Master's Dissertation
DOI
10.11606/D.45.2009.tde-02082009-192253
Document
Author
Full name
Pedro da Silva Peixoto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2009
Supervisor
Committee
Barros, Saulo Rabello Maciel de (President)
Gomes, Sonia Maria
Miranda, José Carlos Simon de
Title in Portuguese
Resolução numérica de EDPs utilizando ondaletas harmônicas
Keywords in Portuguese
Método de Galerkin
método espectral
método pseudo-espectral
modelo de propagação de frentes de precipitação.
ondaletas
ondaletas harmônicas
Abstract in Portuguese
Title in English
Numerical resolution of partial differential equations using harmonic wavelets
Keywords in English
Galerkin-Wavelet method
harmonic wavelets
precipitation front propagation model.
pseudo-spectral method
spectral method
wavelets
Abstract in English
Numerical methods to solve partial differential equations based on wavelets have been developed in the last two decades, but there is a lack of studies on their computational characteristics. In this study a Galerkin spectral method using harmonic wavelets base has been thoroughly analyzed. We performed a review on the mathematics of harmonic wavelets, that showed a great similarity with Fourier basis. Several numerical experiments were made. Analyzing the use of the Galerkin method, with harmonic wavelets, on linear and non linear transport equations, we achieved good approximations in respect to the expected solution. The computational cost resulted to be similar to the same method with Fourier basis. On the other hand, employing harmonic wavelets we were able to obtain local information of the solution by simple inspection of the spectral coeffcients. We also analyzed a pseudo-spectral method based on harmonic wavelets for the non linear equations, resulting in a great improvement in efficiency. Looking towards using the locality propriety of harmonic wavelets, we tested the Galerkin method on a precipitation front propagation model. The method resulted in good approximations to the expected solution, optimal computational cost and the possibility of obtaining information on the locality of the precipitation fronts spectrally.