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

Carlo Cattani

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.

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DOI: http://dx.doi.org/10.1478/C1A0802003