  The Helmholtz equation arises when modeling wave propagation in the frequency
domain. The equation is discretized as an indefinite linear system, which is
difficult to solve at high wave numbers. In many applications, the solution of
the Helmholtz equation is required for a point source. In this case, it is
possible to reformulate the equation as two separate equations: one for the
travel time of the wave and one for its amplitude. The travel time is obtained
by a solution of the factored eikonal equation, and the amplitude is obtained
by solving a complex-valued advection-diffusion-reaction (ADR) equation. The
reformulated equation is equivalent to the original Helmholtz equation, and the
differences between the numerical solutions of these equations arise only from
discretization errors. We develop an efficient multigrid solver for obtaining
the amplitude given the travel time, which can be efficiently computed. This
approach is advantageous because the amplitude is typically smooth in this
case, and hence, more suitable for multigrid solvers than the standard
Helmholtz discretization. We demonstrate that our second order ADR
discretization is more accurate than the standard second order discretization
at high wave numbers, as long as there are no reflections or caustics.
Moreover, we show that using our approach, the problem can be solved more
efficiently than using the common shifted Laplacian multigrid approach.
