A Semicoarsening-based Multigrid Preconditioner for 3D Inhomogeneous Helmholtz Equations

In this paper an iterative solution method for the 3D Helmholtz equa-tion is presented. The method is a generalization of the method presented in [Erlangga, Oosterlee, Vuik, SIAM J. Sci. Comput., to appear] for the 2D heterogeneous Helmholtz equation. The method employs 3D multi-grid with 2D semicoarsening as a preconditioner for a Krylov subspace iteration method. This multigrid method is, however, not applied to the Helmholtz operator directly, but to a Helmholtz operator with complex shift, a so-called shifted Laplacian preconditioner. Numerical results ob-tained on a sequential machine indicate the eciency and the robustness of the method