We present a technique based on element agglomeration for constructing
coarse subspaces of:
(a) the lowest order tetrahedral Nédélec space, and (b) the scalar
piecewise-linear finite element
space, in both cases assuming general unstructured mesh. The constructed
coarse spaces, together with coarse
and
spaces described
in our previous work,
form an exact sequence with respect to the exterior
derivative operators (for domains homeomorphic to a ball). The constructed
coarse counterparts of the Nédélec and Raviart-Thomas spaces locally
contain the vector constant functions,
whereas the respective coarse version of the scalar piecewise-linear
space locally contains all linear functions.
These properties hold regardless of the shape of the agglomerates, as
long as each agglomerate stays
homeomorphic to a ball (which is easily ensured in practice).
We illustrate the approximation properties of the constructed coarse
spaces as well as the convergence
of respective two-level AMGe methods associated with them.