Helmholtz-Hodge Decomposition on [0; 1]d by Divergence-free and Curl-free Wavelets

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

1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

This paper deals with the Helmholtz-Hodge decomposition of a vector field in bounded domain. We present a practical algorithm to compute this decomposition in the context of divergence-free and curl- free wavelets satisfying suitable boundary conditions. The method requires the inversion of divergence-free and curl-free wavelet Gram matrices. We propose an optimal preconditioning which allows to solve the systems with a small number of iterations. Finally, numerical examples prove the accuracy and the efficiency of the method.

Mots clés: Divergence-free and curl-free wavelets; Helmholtz-Hodge decomposition

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

Souleymane Kadri Harouna, Valérie Perrier. Helmholtz-Hodge Decomposition on [0; 1]d by Divergence-free and Curl-free Wavelets. 7th International Conference on Curves and Surfaces, Jun 2010, Avignon, France. pp.311-329, ⟨10.1007/978-3-642-27413-8_20⟩. ⟨hal-00558479⟩