Before revision:  The method is based on novel results for  smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet  .
After revision:  The method is based on novel results for the smooth and discrete Hodge-Morrey-Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into the five components: gradient (curl-free), co-gradient (divergence-free), and three harmonic fields induced from the boundary : center, Neumann and Dirichlet .