## How Large a Shift is Needed in the Shifted Helmholtz Preconditioner for its Effective Inversion by Multigrid?

- Pierre-Henri Cocquet, Martin J. Gander
- SIAM J. Scientific Computing
- 2017

Highly Influenced

@inproceedings{Ernst2013MultigridMF, title={Multigrid Methods for Helmholtz Problems : A Convergent Scheme in 1 D Using Standard Components}, author={Oliver G. Ernst and Martin J. Gander}, year={2013} }

- Published 2013

We analyze in detail two-grid methods for solving the 1D Helmholtz equation discretized by a standard finite-difference scheme. We explain why both basic components, smoothing and coarse-grid correction, fail for high wave numbers, and show how these components can be modified to obtain a convergent iteration. We show how the parameters of a two-step Jacobi method can be chosen to yield a stable and convergent smoother for the Helmholtz equation. We also stabilize the coarse-grid correction by… CONTINUE READING