A double-sweeping preconditioner for the Helmholtz equation

A new preconditioner is developed to increase the efficiency of iterative solution of the Helmholtz equation. The key idea of the proposed preconditioner is to split the domain of interest into smaller subdomains and sequentially approximate the forward and backward components of the solution. The sequential solution is facilitated by approximate interface conditions that ignore the effect of multiple reflections. The efficiency of the proposed method is tested using various 2-D heterogeneous media. We observe that the proposed preconditioner results in good convergence, with number of iterations growing very slowly with increasing frequency. We also note that the mesh size and number of subdomains do not affect the convergence rate. Finally, we find that the overall computational time is much smaller than that of the sweeping preconditioner.