The finite difference method discretization of Helmholtz equations usually leads to the large spare linear systems. Since the coefficient matrix is frequently indefinite, it is difficult to solve iteratively. In this paper, a modified symmetric successive overrelaxation (MSSOR) preconditioning strategy is constructed based on the coefficient matrix and employed to speed up the convergence rate of iterative methods. The idea is to increase the values of diagonal elements of the coefficient matrix to obtain better preconditioners for the original linear systems. Compared with SSOR preconditioner, MSSOR preconditioner has no additional computational cost to improve the convergence rate of iterative methods. Numerical results demonstrate that this method can reduce both the number of iterations and the computational time significantly with low cost for construction and implementation of preconditioners.
Shi-Liang Wu. Cui-Xia Li. "A Modified SSOR Preconditioning Strategy for Helmholtz Equations." J. Appl. Math. 2012 (SI12) 1 - 9, 2012. https://doi.org/10.1155/2012/365124