Preconditioners for Indefinite Linear System from the Helmholtz Equation

Abstract

Using the finite difference method to discretize the Helmholtz equation usually leads to a large spare linear system. Since the coefficient matrix of the linear system is frequently indefinite, it is difficult to solve iteratively. The approach taken in this paper is to precondition this linear system with SSOR and ILU preconditioners and then to solve it iteratively by using Krylov subspace method such as LSQR method. Numerical experiments are given in order to demonstrate the efficiency of the presented preconditioners. Key Words: Helmholtz equation; Krylov subspace method; Preconditioner