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 evaluate the performance with several numerical
experiments. The method is an alternative to the complex shifted Laplacian and
it gives a comparable performance for the studied model problems