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{\large Ira Livshits \\
{\bf An AMG solver for the Helmholtz equation. }}

Ball State University \\ Department of Mathematical Sciences \\ Muncie \\ IN 47304
\\
{\tt ilivshits@bsu.edu}\end{center}

We discuss an adaptive algebraic multigrid algorithm for solving
indefinite Helmholtz equations. Our approach is reminiscent of the
wave-ray algorithm developed by Brandt and Livshits in the geometric
framework -- it is too provides a special treatment to the null- and
near-null components of the Helmholtz operator.

Unlike it predecessor, our solver
does not have to rely on analytical solutions but rather computes their
numerical approximations and fits them using Brandt's least squares
approach for computing interpolation operators, allowing accurate and
smooth coarse-grid representation. In this talk, we present preliminary
one-dimensional results and discuss how this approach can be naturally
extended to two dimensions.


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