Multigrid Methods for Helmholtz Problems : A Convergent Scheme in 1 D Using Standard Components

@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}
}
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

References

Publications referenced by this paper.
SHOWING 1-10 OF 37 REFERENCES

An Incomplete LU Preconditioner for Problems in Acoustics

  • Martin J. Gander, Frédéric Nataf
  • Journal of Computational Acoustics
  • 2005
Highly Influential
1 Excerpt

Multigrid preconditioners based on polynomial smoothers for the Helmholtz equation with absorbing layers

  • Wim Vanroose, Bram Reps, Hisham Bin Zubair
  • in: International Conference On Preconditioning…
  • 2011
1 Excerpt

Advances in Iterative Methods and Preconditioners for the Helmholtz Equation

  • Y. A. Erlangga
  • Archives Comput. Methods in Engin
  • 2008
1 Excerpt

Similar Papers

Loading similar papers…