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{\large Robert D. Falgout \\
{\bf Multigrid Smoothers for Ultra-Parallel Computers}}

Center for Applied Scientific Computing \\ Lawrence Livermore National Laboratory \\ P O Box 808 \\ L-561 \\ Livermore \\ CA 94551 \\ USA
\\
{\tt rfalgout@llnl.gov}\\
Allison Baker\\
Tzanio Kolev\\
Ulrike Yang\end{center}

Multigrid methods are often critical for solving huge linear systems
efficiently, and they have demonstrated scalability on hundreds of thousands of
processors. However, the petascale architectures on the horizon are expected to
have millions of processors, and future exascale machines could have even more.
The immense degree of parallelism on these machines requires a similar level of
concurrency in the algorithms that run on them. One major component of
multigrid is the smoother, but many of the most effective smoothers used today
unfortunately don't exhibit this degree of concurrency without losing their good
smoothing properties. In this talk, we will discuss several approaches for
doing effective smoothing in highly concurrent settings and we will also present
supporting numerical results.


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