Helmholtz-Hodge decomposition on [0,1]d by divergence-free and curl-free wavelets

Authors:
Souleymane Kadri Harouna;Valérie Perrier
Affiliations:
Laboratoire Jean Kuntzmann, University of Grenoble, and CNRS, Grenoble Cedex 9, France;Laboratoire Jean Kuntzmann, University of Grenoble, and CNRS, Grenoble Cedex 9, France
Venue:
Proceedings of the 7th international conference on Curves and Surfaces
Year:
2010

Citing 7
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Abstract

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.