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Computer Methods in Applied Mechanics and Engineering
Volume 116, Issues 1-4 , 1994, Pages 301-307

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Copyright © 1994 Published by Elsevier B.V.

Towards a method for solving partial differential equations by using wavelet packet bases

Pascal Jolya, Yvon Madaya and Valérie Perrierb

aLaboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France
bURA 742 CNRS, Université Paris Nord, et Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France

Available online 7 March 2005.


Abstract

In this paper we present a new methodology based on the wavelet packet concept, in order to define an adaptive method for the approximation of partial differential equations. The wavelet packet framework allows us to define the notion of a minimal basis that has proven to be an efficient procedure for data compression. The purpose here is to take benefit of this compression to represent accurately and economically the solution of a time dependent PDE. The time discretization is a standard multistep scheme. The spacial discretization is defined by inferring a reduced basis for the solution at the new time step, from the knowledge of the previous ones.



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Computer Methods in Applied Mechanics and Engineering
Volume 116, Issues 1-4 , 1994, Pages 301-307


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