预处理程序
广义最小残差法
数学
亥姆霍兹方程
离散化
收敛速度
Krylov子空间
迭代法
应用数学
趋同(经济学)
数学分析
基质(化学分析)
线性系统
数学优化
边值问题
计算机科学
频道(广播)
经济增长
复合材料
经济
计算机网络
材料科学
作者
T. Y. Li,Fang Chen,Zhi-Wei Fang,Hai‐Wei Sun,Zhi Wang
标识
DOI:10.1080/00207160.2023.2301570
摘要
For effectively solving the nonsymmetric and indefinite linear system originating from the discretized Helmholtz equation with complex wavenumber, we propose a two-parameter modified matrix splitting iteration method. We establish the asymptotic convergence theory for this method and demonstrate its convergence under certain conditions. The proposed iteration method leads to a new preconditioner that can be efficiently inverted by using the discrete sine transform. Numerical experiments are carried out to show that the new preconditioner significantly improves the convergence rate of the GMRES method, which results in effective preconditioned GMRES method for solving the Helmholtz equation of high wavenumber.
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