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{\large Jari Toivanen \\
{\bf An AMG preconditioner based on damped operators for time-harmonic wave equations}}

Institute for Computational and Mathematical Engineering \\ Durand Building \\ Room 023A \\ Stanford University \\ Stanford \\ CA 94305
\\
{\tt toivanen@stanford.edu}\\
Tuomas Airaksinen\\
{\em University of Jyv\"askyl\"a, Finland}\\
Anssi Pennanen\\
{\em University of Jyv\"askyl\"a, Finland}\end{center}

An algebraic multigrid approximation of the inverse of the physically
damped operators is used as a preconditioner for time-harmonic scattering
problems in fluids and solids. The AMG uses graph based coarsening
together with underrelaxed Jacobi smoother. Several numerical experiments
demonstrate the behavior of the method in complicated two-dimensional and
three-dimensional domains. The number of iterations behaves roughly
linearly with respect to the frequency. This approach leads to efficient
solution procedure for low and medium frequency problems.


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