Harmonic wavelet solution of Poisson's problem with a localized source

Abstract

A method, based on a multiscale (wavelet) decomposition of the solution is proposed for the analysis of the Poisson problem. The solution is approximated by a finite series expansion of harmonic wavelets and is based on the computation of the connection coefficients. It is shown, how a sourceless Poisson's problem, solved with the Daubechies wavelets, can also be solved in presence of a localized source in the harmonic wavelet basis.