Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 583079, 8 pages
http://dx.doi.org/10.1155/2013/583079
Research Article

Low-Frequency Acoustic-Structure Analysis Using Coupled FEM-BEM Method

1School of Aerospace, Tsinghua University, Beijing 100084, China
2Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China
3China Academy of Space Technology, Beijing 100094, China

Received 19 July 2013; Accepted 5 September 2013

Academic Editor: Song Cen

Copyright © 2013 Jinlong Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. J. Bathe, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ, USA, 1996.
  2. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Butterworth-Heinensann, Oxford, UK, 5th edition, 2000.
  3. C. A. Brebbia and J. Dominguez, Boundary Elements: An Introductory Course, McGraw-Hill, London, UK, 1989. View at MathSciNet
  4. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, vol. 1-2, McGraw-Hill, London, UK, 4th edition, 1991.
  5. O. C. Zienkiewicz, D. W. Kelly, and P. Bettess, “The coupling of the finite element method and boundary solution procedures,” International Journal for Numerical Methods in Engineering, vol. 11, no. 2, pp. 355–375, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. C. Spyrakos and D. E. Beskos, “Dynamic response of flexible strip-foundations by boundary and finite elements,” Soil Dynamics and Earthquake Engineering, vol. 5, no. 2, pp. 84–96, 1986. View at Google Scholar · View at Scopus
  7. O. von Estorff, “Coupling of bem and fem in the time domain: some remarks on its applicability and efficiency,” Computers and Structures, vol. 44, no. 1-2, pp. 325–337, 1992. View at Google Scholar · View at Scopus
  8. H. A. Schenck, “Improved integral formulation for acoustic radiation problems,” Journal of the Acoustical Society of America, vol. 44, pp. 41–58, 1968. View at Google Scholar · View at Scopus
  9. A. J. Burton and G. F. Miller, “The application of integral equation methods to the numerical solution of some exterior boundary-value problems,” Proceedings of the Royal Society A, vol. 323, pp. 201–210, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. I. O. Panich, “On the question of solvability of the external boundary value problem for the wave equation and Maxwell's equation,” Russian Mathematical Surveys, vol. 20, no. 1, pp. 221–226, 1965. View at Google Scholar
  11. M. Guiggiani, G. Krishnasamy, T. J. Rudolphi, and F. J. Rizzo, “A general algorithm for the numerical solution of hypersingular boundary integral equations,” Journal of Applied Mechanics, vol. 59, no. 3, pp. 604–614, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. J. Rgo Silva, H. Power, and L. C. Wrobel, “A numerical implementation of a hypersingular boundary element method applied to 3D time-harmonic acoustic radiation problems,” in Boundary Elements XIV, Computational Mechanics Publications, pp. 271–287, Southampton and Elsevier, London, UK, 1992. View at Google Scholar
  13. Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, Pa, USA, 2nd edition, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  14. V. Rokhlin, “Rapid solution of integral equations of classical potential theory,” Journal of Computational Physics, vol. 60, no. 2, pp. 187–207, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” Journal of Computational Physics, vol. 73, no. 2, pp. 325–348, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. P. Peirce and J. A. L. Napier, “A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics,” International Journal for Numerical Methods in Engineering, vol. 38, no. 23, pp. 4009–4034, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Bebendorf, “Approximation of boundary element matrices,” Numerische Mathematik, vol. 86, no. 4, pp. 565–589, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. Bebendorf and S. Rjasanow, “Adaptive low-rank approximation of collocation matrices,” Computing, vol. 70, no. 1, pp. 1–24, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. A. Sommerfeld, Partial Differential Equations in Physics, Academic Press, New York, NY, USA, 1949. View at MathSciNet
  20. A. F. Seybert, B. Soenarko, F. J. Rizzo, and D. J. Shippy, “An advanced computational method for radiation and scattering of acoustic waves in three dimensions,” Journal of the Acoustical Society of America, vol. 77, no. 2, pp. 362–368, 1985. View at Google Scholar · View at Scopus
  21. R. Kress, “Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 38, no. 2, pp. 323–341, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. M. J. Allen and N. Vlahopoulos, “Integration of finite element and boundary element methods for calculating the radiated sound from a randomly excited structure,” Computers and Structures, vol. 77, no. 2, pp. 155–169, 2000. View at Publisher · View at Google Scholar · View at Scopus
  23. O. von Estorff, S. Rjasanow, M. Stolper, and O. Zaleski, “Two efficient methods for a multifrequency solution of the Helmholtz equation,” Computing and Visualization in Science, vol. 8, no. 3-4, pp. 159–167, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  24. I. Benedetti, M. H. Aliabadi, and G. Davì, “A fast 3D dual boundary element method based on hierarchical matrices,” International Journal of Solids and Structures, vol. 45, no. 7-8, pp. 2355–2376, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Saad and M. H. Schultz, “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM Journal on Scientific and Statistical Computing, vol. 7, no. 3, pp. 856–869, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. C. Y. Leung and S. P. Walker, “Iterative solution of large three-dimensional BEM elastostatic analyses using the GMRES technique,” International Journal for Numerical Methods in Engineering, vol. 40, no. 12, pp. 2227–2236, 1997. View at Google Scholar · View at Scopus
  27. M. Merkel, V. Bulgakov, R. Bialecki, and G. Kuhn, “Iterative solution of large-scale 3D-BEM industrial problems,” Engineering Analysis with Boundary Elements, vol. 22, no. 3, pp. 183–197, 1998. View at Google Scholar · View at Scopus
  28. S. Amini and N. D. Maines, “Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation,” International Journal for Numerical Methods in Engineering, vol. 41, no. 5, pp. 875–898, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet