On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning

@article{Reps2010OnTI,
  title={On the indefinite Helmholtz equation: Complex stretched absorbing boundary layers, iterative analysis, and preconditioning},
  author={Bram Reps and Wim Vanroose and Hisham Bin Zubair},
  journal={J. Comput. Physics},
  year={2010},
  volume={229},
  pages={8384-8405}
}
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not only the coordinates in the absorbing layer have an imaginary part, but also the coordinates in the interior region. This results into a preconditioner problem that is invertible with a multigrid cycle. We give a numerical analysis based on the eigenvalues and… CONTINUE READING
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