波动方程基于自然边界归化的区域分解算法

计算物理 ›› 2001, Vol. 18 ›› Issue (5): 417-422.

波动方程基于自然边界归化的区域分解算法

杜其奎^1,2, 余德浩²

1. 南京师范大学数学与计算机科学学院, 南京 210097;
2. 中国科学院数学与系统科学研究院计算数学与科学工程计算研究所, 北京 100080

收稿日期:2000-12-13 修回日期:2001-05-08 出版日期:2001-09-25 发布日期:2001-09-25
作者简介:杜其奎(1963-),maie,Anhui,professor,Pd D,computational mathematics.
基金资助:
The Project Supported in part by National Natural Scienc Foundation of China(No .1970 10 0 1) ;and in part by the Special Funds for State Major Basic Research Projects(No .G19990 32 8)

DOMAIN DECOMPOSITION METHODS BASED ON NATURAL BOUNDARY REDUCTION FOR WAVE EQUATION

DU Qi-kui^1,2, YU De-hao²

1. School of Mathematics & Computer Sciences, Nanjing Normal University, Nanjing 210097, P R China;
2. LSEC, ICMSEC, AMSS, Chinese Academy of Sciences, Beijing 100080, P R China

Received:2000-12-13 Revised:2001-05-08 Online:2001-09-25 Published:2001-09-25
Supported by:
The Project Supported in part by National Natural Scienc Foundation of China(No .1970 10 0 1) ;and in part by the Special Funds for State Major Basic Research Projects(No .G19990 32 8)

摘要/Abstract

摘要： 提出了无界区域波动方程的区域分解算法.基于自然边界归化,分别研究了重叠型与非重叠型区域分解算法.首先将控制方程对时间进行离散化,得到关于时间步长离散化格式,对每一时间步长给出了Dirichlet Neumann和Schwartz交替算法.对Schwartz交替算法,给出了算法的收敛性,对圆外区域研究了压缩因子,并给出了数值例子.

关键词: 波动方程, 自然边界归化, 区域分解算法, 外问题

Abstract: Some new domain decomposition methods based on natural boundary reduction are suggested for overlapping and non-overlapping domains. A two-dimensional scalar wave equation is taken as a model to illustrate these methods. The governing equation is discretized in time, leading to time-stepping scheme, where an exterior elliptic problem has to be solved in each time step. The Dirichlet-Neumann method and Schwartz alternating method are proposed respectively. For the Schwartz alternating method, the convergence of the algorithm and the contraction factor for exterior circular domain are given. Finally, some numerical examples are devoted to illustrate these methods.

Key words: wave equation, natural boundary reduction, domain decomposition method (DDM), exterior problem

中图分类号:

杜其奎, 余德浩. 波动方程基于自然边界归化的区域分解算法[J]. 计算物理, 2001, 18(5): 417-422.

DU Qi-kui, YU De-hao. DOMAIN DECOMPOSITION METHODS BASED ON NATURAL BOUNDARY REDUCTION FOR WAVE EQUATION[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2001, 18(5): 417-422.

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