Finite element handbook
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Resultant fields for mixed plate bending elements
Computer Methods in Applied Mechanics and Engineering
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 other bases for fast numerical linear algebra
Wavelets: a tutorial in theory and applications
Orthonormal wavelets, analysis of operators, and applications to numerical analysis
Wavelets: a tutorial in theory and applications
Orthonormal wavelet bases adapted for partial differential equations with boundary conditions
SIAM Journal on Mathematical Analysis
Wavelet methods for PDEs — some recent developments
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Connection coefficients on an interval and wavelet solutions of Burgers equation
Journal of Computational and Applied Mathematics
Wavelet-Galerkin method for solving parabolic equations in finite domains
Finite Elements in Analysis and Design
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
Identification of crack in a rotor system based on wavelet finite element method
Finite Elements in Analysis and Design
A study of multiscale wavelet-based elements for adaptive finite element analysis
Advances in Engineering Software
Hi-index | 7.29 |
An important property of wavelet multiresolution analysis is the capability to represent functions in a dynamic multiscale manner, so the solution in the wavelet domain enables a hierarchical approximation to the exact solution. The typical problem that arises when using Daubechies wavelets in numerical analysis, especially in finite element analysis, is how to calculate the connection coefficients, an integral of products of wavelet scaling functions or derivative operators associated with these. The method to calculate multiscale connection coefficients for stiffness matrices and load vectors is presented for the first time. And the algorithm of multiscale lifting computation is developed. The numerical examples are given to verify the effectiveness of such a method.