  The analysis of vector fields is crucial for the understanding of several
physical phenomena, such as natural events (e.g., analysis of waves), diffusive
processes, electric and electromagnetic fields. While previous work has been
focused mainly on the analysis of 2D or 3D vector fields on volumes or
surfaces, we address the meshless analysis of a vector field defined on an
arbitrary domain, without assumptions on its dimension and discretisation. The
meshless approximation of the Helmholtz-Hodge decomposition of a vector field
is achieved by expressing the potential of its components as a linear
combination of radial basis functions and by computing the corresponding
conservative, irrotational, and harmonic components as solution to a
least-squares or to a differential problem. To this end, we identify the
conditions on the kernel of the radial basis functions that guarantee the
existence of their derivatives. Finally, we demonstrate our approach on 2D and
3D vector fields measured by sensors or generated through simulation.
