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.
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Harouna, S.K., Perrier, V. (2012). Helmholtz-Hodge Decomposition on [0,1]d by Divergence-Free and Curl-Free Wavelets. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27413-8_20
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DOI: https://doi.org/10.1007/978-3-642-27413-8_20
Publisher Name: Springer, Berlin, Heidelberg
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