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Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 49))

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Abstract

We consider a boundary-value problem related to acoustic radiation and scattering governed by the Helmholtz equation in a d-dimensional unbounded region RR d with internal boundary Γ. The unbounded domain R is partitioned by a smooth artificial boundary Γ R into a bounded inner domain Ωi and its unbounded outer complement Ωo (Fig. 1).

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References

  • Astley, R.J., Macaulay, G.J., and Coyette, J.-P., 1994, “Mapped Wave Envelope Elements for Acoustical Radiation and Scattering,” J. Sound Vib., Vol. 170, pp. 97–118.

    Article  MATH  Google Scholar 

  • Bettess, P., 1977, “Infinite Elements,” Int. J. Numer. Methods Eng., Vol. 11, pp. 53–64.

    Article  MATH  Google Scholar 

  • Burnett, D.S., 1994, “A Three-dimensional Acoustic Infinite Element Based on a Prolate Spheroidal Multipole Expansion,” J. Acoust. Soc. Am., Vol. 96, pp. 2798–2816.

    Article  MathSciNet  Google Scholar 

  • Gerdes, K., and Demkowicz, L., 1996, “Solution of 3D-Laplace and Helmholtz Equations in Exterior Domains Using hp-infinite Elements,” Comput. Methods App[. Mech. Eng., Vol. 137, pp. 239–273.

    Article  MathSciNet  MATH  Google Scholar 

  • Givoli, D., and Keller, J.B., 1989, “A Finite Element Method for Large Domains,” Comput. Methods Appl. Mech. Eng., Vol. 76, pp. 41–66.

    Article  MathSciNet  MATH  Google Scholar 

  • Harari, I., Barbone, P.E., and Montgomery, J.M., 1997, “Finite Element Formulations for Exterior Domains: Application to Hybrid Methods, Non-reflecting Boundary Conditions and Infinite Elements,” Int. J. Numer. Methods Eng.,Vol. 40, In press.

    Google Scholar 

  • Hughes, T.J.R.H., 1995, “Multiscale Phenomena: Green’s Functions, the Dirichlet-toNeumann Formulation, Subgrid Scale Models, Bubbles, and the Origins of Stabilized Methods,” Comput. Methods Appl. Mech. Eng., Vol. 127, pp. 387–401.

    Article  MATH  Google Scholar 

  • Zienkiewicz, O.C., Bando, K., Bettess, P., Emson, C., and Chiam, T.C., 1985, “Mapped Infinite Elements for Exterior Wave Problems,” Int. J. Numer. Methods Eng., Vol. 21, pp. 1229–1251.

    Article  MathSciNet  MATH  Google Scholar 

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© 1998 Springer Science+Business Media Dordrecht

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Harari, I. (1998). A Variational Formulation for Partitioned Exterior Problems. In: Geers, T.L. (eds) IUTAM Symposium on Computational Methods for Unbounded Domains. Fluid Mechanics and Its Applications, vol 49. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9095-2_20

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  • DOI: https://doi.org/10.1007/978-94-015-9095-2_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5106-6

  • Online ISBN: 978-94-015-9095-2

  • eBook Packages: Springer Book Archive

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