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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 57))

Abstract

Recently, very intensive efforts have been devoted to develop meshless or element free methods that eliminate the need of element connectivity in the solution of PDEs. The motivation is to cut down modelling costs in industrial applications by avoiding the labor intensive step of mesh generation. In addition, these methods are particularly attractive in problems with moving interfaces since no remeshing is necessary.

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References

  1. A. I. Fedoseyev, M. J. Friedman, and E. J. Kansa, Improved multiquadric method for elliptic partial differential equations via PDE collocation on the Boundary, Comput. Math. Appl., 43 (2002), 439–455.

    Article  MATH  MathSciNet  Google Scholar 

  2. B. Fornberg, T. A. Driscoll, G. Wright and R. Charles, Observation of the behavior of radial basis function approximations near boundaries, Comput. Math. Appl., 43 (2002), 473–490.

    Article  MATH  MathSciNet  Google Scholar 

  3. R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res., 176 (1971), 1905–1915.

    Google Scholar 

  4. C. A. Hieber and S. F. Shen, A finite-element/finite difference simulation of the injection-molding filling process, Journal of Non-Newtonian Fluid Mechanics, 7 (1979), 1–32.

    Article  Google Scholar 

  5. E. J. Holm and H. P. Langtangen, A unified finite element model for the injection molding process, Comput. Methods Appl. Mech. Engrg., 178 (1999), 413–429.

    Article  MATH  Google Scholar 

  6. E. J. Kansa, Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates, Comput. Math. Appls., 19 (1990), 127–145.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. J. Kansa, Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations, Comput. Math. Appls., 19 (1990), 147–161.

    Article  MATH  MathSciNet  Google Scholar 

  8. T. H. Kwon and J. B. Park, Finite element analysis modeling of powder injection molding filling process including yield stress and slip phenomena, Polymer Engineering and Science, 35 (1995), 741–753.

    Article  MathSciNet  Google Scholar 

  9. J. Moody and C. J. Daken, Fast learning in networks of locally-tuned processing units, Neural Comput., 1 (1989), 281–294.

    Article  Google Scholar 

  10. W. Noh and PC. Woodward, A simple line interface calculation, Proc. 5th Int. Conf. on Fluid Dynamics, Eds. A.I. vn de Vooran and P.J. Zandberger, Springer-Verlag (1976).

    Google Scholar 

  11. S. Osher and J. A. Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12–49.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces, Springer-Verlag (2003).

    Google Scholar 

  13. J. A. Sethian, Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision and materials science, Cambridge University Press (1999).

    Google Scholar 

  14. O. Verhoyen and F. Dupret, A simplified method for introducing the Cross viscosity law in the numerical simulation of Hele Shaw flow, Journal of Non-Newtonian Fluid Mechanics, 74 (1998), 25–46.

    Article  MATH  Google Scholar 

  15. I. Babuška, U. Banerjee, and J. E. Osborn, Meshless and Generalized Finite Element Methods: A Survey of Some Major Results, Meshfree Methods for Partial Differential Equations (M. Griebel and M. A. Schweitzer, eds.), Lecture Notes in Computational Science and Engineering, vol. 26, Springer, 2002, pp. 1–20.

    Google Scholar 

  16. T. Belytschko, Y. Y. Lu, and L. Gu, Element-free Galerkin methods, Int. J. Numer. Meth. Engrg. 37 (1994), 229–256.

    Article  MATH  MathSciNet  Google Scholar 

  17. D. Braess, Finite elements: Theory, fast solvers, and applications in solid mechanics, Cambridge University Press, 2001.

    Google Scholar 

  18. M. Griebel and M. A. Schweitzer (eds.), Meshfree Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, vol. 26, Springer, 2002

    Google Scholar 

  19. M. Griebel and M. A. Schweitzer (eds.), Meshfree Methods for Partial Differential Equations II, Lecture Notes in Computational Science and Engineering, vol. 43, Springer, 2005.

    Google Scholar 

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Bernal, F., Kindelan, M. (2007). An RBF Meshless Method for Injection Molding Modelling. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations III. Lecture Notes in Computational Science and Engineering, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46222-4_3

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