===affil2:
Center for Applied Scientific Computing,
Lawrence Livermore National Laboratory
===firstname:
Umberto
===firstname4:

===firstname3:

===lastname2:
Vassilevski
===lastname:
Villa
===firstname5:

===affil6:

===lastname3:

===email:
uvilla@emory.edu
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===affil7:

===firstname7:

===postal:
Dept. of Mathematics & Computer Science,
Emory University
400 Dowman Dr,
Atlanta, GA, 30322
===firstname6:

===ABSTRACT:
\newcommand{\curl}{\operatorname{curl}}
\renewcommand{\div}{\operatorname{div}}

The Brinkman model is a unified law governing the flow of a viscous fluid in cavity (Stokes equations) and in porous media (Darcy equations). 
It was initially proposed as a homogenization technique for the Navier-Stokes equations. 
Typical applications of this model are in underground water hydrology, petroleum industry, automotive industry, biomedical engineering, and heat pipes modeling.
In this talk, we present a novel mixed formulation of the Brinkman problem. Introducing the flow's vorticity as additional unknown, this formulation leads to a uniformly stable and conforming discretization by standard finite element (N\'ed\'elec, Raviart-Thomas, piecewise discontinuous). Based on stability analysis of the problem in the $H(\curl)-H(\div)-L^2$ norms, we derive a scalable block diagonal preconditioner which is optimal in the constant coefficient case. Such preconditioner is based on the auxiliary space AMG solvers for $H(\curl)$ and $H(\div)$ problems available in  hypre (http://www.llnl.gov/CASC/hypre/). The theoretical results are illustrated by numerical experiments.\\

This work was performed under the auspices of the U.S. Department
of Energy by Lawrence Livermore National Laboratory under Contract
DE-AC52-07NA27344.\\

{\bf keywords}: Brinkman problem; Stokes-Darcy coupling; saddle point problems; block preconditioners; algebraic multigrid.
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===affilother:

===title:
A block-diagonal algebraic multigrid preconditioner for the Brinkman problem
===firstname2:
Panayot S.