Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

作     者：尚月强 何银年 

作者机构：Faculty of Science Xi'an Jiaotong University School of Mathematics and Computer Science Guizhou Normal University 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2009年第30卷第9期

页      面：1177-1182页

核心收录：

学科分类：07[理学] 080103[工学-流体力学] 08[工学] 080104[工学-工程力学] 070102[理学-计算数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China (No. 10671154) the Na-tional Basic Research Program (No. 2005CB321703) the Science and Technology Foundation of Guizhou Province of China (No. 2123) 

主　　题：domain decomposition algorithm Schwarz method Fourier transform biharmonic equation 

摘      要：Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.