vib. 235, 813-845.
    • (2000) J. Sound Vib. , vol.235 , pp. 813-845
    • Kuo, S.R.1    Yeih, W.2    Wu, Y.C.3
  • 31
    • 0002690421 scopus 로고
    • On the null-field equations for the exterior problems of acoustics
    • Martin, P. A. 1980 On the null-field equations for the exterior problems of acoustics. Q. J. Mech. Appl. Math. 27, 386-396.
    • (1980) Q. J. Mech. Appl. Math. , vol.27 , pp. 386-396
    • Martin, P.A.1
  • 32
    • 0001645140 scopus 로고
    • The multiple reciprocity method - A new approach for transforming BEM domain integrals to the boundary
    • Nowak, A. J. & Brebbia, C. A. 1989 The multiple reciprocity method - a new approach for transforming BEM domain integrals to the boundary. Engng Analysis Bound. Elem. 6, 164-167.
    • (1989) Engng Analysis Bound. Elem. , vol.6 , pp. 164-167
    • Nowak, A.J.1    Brebbia, C.A.2
  • 35
    • 84953655023 scopus 로고
    • Improved integral formulation for acoustic radiation problem
    • Schenck, H. A. 1968 Improved integral formulation for acoustic radiation problem. J. Acoust. Soc. Am. 44, 41-58.
    • (1968) J. Acoust. Soc. Am. , vol.44 , pp. 41-58
    • Schenck, H.A.1
  • 36
    • 0001000229 scopus 로고
    • The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations
    • Seybert, A. F. & Rengarajan, T. K. 1987 The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations. J. Acoust. Soc. Am. 81, 1299-1306.
    • (1987) J. Acoust. Soc. Am. , vol.81 , pp. 1299-1306
    • Seybert, A.F.1    Rengarajan, T.K.2
  • 37
    • 0016103212 scopus 로고
    • Helmholtz equation eigenvalues and eigenmodes for arbitrary domains
    • Tai, G. R. G. & Shaw, R. P. 1974 Helmholtz equation eigenvalues and eigenmodes for arbitrary domains. J. Acoust. Soc. Am. 56, 796-804.
    • (1974) J. Acoust. Soc. Am. , vol.56 , pp. 796-804
    • Tai, G.R.G.1    Shaw, R.P.2
  • 38
    • 0032490775 scopus 로고    scopus 로고
    • On the polygonal membrane with a circular core
    • Wang, C. Y. 1998 On the polygonal membrane with a circular core. J. Sound Vib. 215, 195-199.
    • (1998) J. Sound Vib. , vol.215 , pp. 195-199
    • Wang, C.Y.1


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