A dynamic multiscale lifting computation method using Daubechies wavelet

Journal of Computational and Applied Mathematics

Volumn 188, Issue 2, 2006, Pages 228-245

  Chen, Xuefeng ^a   He, Zhengjia ^a   Xiang, Jiawei ^a   Li, Bing ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Connection coefficients; Daubechies Wavelet; Multiscale

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FINITE ELEMENT METHOD; FUNCTIONS; HIERARCHICAL SYSTEMS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; VECTORS; WAVELET TRANSFORMS;

CONNECTION COEFFICIENTS; DAUBECHIES WAVELET; MULTIRESOLUTION ANALYSIS; MULTISCALE;

COMPUTATIONAL METHODS;

EID: 28244494640     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.04.015     Document Type: Article

References (30)

1. M. Al-Qassab, and S. Nair Wavelet-Galerkin method for the free vibrations of an elastic cable carrying an attached mass J. Sound Vibrat. 270 2004 191 206
2. K. Amaratunga, J.R. Willianms, S. Qian, and J. Weiss Wavelet-Galerkin solution for one dimensional partial differential equations Internat. J. Numer. Methods Eng. 37 1994 2703 2716
3. S. Bertoluzza, and M. Verani Convergence of a nonlinear wavelet algorithm for the solution of PDEs Appl. Math. Lett. 16 2003 113 118
4. G. Beylkin On the representation of operators in bases of compactly supported wavelets SIMA J. Numer. Anal. 6 1992 1716 1740
5. A. Boggess, and F.J. Narcowich A First Course in Wavelets With Fourier Analysis 2001 Prentice Hall NJ
6. K.A. Bradley Wavelets and other based for fast numerical linear algebra C. Chui Wavelets: a Tutorial in Theory and Applications 1992 Academic Press New York 200 250
7. L. Castro, and J. Freitas Wavelets in hybrid-mixed stress elements Comput. Methods Appl. Mech. Eng. 190 2001 3977 3998
8. M.Q. Chen, C. Hwang, and Y.P. Shih The computation of wavelet-Galerkin approximation on a bounded interval Internat. J. Numer. Methods Eng. 39 1996 2921 2944
9. X.F. Chen, S.J. Yang, J.X. Ma, and Z.J. He The construction of wavelet finite element and its application Finite Elements Anal. Design 40 2004 541 554
10. M.A. Christon, and D.W. Roach Numerical performance of wavelets for PDEs: the multi-scale finite element Comput. Mech. 25 2000 230 244
11. A. Cohen Numerical Analysis of Wavelet Methods 2003 Elsevier North-Holland
12. W. Dahmen Wavelet methods for PDEs - some recent developments J. Comput. Appl. Math. 128 2001 133 185
13. W. Dahmen, and C. Micchelli Using the refinement equation for evaluating integrals of wavelets SIAM J. Numer. Anal. 30 1993 507 537
14. W. Dahmen, R. Schneider, and Y. Xu Nonlinear functionals of wavelet expansions - adaptive reconstruction and fast evaluation Numer. Math. 86 2000 21 48
15. I. Daubechies Orthonormal bases of compactly supported wavelets Commun. Pure Appl. Math. 41 1988 909 996
16. S.L. Ho, and S.Y. Yang Wavelet-Galerkin method for solving parabolic equations in finite domains Finite Elements Anal. Design 37 2001 1023 1037
17. G. Jang, J. Kim, and Y. Kim Multiscale Galerkin method using interpolation wavelets for two-dimensional elliptic problems in general domains Internat. J. Numer. Methods Eng. 59 2004 225 253
18. S. Jaffard, and P. Laurencot Orthonormal wavelets analysis of operators and applications to numerical analysis C. Chui Wavelets: a tutorial in theory and applications 1992 Academic Press New York 543 601
19. H. Kardestuncer Finite Element Handbook 1987 McGraw-Hill New York
20. J. Ko, A.J. Kurdila, and M.S. Pilant A class of finite element methods based on orthonormal, compactly supported wavelets Comput. Mech. 16 1995 235 244
21. J. Ko, A.J. Kurdila, and M.S. Pilant Triangular wavelet based finite elements via multivalued scaling equations Comput. Methods Appl. Mechanics Eng. 146 1997 1 17
22. B. Li, X.F. Chen, Z.J. He, Detection of crack location and size in structures using wavelet finite element methods, J. Sound Vibration, in press.
23. E.B. Lin, and X. Zhou Connection coefficients on an interval and wavelet solutions of Burgers equation J. Comput. Appl. Math. 135 2001 63 78
24. J.X. Ma, J.J. Xue, S.J. Yang, and Z.J. He A study of the construction and application of a Daubechies wavelet-based beam element Finite Elements Anal. Design 39 2003 965 975
25. S.G. Mallat A theory for multiresolution signal decomposition the wavelet representation IEEE Trans. Pattern Anal. Machine Intel. 11 1989 674 693
26. P. Monasse, and V. Perrier Orthonormal wavelet bases adapted for partial differential equations with boundary conditions SIAM J. Math. Anal. 29 1998 1040 1065
27. P.S. Vassilevski, and J.P. Wang The Wavelet-like methods in the design of efficient multilevel preconditioners for elliptic PDEs W. Dahmen Mutiscale Wavelet Methods for PDEs 1997 Academic Press San Diego 59 105
28. D. Wang, and J. Pan A wavelet-Galerkin scheme for the phase field model of microstructural evolution of materials Comput. Mater. Sci. 29 2004 221 242
29. S.L. Weissman, and R.L. Taylor Resultant fields for mixed plate bending elements Comput. Methods Appl. Mech. Eng. 79 1990 321 355
30. S.Y. Yang, and G.Z. Ni Wavelet-Galerkin method for computations of electromagnetic fields-computation of connection coefficients IEEE Trans. Magnetics 36 2000 644 648