A new preconditioning algorithm is presented for effectively solving the large complex symmetric and always highly indefinite linear equations arising from the finite element method (FEM) discretizing Helmholtz equation. The proposed preconditioner is constructed by combing the complex shifted Laplace (CSL) operator with a modified AINV (MAINV) approximate inverse algorithm. By improving the FEM linear system’s eigenvalue spectrum, the proposed preconditioner can avoid most of the breakdowns during the iterative process, and enhance the solving efficiency. Numerical examples demonstrate the proposed preconditioning algorithm is more effective than some standard ones.
