===firstname:
Johann
===firstname3:
Omar
===affil6:

===lastname3:
Ghattas
===email:
johann@ices.utexas.edu
===keyword_other2:

===lastname6:

===affil5:

===lastname4:

===lastname7:

===affil7:

===postal:
The University of Texas at Austin
201 East 24th Street, Stop C0200
Austin TEXAS 78712-1229
===ABSTRACT:
We present $\mu$-BFBT, an approximation for the inverse Schur complement of a
Stokes system with strongly heterogeneous viscosity.

When used as part of a Schur complement preconditioner, we observe robust
convergence rates for Stokes problems with smooth but strongly varying (up to
10 orders of magnitude) viscosities, optimal algorithmic scalability with
respect to mesh refinement, and a merely mild dependence on the polynomial
order of high-order finite element discretizations 
($Q_{k} \times P_{k-1}^{disc}$, order $k\ge2$).

For certain problems, $\mu$-BFBT significantly improves Stokes solver
convergence over the widely used Schur approximation with an inverse viscosity
weighted pressure mass matrix.  Using detailed numerical experiments, we
discuss modifications to $\mu$-BFBT at Dirichlet boundaries, which decrease the
number of iterations.

The overall algorithmic performance of the Stokes solver is governed by the
efficacy of $\mu$-BFBT as a Schur complement approximation and, in addition, by
our parallel hybrid spectral-geometric-algebraic multigrid (HMG) method, used
for approximating the inverses of the viscous block and variable-coefficient
pressure Poisson operators within $\mu$-BFBT.

Building on the scalability of HMG, our Stokes solver achieves parallel weak
scalability of 90% for a more than 600-fold increase from 48 to all 30,000
cores of TACC's Lonestar 5 supercomputer.
===affil3:
The University of Texas at Austin
===title:
$\mu$-BFBT Preconditioner for Stokes Flow Problems with Strongly Heterogeneous Viscosity
===affil2:
New York University
===lastname2:
Stadler
===firstname4:

===keyword1:
Iterative solvers/linear algebra on high concurrency node architectures
===workshop:
no
===lastname:
Rudi
===firstname5:

===keyword2:
Solvers for indefinite systems
===otherauths:

===affil4:

===competition:
yes
===firstname7:

===firstname6:

===keyword_other1:

===lastname5:

===affilother:

===firstname2:
Georg