Effective construction of divergence-free wavelets on the square

Souleymane Kadri Harouna (1, 2) , Valérie Perrier (3)

1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
2 MIA - Mathématiques, Image et Applications - EA 3165
3 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

We present an effective construction of divergence-free wavelets on the square, with suitable boundary conditions. Since 2D divergence-free vector functions are the curl of scalar stream-functions, we simply derive divergence-free multiresolution spaces and wavelets by considering the curl of standard biorthogonal multiresolution analyses (BMRAs) on the square. The key point of the theory is that the derivative of a 1D BMRA is also a BMRA, as established by Jouini and Lemari'e-Rieusset [11]. We propose such construction in the context of generic compactly supported wavelets, which allows fast algorithms. Examples illustrate the practicality of the method.

Mots clés: Divergence-free wavelets; biorthogonal multiresolution analyses; Dirichlet boundary conditions

Domaines: Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Souleymane Kadri Harouna, Valérie Perrier. Effective construction of divergence-free wavelets on the square. Journal of Computational and Applied Mathematics, 2013, 240, pp.74-86. ⟨10.1016/j.cam.2012.07.029⟩. ⟨hal-00727038⟩