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Section B

Solving biharmonic equation using the localized method of approximate particular solutions

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Pages 1790-1801 | Received 30 Jul 2013, Accepted 30 Oct 2013, Published online: 06 May 2014

References

  • I. Altas, J. Dym, M. Gupta, and R. Manohar, Multigrid solution of automatically generated high-order discretizations for the biharmonic equation, SIAM J. Sci. Comput. 19 (1998), pp. 1575–1585.
  • D. Arnold, F. Brezzi, C. Bernardo, and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal. 39(5) (2002), pp. 1749–1779.
  • M. Ben-Artzi, I. Chorev, J.P. Croisille, and D. Fishelov, A compact difference scheme for the biharmonic equation in planar irregular domains, SIAM J. Numer. Anal. 47(4) (2009), pp. 3087–3108.
  • J. Bentley, Multidimensional binary search trees used for associative searching, Commun. ACM 18 (1975), pp. 509–517.
  • B. Bialecki, A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles, J. Comput. Phys. 191 (2003), pp. 601–621.
  • S. Chantasiriwan, Solutions to harmonic and biharmonic problems with discontinuous boundary conditions by collocation methods using multiquadrics as basis functions, Int. Commun. Heat Mass Transfer 34 (2007), pp. 313–320.
  • C.S. Chen, C. Fan, and P. Wen, The method of particular solutions for solving elliptic problems with variable coefficients, Int. J. Comput. Methods 8 (2011), pp. 545–559.
  • C.S. Chen, C. Fan, and P. Wen, The method of particular solutions for solving certain partial differential equations, Numer. Methods Partial Differ. Equ. 28 (2012), pp. 506–522. doi:10.1002/num.20631
  • G. Chen, Z. Li, and P. Lin, A fast finite difference method for biharmonic equations on irregular domains, Adv. Comput. Math. 29(2) (2008), pp. 113–133.
  • E.H. Georgoulis and P. Houston, Discontinuous Galerkin methods for the biharmonic problem, J. Numer. Anal. 29(3) (2009), pp. 573–594.
  • N.A. Gumerov and R. Duraiswami, Fast multipole method for the biharmonic equation, J. Comput. Phys. 215 (2006), pp. 363–383.
  • A. Hussain, T.S. Mohyud-Din, and A. Yildirim, Solution of biharmonic equations using homotopy analysis method, Stud. Nonlinear Sci. 2(1) (2011), pp. 26–30.
  • C.K. Lee, X. Liu, and S.C. Fan, Local multiquadric approximation for solving boundary value problems, Comput. Mech. 30 (2003), pp. 396–409.
  • B. Sarler and R. Vertnik, Meshfree explicit local radial basis function collocation method for diffusion problems, Comput. Math. Appl. 21 (2006), pp. 1269–1282.
  • H. Sheng and Z. Zhang, Invalidity of decoupling a biharmonic equation to two Poisson equations on non-convex polygons, Int. J. Numer. Method Model. 5 (2008), pp. 73–76.
  • T. Wang, A mixed finite volume element method based on rectangular mesh for biharmonic equations, J. Comput. Appl. Math. 172 (2004), pp. 117–130.
  • G. Yao, C.S. Chen, and J. Kolibal, A localized approach for the method of approximate particular solutions, Comput. Math. Appl. 61 (2011), pp. 2376–2387.
  • G. Yao, C. Tsai, and W. Chen, The comparison of three meshless methods for solving high order elliptic partial differential equations, Eng. Anal. Bound. Elem. 34 (2010), pp. 625–631.

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