Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and related applications

Souleymane Kadri Harouna (1) , Valérie Perrier (2)

1 MIA - Mathématiques, Image et Applications - EA 3165
2 CVGI - Calcul des Variations, Géométrie, Image

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.

Mots clés: Divergence-free wavelets; wavelet on the interval; Poisson equations; Boundary condition

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Souleymane Kadri Harouna, Valérie Perrier. Homogeneous Dirichlet wavelets on the interval diagonalizing the derivative operator, and related applications. 2018. ⟨hal-01568431v2⟩