Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and related applications
Résumé
This paper presents a new construction of a homogeneous Dirichlet wavelet basis on the unit interval, linked by a diagonal differentiation-integration relation to a standard biorthogonal wavelet basis. This allows to compute the solution of Poisson equation by renormalizing the wavelet coefficients - as in Fourier domain but using locally supported basis functions with boundary conditions-, 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.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...