# Semi matrix-free twogrid shifted Laplacian preconditioner for the Helmholtz equation with near optimal shifts

@article{Drzisga2021SemiMT, title={Semi matrix-free twogrid shifted Laplacian preconditioner for the Helmholtz equation with near optimal shifts}, author={Daniel Drzisga and Tobias K{\"o}ppl and Barbara I. Wohlmuth}, journal={ArXiv}, year={2021}, volume={abs/2104.01439} }

Due to its significance in terms of wave phenomena a considerable effort has been put into the design of preconditioners for the Helmholtz equation. One option to derive a preconditioner is to apply a multigrid method on a shifted operator. In such an approach, the wavenumber is shifted by some imaginary value. This step is motivated by the observation that the shifted problem can be more efficiently handled by iterative solvers when compared to the standard Helmholtz equation. However, up to…

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