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Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM. (English) Zbl 1021.76034
The aim is to predict analytically where spurious eigenvalues will occur and how the spurious eigenmodes will behave if only the singular or hypersingular integral equation is used in the multiple reciprocity method. Numerical experiments using the real part dual boundary element method (BEM) are performed for comparison. The real part dual BEM is employed to solve the acoustic problem for a circular cavity. After assembling the dual equations, the singular value decomposition technique is used to filter out spurious eigenvalues for two-dimensional cavities. Two examples for a circular domain, including Dirichlet and Neumann problems, are employed to validate the proposed method.
Reviewer: N.S.Mera (Leeds)

MSC:
76M15 Boundary element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
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References:
[1] De Mey, International Journal for Numerical Methods in Engineering 10 pp 59– (1976) · Zbl 0325.65049
[2] De Mey, International Journal for Numerical Methods in Engineering 11 pp 1340– (1977) · Zbl 0364.65079
[3] An alternative BEM formulation applied to membrane vibrations. In: Boundary Elements VII, (eds). Springer: Berlin, 1985.
[4] Tai, Journal of the Acoustical Society of America 56 pp 796– (1974)
[5] Recent development of dual BEM in acoustic problems, keynote lecture. Proceedings of the fourth World Congress on Computational Mechanics, (eds). Ceride Publications: Argentina, 1998; 106.
[6] Chen, Engineering Analysis with Boundary Elements 20 pp 25– (1997)
[7] Liou, Journal of the Chinese Institute of Civil Hydraulics Engineering 11 pp 299– (1999)
[8] Chen, Journal of Sound and Vibration 217 pp 75– (1998)
[9] Analysis and experiment for acoustic modes of a cavity containing an incomplete partition. Proceedings of the Fourth National Conference on Structural Engineering, vol. 1, 1998; 349-356.
[10] Chen, Engineering Analysis with Boundary Elements 21 pp 105– (1998) · Zbl 1062.76533
[11] Boundary Element Method, (2nd Edn). New World Press: Taipei, 1992 (in Chinese).
[12] Chen, Chinese Journal of Mechanics 14 pp 1– (1998)
[13] Chen, Applied Acoustics 57 pp 293– (1999)
[14] Chen, Transactions of the ASME, Applied Mechanics Review 52 pp 17– (1999)
[15] Yeih, Advances in Engineering Software 29 pp 7– (1997)
[16] Yeih, Advances in Engineering Software 30 pp 459– (1999) · Zbl 05467451
[17] Yeih, Engineering Analysis with Boundary Elements 23 pp 339– (1999) · Zbl 0957.74076
[18] Chen, Computational Mechanics 24 pp 41– (1999) · Zbl 0951.76051
[19] Chen, Wave Motion 30 pp 367– (1999)
[20] Kamiya, Advances in Engineering Software 26 pp 219– (1996) · Zbl 05470401
[21] (eds). Multiple Reciprocity Boundary Element Method, Comp. Mech. Publ., Southampton, 1994. · Zbl 0868.73006
[22] Matrix Theory with Applications. McGraw-Hill: New York, 1991.
[23] Numerical Recipes in FORTRAN (2nd edn). Cambridge University Press: New York, 1992. · Zbl 0778.65002
[24] Matrix Computations (2nd edn). The Johns Hopkins University Press: Baltimore, 1989.
[25] Chen, Journal of the Chinese Institute of Engineers 22 pp 729– (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.