Multiresolution Reproducing Kernel Particle Methods in acoustics

Journal of Computational Acoustics

Volumn 5, Issue 1, 1997, Pages 71-94

  Uras, R A ^a   Chang, C T ^b   Chen, Y ^b   Liu, W K ^b  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031506587     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X9700006X     Document Type: Article

References (16)

1. W. K. Liu and C. Oberste-Brandenburg, "Reproducing kernel and wavelet particle methods," in Aerospace Structures: Nonlinear Dynamics and System Response, eds. J. P. Cusumano, C. Pierre and S. T. Wu, AD 33, ASME (1993), pp. 39-56.
2. W. K. Liu, S. Jun and Y. F. Zhang, "Reproducing kernel particle methods," Int. J. Numerical Methods in Fluids 20 (1995), 1081-1106.
3. W. K. Liu, J. Adee and S. Jun, "Reproducing kernel particle methods for elastic and plastic problems," in Advanced Computational Methods for Material Modeling, eds. D. J. Benson and R. A. Asaro, AMD 180 and PVP 268, ASME (1993), pp. 175-190.
4. W. K. Liu, S. Jun, S. Li, J. Adee and T. Belytschko, "Reproducing kernel particle methods for structural dynamics," Int. J. Numerical Methods in Engineering 38 (1994), 1655-1679.
5. G. R. Beklkin, I. Coifman, S. Daubechies, Y. Mallat, L. R. Meyer and B. Ruskai, (eds.), Wavelets and Their Applications (Cambridge, MA, 1992), and references therein.
6. C. K. Chui, An Introduction to Wavelets (Academic Press, 1992), and references therein.
7. W. K. Liu and Y. J. Chen, "Wavelet and multiple scale reproducing kernel methods," Int. J. Numerical Methods in Fluids 21 (1994), 901-932.
8. S. Mallat, "Multi-resolution approximations and wavelet orthogonal bases of L2(R)," Trans. Amer. Math. Soc. 315 (1989), 69-87.
9. G. Strang, "Wavelets and dilation equations: A brief introduction," SIAM Review 31 (1989), 614-627.
10. J. J. Monaghan, "Introduction to SPH," Comp. Phys. Comm. 48 (1988), 89-96.
11. W. K. Liu, Y. Chen, S. Jun, J. S. Chen, T. Belytschko, C. Pan, R. A. Uras and C. T. Chang, "Overview and applications of the reproducing kernel particle methods," Archives of Computational Methods in Engineering, State of the Art Reviews 3 (1996), 3-80.
12. I. Babuska and A. Miller, "A feedback finite element method with a Posteriori error estimation," Computer Methods in Applied Mechanics and Engineering 61 (1987), 1-40.
13. J. T. Oden, "Parallel adaptive hp-finite element methods for problems in fluid and solid mechanics," in Recent Developments in Finite Element Analysis, A Book Dedicated to Robert L. Taylor, eds. T. J. R. Hughes, E. Onate and O. C. Zienkiewicz (1994), pp. 29-36.
14. M. Shephard, C. L. Bottasso, H. L. De Cougny and O. Ozturan, "Parallel adaptive hp-finite element analysis of fluid flows on distributed memory computers," in Recent Developments in Finite Element Analysis, A Book Dedicated to Robert L. Taylor, eds. T. J. R. Hughes, E. Onate and O. C. Zienkiewicz (1994), pp. 205-214.
15. O. C. Zienkiewicz and J. Z. Zhu, "The superconvergent patch recovery and a posteriori error estimates," Int. J. Numerical Methods 33 (1992), 1331-1364.
16. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in FORTRAN (Cambridge, University Press, 1992).