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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 828615, 16 pages
http://dx.doi.org/10.1155/2013/828615
Research Article

A Nonoverlapping Domain Decomposition Method for an Exterior Anisotropic Quasilinear Elliptic Problem in Elongated Domains

Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210023, China

Received 2 September 2012; Accepted 17 December 2012

Academic Editor: Yong-Kui Chang

Copyright © 2013 Baoqing Liu and Qikui Du. 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. G. Ben-Porat and D. Givoli, “Solution of unbounded domain problems using elliptic artificial boundaries,” Communications in Numerical Methods in Engineering, vol. 11, no. 9, pp. 735–741, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Y. Boubendir, X. Antoine, and C. Geuzaine, “A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation,” Journal of Computational Physics, vol. 231, no. 2, pp. 262–280, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Q. Y. Hu, S. Shu, and J. Wang, “Nonoverlapping domain decomposition methods with a simple coarse space for elliptic problems,” Mathematics of Computation, vol. 79, no. 272, pp. 2059–2078, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. Siahaan, C. H. Lai, and K. Pericleous, “A nonoverlapping domain decomposition method for nonlinear physical processes,” Proceedings in Applied Mathematics and Mechanics, vol. 7, pp. 2140003–2140004, 2007. View at Publisher · View at Google Scholar
  5. Q. Du and D. Yu, “A domain decomposition method based on natural boundary reduction for nonlinear time-dependent exterior wave problems,” Computing, vol. 68, no. 2, pp. 111–129, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D.-H. Yu, Natural Boundary Integral Method and its Applications, vol. 539 of Mathematics and its Applications, Science Press & Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002. View at MathSciNet
  7. M. Yang and Q. Du, “A Schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle,” Applied Mathematics and Computation, vol. 159, no. 1, pp. 199–220, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. H. Yu, “Domain decomposition method for unbounded domains,” in Proceedings of the 8th International Conference on Domain Decomposition Methods, pp. 125–132, Beijing, China, 1997.
  9. Q. K. Du and D. H. Yu, “Domain decomposition methods based on natural boundary reduction for wave equation,” Chinese Journal of Computational Physics, vol. 18, pp. 417–422, 2001.
  10. Q. Du and M. Zhang, “A non-overlapping domain decomposition algorithm based on the natural boundary reduction for wave equations in an unbounded domain,” Numerical Mathematics, vol. 13, no. 2, pp. 121–132, 2004. View at Zentralblatt MATH · View at MathSciNet
  11. H. Han, Z. Huang, and D. Yin, “Exact artificial boundary conditions for quasilinear elliptic equations in unbounded domains,” Communications in Mathematical Sciences, vol. 6, no. 1, pp. 71–83, 2008. View at Zentralblatt MATH · View at MathSciNet
  12. I. Hlaváček, M. Křížek, and J. Malý, “On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type,” Journal of Mathematical Analysis and Applications, vol. 184, no. 1, pp. 168–189, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. I. Hlaváček, “A note on the Neumann problem for a quasilinear elliptic problem of a nonmonotone type,” Journal of Mathematical Analysis and Applications, vol. 211, no. 1, pp. 365–369, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. D. Liu and D. Yu, “A FEM-BEM formulation for an exterior quasilinear elliptic problem in the plane,” Journal of Computational Mathematics, vol. 26, no. 3, pp. 378–389, 2008. View at Zentralblatt MATH · View at MathSciNet
  15. S. Meddahi, M. González, and P. Pérez, “On a FEM-BEM formulation for an exterior quasilinear problem in the plane,” SIAM Journal on Numerical Analysis, vol. 37, no. 6, pp. 1820–1837, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. D. N. Arnold, P. G. Ciarlet, and P. L. Lions, Nonlinear Partial Differential Equations and Their Applications, North-Holland, New York, NY, USA, 2002.
  17. J. B. Keller and M. J. Grote, “Exact non-reflecting boundary conditions,” Journal of Computational Physics, vol. 82, pp. 172–192, 1989. View at Publisher · View at Google Scholar
  18. J. M. Wu and D. H. Yu, “The natural boundary element method for an exterior elliptic domain,” Mathematica Numerica Sinica, vol. 22, no. 3, pp. 355–368, 2000 (Chinese). View at Zentralblatt MATH · View at MathSciNet
  19. G. N. Gatica, G. C. Hsiao, and M. E. Mellado, “A domain decomposition method based on BEM and FEM for linear exterior boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 262, no. 1, pp. 70–86, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. D. B. Ingham and M. A. Kelmanson, Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems, vol. 7 of Lecture Notes in Engineering, Springer, Berlin, Germany, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  21. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, vol. 5 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 1986. View at Publisher · View at Google Scholar · View at MathSciNet