none: Do nothing during synchronization, prolongation, or restriction; the respective grid points remain untouched, and if not otherwise defined, remain undefined. This is
commonly used e.g. for integer values that are calculated or determined pointwise.
sync: Synchronize only, do nothing for prolongation or restriction. This is similarly useful e.g. for integer data.
restrict: Only synchronize and restrict from coarser to finer grids, do nothing during prolongation. For vertex centred data where restriction is an injection, this can also still be used for integer values. Otherwise this may be useful for data that are not needed in prolongation regions, but where the coarse grid has data worse than the fine grid, e.g. for constraints.
copy: Copy from the nearest neighbour instead of interpolating. This can likewise be used for integer data.
All other settings define actual prolongation operators.
-erik