The Wavelet Digest Homepage
Return to the homepage
Search the complete Wavelet Digest database
Help about the Wavelet Digest mailing list
About the Wavelet Digest
The Digest The Community
 Latest Issue  Back Issues  Events  Gallery
The Wavelet Digest
   -> Latest Issue


Thesis: Use of Wavelet Transform-based tools for numerical solution of differential equations
 
images/spacer.gifimages/spacer.gif Reply into Digest
Previous :: Next  
Author Message
Victoria Vampa (victoriavampa@gmail.com)
Guest





PostPosted: Tue Mar 20, 2012 11:45 am    
Subject: Thesis: Use of Wavelet Transform-based tools for numerical solution of differential equations
Reply with quote

Summary: The aim of this thesis is the development of tools and strategies based on wavelet transform to solve differential equations. At a first stage we analyze the feasibility and capability of using wavelet bases in the Finite Element method. In a second part, which is the most original aspect of this thesis, a new method is proposed to solve a second order coercive boundary value problem using B-cubic-spline functions in an efficient manner.

The aim of this thesis is the development of tools and strategies based on wavelet transform to solve differential equations.

At a first stage we analyze the feasibility and capability of using wavelet bases in the Finite Element method. In particular, for Mindlin-Reissner plate model, Daubechies Scaling Wavelet elements (DSWN) were designed. These elements can be easily constructed using independent interpolation of each displacement function. Due to orthonormality, compactly supported and nesting properties of the Daubechies wavelets, numerical results obtained with DSWN elements have very good accuracy and non-locking behavior.
Consequently, they are efficient for solving plate bending problems,
in both cases: thick and thin plates, and also when they are applied to problems having localized
singularities.

In a second part, which is the most original aspect of this thesis, a new method is proposed to solve a second order coercive boundary value problem using B-cubic-spline functions in an efficient manner.

This proposal combines variational equations with a collocation scheme using B-splines as scaling functions and yields an approximation at an initial scale. Bases of wavelets are designed in order to have a multiresolution structure on the interval. Then, a refinement process using wavelets is presented and convergence is proved. Bound of the approximation error are derived. Through the algorithm proposed, an improved solution
with minimal computational effort is obtained.

We present several numerical results showing the good behavior of the method. Approximate solutions are computed in scaling-spline form and improved with wavelets. Convergence of the solutions obtained using the proposed method are found to compare favorably to other numerical techniques.


keywords
Wavelet-finite element, beam element, plate element, B-spline functions, Multiresolution Analysis, Wavelet-Galerkin.

http://www.mate.unlp.edu.ar/tesis/tesis_VVampa.pdf
All times are GMT + 1 Hour
Page 1 of 1

 
Jump to: 
 


disclaimer - webmaster@wavelet.org
Powered by phpBB

This page was created in 0.025499 seconds : 19 queries executed : GZIP compression disabled