Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and related applications
Résumé
This paper presents a new construction of homogeneous Dirichlet wavelet basis on the unit interval, linked by a diagonal differentiation-integration relation to a standard biorthogonal wavelet basis. This new wavelet basis allows to compute the solution of the Poisson equation only by a wavelet coefficient renormalization - like in Fourier domain -, which yields a linear complexity O(N) for this problem. Another application concerns the construction of free-slip divergence-free wavelet bases of the hypercube, in general dimension, with an associated decomposition algorithm as simple as in the periodic case.
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