| 结构三角网上抛物方程的有限差分区域分解算法 |
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| 引用本文： | 吕桂霞,马富明.结构三角网上抛物方程的有限差分区域分解算法[J].高等学校计算数学学报,2007,29(2):133-145. |
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| 作者姓名： | 吕桂霞 马富明 |
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| 作者单位： | 1. 北京应用物理与计算数学研究所计算物理实验室,北京,100088
2. 吉林大学数学科学学院,长春,130012 |
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| 基金项目： | 国家重点基础研究专项经费(G1999032802)，国家自然科学基金(10076006)． |
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| 摘 要： | 1引言对于大型科学与工程计算问题,并行计算是必需的．构造高效率的数值并行方法一直是人们关心的问题,并且已有了大量的研究．在三层交替计算方法的研究中出现了许多既具有明显并行性又绝对稳定的差分格式(见1]-5])．在只涉及两个时间层的算法研究中,Dawson等人(见6])首先发展了求解一维热传导方程的区域分解算法,并将其推广到
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| 关 键 词： | 结构三角网上 抛物方程 有限差分 区域分解算法 |
| 修稿时间： | 2005-04-07 |
FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHMS ON STRUCTURED TRIANGULAR MESH FOR PARABOLIC EQUATION |
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| Lü Guixia,Ma Fuming.FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHMS ON STRUCTURED TRIANGULAR MESH FOR PARABOLIC EQUATION[J].Numerical Mathematics A Journal of Chinese Universities,2007,29(2):133-145. |
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| Authors: | Lü Guixia Ma Fuming |
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| Institution: | Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088;Institute of Mathematics, Jilin University, Changchun 130012 |
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| Abstract: | In this paper, two finite difference domain decomposition algorithms on structured triangular mesh for numerically solving the two-dimensional heat equation are studied. In these procedures, the domain over which the problem is defined is divided into subdomains by introducing different kinds of interface points. Problems defined on subdomains which are enclosed by interface points can be solved in parallel. Once these problems are solved, other subdomain problems can be solved in parallel. Stability conditions and maximum norm error estimates for these procedures are derived, which demonstrate that our schemes have satisfactory stabilities and higher convergence orders. |
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| Keywords: | parabolic equation finite difference structured triangular mesh domain decomposition |
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