Positive stable preconditioners for symmetric indefinite linear systems arising from Helmholtz equations

Using the finite difference method to discretize Helmholtz equations usually leads to a large spare linear system of equations Ax=bAx=b. Since the coefficient matrix AA is frequently indefinite, it is difficult to solve iteratively. The approach taken in this Letter is to precondition this linear system with positive stable preconditioners and then to solve it iteratively using Krylov subspace methods. Numerical experiments are given in order to demonstrate the efficiency of the presented preconditioners.