A multigrid-based preconditioned solver for the Helmholtz equation with a discretization by 25-point difference scheme

作     者：Cheng, Dongsheng Liu, Zhiyong Wu, Tingting 

作者机构：Shenzhen Inst Informat Technol Sch Software Engn Shenzhen 518172 Peoples R China Shenzhen Polytech Ind Ctr Shenzhen 518055 Peoples R China Shandong Normal Univ Dept Math Jinan Peoples R China 

出 版 物：《MATHEMATICS AND COMPUTERS IN SIMULATION》 (系统模拟中的数学与计算机)

年 卷 期：2015年第117卷

页      面：54-67页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China [11101163, 11226105, 71101096, 11301310] China Postdoctoral Science Foundation [2013M531884] Science Research Project of Shenzhen Polytechnic [601522k35010] Guangdong Province Key Laboratory of Computational science at the Sun Yat-sen University 

主　　题：Helmholtz equation Preconditioner Multigrid Prolongation operator 

摘      要：In this paper, a preconditioned iterative method is developed to solve the Helmholtz equation with perfectly matched layer (Helmholtz-PML equation). The complex shifted-Laplacian is generalized to precondition the Helmholtz-PML equation, which is discretized by an optimal 25-point finite difference scheme that we presented in Chen et al. (2011). A spectral analysis is given for the discrete preconditioned system from the perspective of linear fractal mapping, and Bi-CGSTAB is used to solve it. The multigrid method is employed to invert the preconditioner approximately, and a new matrix-based prolongation operator is constructed in the multigrid cycle. Numerical experiments are presented to illustrate the efficiency of the multigrid-based preconditioned Bi-CGSTAB method with the new prolongation operator. Numerical results are also given to compare the performance of the new prolongation operator with that of the prolongation operator based on the algebraic multigrid (AMG) principle. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.