===affil2:
LLNL
===firstname:
ILYA
===firstname4:

===firstname3:

===lastname2:
VASSILEVSKI
===lastname:
LASHUK
===firstname5:

===affil6:

===lastname3:

===email:
LASHUK2@LLNL.GOV
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===affil7:

===firstname7:

===postal:
7000 East Ave, L-560
LIVERMORE, CA, 94550
===firstname6:

===ABSTRACT:
\newcommand{\dvg}{\mathbf{div}}
\newcommand{\curl}{\mathbf{curl}}
\def\Nedelec{N\'ed\'elec}

We present a technique based on element agglomeration for constructing coarse subspaces of:
(a) the lowest order tetrahedral \Nedelec~ space, and (b) the scalar piecewise-linear finite element
space, in both cases assuming general unstructured mesh. The constructed coarse spaces, together with coarse $H(\dvg)$ and $L_2$ 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 \Nedelec~ 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.
===affil3:

===lastname5:

===affilother:

===title:
COARSE DE RHAM COMPLEXES WITH IMPROVED APPROXIMATION PROPERTIES
===firstname2:
PANAYOT