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   -> Volume 3, Issue 18


Preprints: Wavelet-Galerkin methods
 
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Juan Restrepo (restrepo@mcs.anl.gov)
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PostPosted: Mon Dec 02, 2002 1:28 pm    
Subject: Preprints: Wavelet-Galerkin methods
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Preprints: Wavelet-Galerkin methods

The following preprints are available through the web:

http://www.mcs.anl.gov/home/restrepo/

Title: Wavelet-Galerkin Discretization of Hyperbolic Equations

Author: Juan Mario Restrepo, Gary Leaf
Abstract: The relative merits of the wavelet-Galerkin solution of hyperbolic
partial differential equations, typical of geophysical problems, are
quantitatively and qualitatively compared to traditional finite
difference and Fourier-pseudo-spectral methods. The wavelet-Galerkin
solution presented here is found to be a viable alternative to the
two conventional techniques.

Title: Periodized Daubechies Wavelets

Author: Juan Mario Restrepo, Gary Leaf, George Schlossnagle
Abstract: The properties of periodized Daubechies wavelets on $[0,1]$ are
detailed and contrasted with their counterparts which form a basis
for $L^2 (Bbb R)$. Numerical examples illustrate the
analytical estimates for convergence and demonstrate by
comparison with Fourier spectral methods the superiority of wavelet
projection methods for approximations. The analytical
solution to inner products of periodized wavelets and their
derivatives, which are known as connection coefficients, is presented,
and their use is illustrated in the approximation of two commonly used
differential operators. The periodization of the connection
coefficients in Galerkin schemes is presented in detail.

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