A Parallel Preconditioned Solver for the 3D Helmholtz Equation

Discretization of the 3D Helmholtz equation leads to a linear system of a large size. The resulting linear system is difficult to be solved by a sequential method. In this paper, we propose a parallel preconditioned Bi-CGSTAB method for solving the system based on MPI(Message Passing Interface). We precondition the 3D Helmholtz equation by the complex shifted-Laplacian preconditioner, and employ the Krylov subspace method Bi-CGSTAB combined with the multi-grid to solve the resulting system. Numerical experiments are presented to illustrate the efficiency of the parallel Preconditioned solver.