A Modified SSOR Preconditioning Strategy for Helmholtz Equations

[摘要] The finite difference method discretization of Helmholtz equations usually leads tothe large spare linear systems. Since the coefficient matrix is frequently indefinite, itis difficult to solve iteratively. In this paper, a modified symmetric successive overrelaxation (MSSOR) preconditioning strategy is constructed based on the coefficientmatrix and employed to speed up the convergence rate of iterative methods. The ideais to increase the values of diagonal elements of the coefficient matrix to obtain betterpreconditioners 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 canreduce both the number of iterations and the computational time significantly withlow cost for construction and implementation of preconditioners.

[学科分类] 应用数学