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{\large Lei Tang \\
{\bf Parallelization of efficiency-based adaptive local refinement for FOSLS-AMG}}

Department of Applied Mathematics \\ 526 UCB \\ University of Colorado \\ Boulder \\ CO 80309-0526
\\
{\tt lei.tang@colorado.edu}\\
Marian Brezina\\
{\em Department of Applied Mathematics,
University of Colorado at Boulder}\\
Tom Manteuffel\\
{\em Department of Applied Mathematics,
University of Colorado at Boulder}\\
Steve McCormick\\
{\em Department of Applied Mathematics,
University of Colorado at Boulder}\\
Josh Nolting\\
{\em GeoEye Inc., Thornton, Colorado}\\
John Ruge\\
{\em Department of Applied Mathematics,
University of Colorado at Boulder}\end{center}

A new adaptive local refinement strategy (ACE), in which the refinement
decisions are based on optimizing the
computational efficiency, has recently been developed. The first-order
system least-squares (FOSLS) finite
element methods, together with algebraic multigrid methods (AMG),
complement this idea, resulting in a powerful tool for numerical
solutions of many PDEs. However, in parallel environment, the global
sorting of element local error indicators used by the original approach
results in undesirable communication between processors. A strategy
circumventing the global sorting is proposed. The test results show that
the strategy has the potential of greatly reducing communication, while
producing a sequence of refined grids with essentially the same quality
as before.


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