Multiresolution analysis for finite element method using interpolating wavelet and lifting scheme

Communications in Numerical Methods in Engineering

Volumn 24, Issue 11, 2008, Pages 1045-1066

  He, Yumin ^a   Chen, Xuefeng ^a   Xiang, Jiawei ^a   He, Zhengjia ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Finite element method; Interpolating; Lifting scheme; Multiresolution analysis

Indexed keywords

ADAPTIVE ALGORITHMS; MULTIRESOLUTION ANALYSIS; STIFFNESS MATRIX; WAVELET TRANSFORMS;

APPROXIMATION SPACES; FIELD PROBLEMS; FINITE ELEMENT EQUATIONS; FINITE ELEMENTS; INTERPOLATING; INTERPOLATING WAVELETS; INTERPOLATION FUNCTIONS; LIFTING SCHEME; NUMERICAL EXAMPLES;

FINITE ELEMENT METHOD;

EID: 57749188883     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.1011     Document Type: Article

References (16)

1. Mallat SG. The theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 1989; 11(7):674-693.
2. Ko J, Kurdila AJ, Pilant MS. A class of finite element methods based on orthonormal, compactly supported wavelets. Computational Mechanics 1995; 16:235-244.
3. Chen XF, Yang SJ, Ma JX, He ZJ. The construction of wavelet finite element and its application. Finite Elements in Analysis and Design 2004; 40:541-554.
4. Han JG, Ren WX, Huang Y. A spline wavelet finite-element method in structural mechanics. International Journal for Numerical Methods in Engineering 2006; 66:166-190.
5. Sweldens W. The lifting scheme: a construction of second generation wavelets. SIAM Journal on Mathematical Analysis 1998; 29(2):511-546.
6. Sweldens W. The lifting scheme: a custom-design construction of biorthogonal wavelets. Applied and Computational Harmonic Analysis 1996; 3(2): 186-200.
7. Sweldens W, Schröder P. Building your own wavelets at home. Wavelets in Computer Graphics. ACM SIGGRAPH Course Notes. ACM: New York, 1996; 15-87.
8. D'Heedene S, Amaratunga K, Castrillón-Candás JE. Generalized hierarchical bases: a Wavelet-Ritz-Galerkin framework for Lagrangian FEM. Engineering Computations: International Journal for Computer-aided Engineering and Software 2005; 22(1):15-37.
9. Amaratunga K, Sudarshan R. Multiresolution modeling with operator-customized wavelets derived from finite elements. Computer Methods in Applied Mechanics and Engineering 2006; 195:2509-2532.
10. Sudarshan R, Amaratunga K, Grätsch T. A combined approach for goal-oriented error estimation and adaptivity using operator-customized finite element wavelets. International Journal for Numerical Methods in Engineering 2006; 66:1002-1035.
11. Mallat S. A Wavelet Tour of Signal Processing. China Machine Press: Beijing, 2003.
12. Donoho DL. Interpolating wavelet transforms. Technical Report 408, Department of Statistics, Stanford University, 1992.
13. Harten A. Adaptive multiresolution schemes for shock computations. Journal of Computational Physics 1994; 115:319-338.
14. Deslauriers G, Dubuc S. Interpolation dyadique. Fractals, Dimensions Non Entières et Applications. Masson: Paris, 1987; 44-55.
15. Deslauriers G, Dubuc S. Symmetric iterative interpolation processes. Constructive Approximation 1989; 5(1): 49-68.
16. Carnicer J, Dahmen W, Peña J. Local decompositions of refinable spaces. Applied and Computational Harmonic Analysis 1996; 3:125-153.