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{\large Scott MacLachlan \\
{\bf A Non-Hermitian Coarsening Strategy for Algebraic Multigrid}}

Department of Mathematics \\ Tufts University \\ 503 Boston Ave \\ Medford \\ MA 02155
\\
{\tt scott.maclachlan@tufts.edu}\end{center}

In recent years, there has been a significant renewed interest in the
development of optimally efficient algebraic multigrid solvers and
preconditioners for the non-symmetric and non-Hermitian matrices that
arise in applications such as fluid dynamics. While much of this work
has evolved, either directly or indirectly, from multigrid algorithms
for Hermitian problems, not all non-Hermitian matrices can be
effectively addressed in this way. In this talk, I will introduce a
new inherently non-Hermitian algebraic coarsening algorithm, adapted
from multilevel block factorization preconditioners, and the
corresponding algebraic multigrid algorithm. While the proposed
strategy requires no assumptions on, for example, the diagonal
dominance of the matrix, it reduces to a reasonable multigrid method
for such problems. The resulting algorithm is, then, more robust
than traditional AMG approaches; however, it is also less efficient
for the HPD problems for which classical AMG excels.


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