The construction of 1D wavelet finite elements for structural analysis

Computational Mechanics

Volumn 40, Issue 2, 2007, Pages 325-339

  Xiang, J W ^a   Chen, X F ^a   He, Z J ^a   Dong, H B ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

B spline wavelet on the interval; Lifting scheme; Transformation matrix; Wavelet finite elements

Indexed keywords

FINITE ELEMENT METHOD; FUNCTIONS; INTERPOLATION; NUMERICAL METHODS; ONE DIMENSIONAL; POLYNOMIALS;

B-SPLINE WAVELET ON THE INTERVAL (BSWI); LIFTING SCHEMES; TRANSFORMATION MATRIX; WAVELET FINITE ELEMENTS;

WAVELET ANALYSIS;

EID: 34247550722     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-006-0102-5     Document Type: Article

References (21)

1. Mallat SG (1999) A wavelet tour of signal processing. Academic, New York
2. Dahmen W (2001) Wavelet methods for PDEs - some recent developments. J Compt Appl Math 128: 133-185
3. Cohen A (2003) Numerical analysis of wavelet method. Elsevier, Amsterdam
4. Canuto C, Tabacco A, Urban K (1999) The wavelet element method part I: construction and analysis. Appl Comput Harmon A 6: 1-52
5. Canuto C, Tabacco A, Urban K (2000) The wavelet element method part II: realization and additional feature in 2D and 3D. Appl Comput Harmon A 8: 123-165
6. Chen WH, Wu CW (1995) Spline wavelets element method for frame structures vibration. Comput Mech 16(1): 11-21
7. Chen WH, Wu CW (1996) Extension of spline wavelets element method to membrane vibration analysis. Comput Mech 18(1): 46-54
8. Zhou YH, Wang JZ, Zheng XJ (1998) Application of wavelet Galerkin FEM to bending of beam and plate structures. Appl Math Mech 19(8): 697-706
9. Ko J, Kurdila AJ, Pilant MS (1995) A class of finite element methods based on orthonormal, compactly supported wavelets. Comput Mech 16: 235-244
10. Basu PK, Jorge AB, Badri S, Lin J (2003) Higher-order modeling of continua by finite-element, boundary-element, Meshless, and wavelet methods. Comput Math Appl 46: 15-33
11. Ma JX, Xue JJ, Yang SJ, He ZJ (2003) A study of the construction and application of a Daubechies wavelet-based beam element. Finite Elem Anal Des 39: 965-975
12. Chen XF, Yang SJ, Ma JX, He ZJ (2004) The construction of wavelet finite element and its application. Finite Elem Anal Des 40: 541-554
13. Bertoluzza S, Naldi G, Ravel JC (1994) Wavelet methods for the numerical solution of boundary value problems on the interval. In: Chui CK, Montefusco L, Puccio L (eds) Wavelets: theory, algorithms, and applications. Academic, New York, pp 425-448
14. Chui CK, Quak E (1992) Wavelets on a bounded interval. Numer Meth Approx Theory 1: 53-57
15. Quak E, Weyrich N (1994) Decomposition and reconstruction algorithms for spline wavelets on a Bounded interval. Appl Comput Harmon A 1(3): 217-231
16. Goswami JC, Chan AK, Chui CK (1995) On solving first-kind integral equations using wavelets on a bounded interval. IEEE T Antenn Propag 43: 614-622
17. Wang XC (2002) The finite element methods (in Chinese). Tsing Hua University Press, Beijing
18. Sapountzakis EJ, Mokos VG (2005) A BEM solution to transverse shear loading of beams. Comput Mech 36: 384-397
19. Ma J, Yang S, Xue J, He Z (2000) Nonlinear finite element analysis of paper movement in air. Int J Plant Eng Manage 5(2): 55-61
20. Dahmen W, Kurdila A, Oswald P (1997) Multiscale wavelet for partial differential equations. Academic San Diego
21. Chen X, He Z, Xiang J, U B (2006) A dynamic multiscale lifting computation method using Daubechies wavelet. J Compt Appl Math 188(2): 228-245