Wavelet transforms are recent mathematical techniques, based on group theory and square
integrable representations, which allows one to unfold a signal, or a field, into both space …

In this paper an overview of wavelet based multiresolution analyses is presented. First, the
continuous wavelet transform in its simplest form is discussed. Then, the definition of a …

More than anything else, the increase of computing power seems to stimulate the greed for
tackling ever larger problems involving large-scale numerical simulation. As a consequence …

We have used wavelet transform techniques to analyze, model, and compute turbulent
flows. The theory and open questions encountered in turbulence are presented. The wavelet …

Publisher Summary This chapter explains basic examples of wavelet methods in numerical
analysis. It introduces the approximations and shows show the way they are related to …

We describe a wavelet collocation method for the numerical solution of partial differential
equations which is based on the use of the autocorrelation functions of Daubechie's …

The Wavelet Element Method (WEM) combines biorthogonal wavelet systems with the
philosophy of Spectral Element Methods in order to obtain a biorthogonal wavelet system on …

A dynamically adaptive multilevel wavelet collocation method is developed for the solution
of partial differential equations. The multilevel structure of the algorithm provides a simple …

We present a new adaptive numerical scheme for solving parabolic PDEs in Cartesian
geometry. Applying a finite volume discretization with explicit time integration, both of …

This paper is concerned with recent developments of wavelet schemes for the numerical
treatment of operator equations with special emphasis on two issues: adaptive solution …