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   -> Volume 7, Issue 6


Thesis: Wavelets in Scientific Computing
 
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"Ole M. Nielsen" (ole.moller.nielsen@uni-c.dk)
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PostPosted: Mon Jun 08, 1998 3:22 pm    
Subject: Thesis: Wavelets in Scientific Computing
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#9 Thesis: Wavelets in Scientific Computing

Title: Wavelets in Scientific Computing

Author: Ole Moller Nielsen <uniomni@uni-c.dk>
Address: Technical University of Denmark
Building 304, DK-2800 Lyngby
URL: http://www.imm.dtu.dk/~omni
Advisors: Professor Vincent A. Barker <vab@imm.dtu.dk>
Professor Per Christian Hansen <pch@imm.dtu.dk>
Professor Mads Peter Sorensen <mps@imm.dtu.dk>

This dissertation revolves around the role of
wavelets in scientific computing and it falls into three parts:

Part I gives an exposition of the theory of orthogonal, compactly
supported wavelets in the context of multiresolution analysis. These
wavelets are particularly attractive because they lead to a stable and
very efficient algorithm, namely the fast wavelet transform (FWT). We
give estimates for the approximation characteristics of wavelets and
demonstrate how and why the FWT can be used as a front-end for
efficient image compression schemes.

Part II deals with vector-parallel implementations of several variants
of the Fast Wavelet Transform. We develop an efficient and scalable
parallel algorithm for the FWT and derive a model for its performance.

Part III is an investigation of the potential for using the special
properties of wavelets for solving partial differential equations
numerically. Several approaches are identified and two of them are
described in detail. The algorithms developed are applied to the
nonlinear Schrodinger equation and Burgers' equation. Numerical
results reveal that good performance can be achieved provided that
problems are large, solutions are highly localized, and numerical
parameters are chosen appropriately, depending on the problem in
question.

A copy of the thesis can be obtained from
http://www.imm.dtu.dk/~omni/thesis.html.
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