H-p Clouds - An h-p Meshless Method

Numerical Methods for Partial Differential Equations

Volumn 12, Issue 6, 1996, Pages 673-705

  Armando Duarte, C ^a   Tinsley Oden, J ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1542580610     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1098-2426(199611)12:6<673::aid-num3>3.0.co;2-p     Document Type: Article

References (34)

1. T. Belytschko, Y. Y. Lu, and L. Gu, "Crack propagation by element free Galerkin methods," in Advanced Computational Methods for Material Modeling, p. 191, 1993. AMD-Vol. 180/PVP-Vol. 268, ASME 1993.
2. Tadeusz Liszka, "An interpolation method for an irregular net of nodes," Inter. J. Numer. Meth. Eng. 20, 1599 (1984).
3. Tadeusz Liszka and J. Orkisz, "Finite difference method for arbitrary irregular meshes in nonlinear problems of applied mechanics," in IV SMiRt, San Francisco, 1977.
4. Tadeusz Liszka and J. Orkisz, "The finite difference method at arbitrary irregular grids and its application in applied mechanics," Comput. Struct. 11, 83 (1980).
5. R. A. Gingold and J. J. Monaghan, "Kernel estimates as a basis for general particle methods in hydrodynamics," J. Comp. Phys. 46, 429 (1982).
6. L. B. Lucy, "A numerical approach to the testing of the fission hypothesis," Astron. J. 82, 1013 (1977).
7. J. J. Monaghan, "Why particle methods work," SIAM J. Sci. Stat. Comput. 3, 422 (1982).
8. J. J. Monaghan, "An introduction to sph," Comp. Phys. Comm. 48, 89 (1988).
9. B. Nayroles, G. Touzot, and P. Villon, "Generalizing the finite element method: Diffuse approximation and diffuse elements," Comp. Mech. 10, 307 (1992).
10. T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free Galerkin methods," Int. J. Num. Meth. Eng. 37, 229 (1994).
11. K. Amarantuga, J. R. Williams, S. Qian, and J. Weis, "Wavelet-Galerkin solutions for one-dimensional partial differential equations," Int. J. Num. Meth. Eng. 37, 2703 (1994).
12. R. Glowinski, M. Lawton, M. Ravachol, and E. Tenenbaum, "Wavelet solutions of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension," in 9th Int. Conf. on Numerical Methods in Applied Sciences and Engineering, SIAM, Philadelphia, 1990.
13. Sam Qian and J. Weiss, "Wavelet and the numerical solution of partial differential equations," J. Comp. Phys. 106, 155 (1993).
14. E. J. Kansa, "Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics - i surface approximations and partial derivative estimates," Comput. Math. Appl. 19, 127 (1990).
15. 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. Appl. 19, 147 (1990).
16. Wing Kam Liu and Yijung Chen, "Wavelet and multiple scale reproducing kernel methods," Inter. J. Num. Meth. Fluids, to appear.
17. Wing Kam Liu, Sukky Jun, Shaofan Li, Jonathan Adee, and Ted Belytschko, "Reproducing kernel particle methods for structural dynamics," Inter. J. Num. Meth. Eng., to appear.
18. Genki Yagawa, "Some remarks on free mesh method: A kind of meshless finite element method," in International Conference on Computational Engineering Science, Hawaii, August 1995.
19. P. Lancaster and K. Salkauskas, "Surfaces generated by moving least squares methods," Math. Comp. 37, 141 (1981).
20. P. Lancaster and K. Salkauskas, Curve and Surface Fitting, an Introduction, Academic Press, San Diego, 1986.
21. C. A. M. Duarte, "A review of some meshless methods to solve partial differential equations," Technical Report 95-06, TICAM, The University of Texas at Austin, 1995.
22. J. W. Swegle, S. W. Attaway, M. W. Heinstein, F. J. Mello, and D. L. Hicks, "An analysis of the smoothed particle hydrodynamics," Technical Report SAND93-2513 UC-705, Sandia, 1994.
23. Y. Y. Lu, Ted Belytschko, and M. Tabbara, "Element-free Galerkin method for wave propagation and dynamic fracture," Comput. Meth. Appl. Mech. Eng., to appear.
24. Richard Franke, "Scattered data interpolation: Test of some methods," Math. Comp. 38, 181 (1982).
25. Y. Y. Lu, T. Belytschko, and L. Gu, "A new implementation of the element free Galerkin method," Comput. Meth. Appl. Mech. Eng. 113, 397 (1994).
26. Mark Ainsworth, Personal communication, 1994.
27. C. A. M. Duarte and J. T. Oden, "Hp clouds - a meshless method to solve boundary-value problems" Technical Report 95-05, TICAM, The University of Texas at Austin, 1995.
28. R. Adams, Sobolev Spaces. Academic Press, Boston, 1978.
29. D. Shepard, "A two-dimensional function for irregularly spaced data," in ACM Nat. Conf. p. 517, 1968.
30. T. Belytschko and S. Beissel, "Nodal integration of the element-free Galerkin method," pre-print, 1995.
31. Philippe G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
32. J. T. Oden and G. F. Carey, Texas Finite Element Series Volume IV - Mathematical Aspects, Prentice-Hall, New Jersey, 1983.
33. I. Babuska and W. C. Rheinboldt, "Error estimates for adaptive finite element computations," SIAM J. Num. Anal. 15, 736 (1978).
34. J. M. Melenk, "On Generalized Finite Element Methods," Ph. D. thesis, The University of Maryland, 1995.