A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Wavelet methods for fast resolution of elliptic problems
SIAM Journal on Numerical Analysis
On the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis
Using the refinement equation for evaluating integrals of wavelets
SIAM Journal on Numerical Analysis
Wavelets and the numerical solution of partial differential equations
Journal of Computational Physics
On the wavelet based differentiation matrix
Journal of Scientific Computing
Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions
SIAM Journal on Numerical Analysis
On the spline-based wavelet differentiation matrix
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Orthonormal wavelet bases adapted for partial differential equations with boundary conditions
SIAM Journal on Mathematical Analysis
Multiresolution schemes on triangles for scalar conservation laws
Journal of Computational Physics
Second-generation wavelet collocation method for the solution of partial differential equations
Journal of Computational Physics
Wavelet methods for PDEs — some recent developments
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A fully adaptive wavelet algorithm for parabolic partial differential equations
Applied Numerical Mathematics
Wavelet-Galerkin method for solving parabolic equations in finite domains
Finite Elements in Analysis and Design
Wavelet Least Squares Methods for Boundary Value Problems
SIAM Journal on Numerical Analysis
Towards a Realization of a Wavelet Galerkin Method on Non-Trivial Domains
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Wavelet applications to the Petrov--Galerkin method for Hammerstein equations
Applied Numerical Mathematics
Parallel iterative solvers involving fast wavelet transforms for the solution of BEM systems
Advances in Engineering Software - Engineering computational technology
A study of the construction and application of a Daubechies wavelet-based beam element
Finite Elements in Analysis and Design
The construction of wavelet finite element and its application
Finite Elements in Analysis and Design
An adaptive multilevel wavelet collocation method for elliptic problems
Journal of Computational Physics
Wavelet-Galerkin approximation of linear translation invariant operators
ICASSP '91 Proceedings of the Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference
Adaptive multiresolution finite element method based on second generation wavelets
Finite Elements in Analysis and Design
Identification of crack in a rotor system based on wavelet finite element method
Finite Elements in Analysis and Design
A modified wavelet approximation of deflections for solving PDEs of beams and square thin plates
Finite Elements in Analysis and Design
Review: Meshless methods: A review and computer implementation aspects
Mathematics and Computers in Simulation
A study of multiscale wavelet-based elements for adaptive finite element analysis
Advances in Engineering Software
A spline wavelet finite element formulation of thin plate bending
Engineering with Computers
Implementation of an hybrid-mixed stress model based on the use of wavelets
Computers and Structures
A multivariable wavelet-based finite element method and its application to thick plates
Finite Elements in Analysis and Design
A dynamic multiscale lifting computation method using Daubechies wavelet
Journal of Computational and Applied Mathematics
Multi-scale Daubechies wavelet-based method for 2-D elastic problems
Finite Elements in Analysis and Design
A second generation wavelet based finite elements on triangulations
Computational Mechanics
Multiscale modelling of bubbly systems using wavelet-based mesh adaptation
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Finite Elements in Analysis and Design
Structural dynamic analysis using hybrid and mixed finite element models
Finite Elements in Analysis and Design
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Wavelet analysis is a new method called 'numerical microscope' in signal and image processing. It has the desirable advantages of multi-resolution properties and various basis functions, which fulfill an enormous potential for solving partial differential equations (PDEs). The numerical analysis with wavelet received its first attention in 1992, since then researchers have shown growing interest in it. Various methods including wavelet weighted residual method (WWRM), wavelet finite element method (WFEM), wavelet boundary method (WBM), wavelet meshless method (WMM) and wavelet-optimized finite difference method (WOFD), etc. have acquired an important role in recent years. This paper aims to make a comprehensive review and classification on wavelet-based numerical analysis and to note their merits, drawbacks, and future directions. And thus the present review helps readers identify research starting points in wavelet-based numerical analysis and guides researchers and practitioners.