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| 离散椭圆方程若干并行预条件子的研究 | |
| 何伟军 | |
| Major | 计算机理论与软件 |
| 1999 | |
| Degree Grantor | 中国科学院软件研究所 |
| Degree Level | 博士 |
| Place of Degree Grantor | 中国科学院软件研究所 |
| Keyword | 椭圆方程 迭代法 预条件子 区域分解算法 |
| English Abstract | 本文将主要讨论离散椭圆方程的数值解法。首先我们讨论椭圆型算子及其离散形式的一些性质，这些性质将在一定程度上影响数值方法的设计。在大型线性系统的解法器中存在两个关键的元素，即预条件子和加速子（迭代法）。我们将简要回顾一下迭代方法，包括经典迭代法和Krylov子空间迭代法，然后讨论本文的主要问题预条件子，特别地是区域分解算法。区域分解算法近来在科学与工程计算领域十分活跃，并受到了极大的关注。之所以如此，一方面是因为区域分解算法非常适合于并行计算且并行计算机的发展也要求用分而治之的思想来解决问题。另一方面，原问题的计算区域可能本来就存在很自然的剖分，例如整体不规则的大区域由一些规则的子区域组成。这样我们就可以运用一些局速解法器。本文我们将分别讨论重叠型和非重叠型区域分解算法，并通过改造和推广提出一些新的方法，相应地我们给出一定的数值结果来帮助分析这些方法及其并行性，同时我们给出加法Schwarz方法条件数估计的两种途径。 |
| Abstract | In this paper we focus on th numerical solution of discrete elliptic equations. First some properties related to elliptic operator and its discrete form are discussed. These properties will impact on the design of numerical methods to some extend. There are two key elements in the solvers for large scale linear systems, i.e., preconditioner and accelerator(iterative methods). We will briefly review the iterative methods including classical iterative methods and Krylov subspace methods. Then we go to our main point in this paper - preconditioners, especially domain decomposition methods. Domain decomposition methods have received a lot of interest recently. On the one hand, it is suitable to implement on multiprocessor systems. On the other hand, a regular partition can make use of fast solvers. In this paper, we discuss overlapping and nonoverlapping domain decomposition methods respectively and propose some new methods. Also corresponding numerical results are given to help us analyze methods and their parallelism. At the same two methods are given to estimate the condition number of the additive Schwarz method. |
| Pages | 47 |
| Language | 中文 |
| Content Type | 学位论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/6658 |
| Collection | 中科院软件所_中科院软件所 |
| Recommended Citation GB/T 7714 | 何伟军. 离散椭圆方程若干并行预条件子的研究[D]. 中国科学院软件研究所. 中国科学院软件研究所,1999. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| LW002872.pdf（1206KB） | 限制开放 | -- | Application Full Text | |||
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