===affil2:
{Johannes Kepler University Linz, Asutria
===firstname:
Panayot
===firstname4:

===firstname3:
Umberto
===lastname2:
Neumueller
===keyword1:
AMG
===lastname:
Vassilevski
===firstname5:

===affil6:

===lastname3:
Villa
===email:
panayot@llnl.gov
===keyword2:
Discretization
===keyword_other2:
upscaling
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===competition:
no
===affil7:

===firstname7:

===postal:
Center for Applied Scientific Computing 
Lawrence Livermore National Laboratory
P.O. Box 808, L-561
Livermore, CA 94550, U.S.A.
===firstname6:

===ABSTRACT:
We consider time-dependent PDEs discretized in combined space-time domains. We first reduce the PDE to a first order system. Very often in practice, one of the equations of the reduced system involves the divergence operator (in space-time). 
The popular FOSLS (first order system least-squares) method is then applied modified by keeping the divergence equation as a constraint which we refer to as CFOSLS (constrained FOSLS). Applying finite elements to discretize the CFOSLS problem leads to a saddle-point system. To alleviate the high memory demand of the combined space-time approach (due to the increased dimension),
 we apply element agglomeration AMG upscaling on space-time elements. This leads to substantially reduced problem sizes with controlled accuracy.
Initial numerical results for model parabolic and scalar hyperbolic problems illustrate the potential of the method.

===affil3:
Center for Computational Geosciences and Optimization, UT Austin
===keyword_other1:
constrained FOSLS (CFOSLS)
===lastname5:

===affilother:

===title:
Space-time constrained FOSLS with AMGe upscaling
===firstname2:
Martin