Conservative interpolation of edge and face data on n dimensional structured grids using differential forms

Interpolation methods for edge and face centered data are described, which preserve line and area integrals under regridding. These interpolation methods complement the multilinear nodal and conservative interpolation methods, which are widely used in climate data processing and other areas. The presented interpolation schemes ensure that curl-free and divergence-free fields remain so after regridding. These edge and face conservative interpolation methods are suitable for general curvilinear structured grids, including those with singular points (poles). Support for masked (invalid) regions is implicitly provided by attaching (partial) line/surface integral field values to cell edges/faces.