Theory An iterative numerical method for solving the wave equation in an inhomogeneous medium with constant density is presented. The method is based on a Krylov iterative method and enhanced by a powerful preconditioner. For the preconditioner, a complex ShiftedLaplace operator is proposed, designed specifically for the wave equation. A multigrid method is used to approximately compute the inverse of the preconditioner. Numerical examples on 2D problems show that the combined method is robust and applicable for a wide range of frequencies. Extension to 3D is straightforward. The time-harmonic wave problem is represented by the Helmholtz equation: