Abstract: Divergence-free wavelets with tangential boundary plays an important role in numerical simulation of vector fields. In view of the zero boundary and the simple structure of Hardin-Marasovich wavelets, a class of three-dimensional isotropic divergence-free wavelets with tangential boundary are studied. Firstly, based on differential relations of Hardin-Marasovich wavelet functions, it is proved that the bi-orthogonal projection of divergence-free vector fields is still divergence-free. Then, the definition of isotropic divergence-free scale functions are given based on the characterization of divergence-free space, and the corresponding divergence-free scale spaces are proved to form a multiresolution analysis. Finally, the isotropic divergence-free multiwavelets are defined, and the relation between the decomposition coefficients of the divergence-free wavelets and the classical wavelets is given, which shows that the divergence-free decomposition coefficients can be fastly computed.

Key words: divergence-free, multiwavelets, tangential boundary, isotropic