求解非对称椭圆型方程的瀑布型两层网格法.doc

摘要

　　　本文采用中心差分方法,分别取步长为h,h/4离散非对称椭圆问题,形成粗网格和细网格,对粗网格精确求解,然后采用线性插值(或二次插值)为细层提供好的初始值,构造出一类求解非对称椭圆型方程的新瀑布型两层网格法.数值实验结果表明,新算法更具有效性.

关键词: 瀑布型两层网格法;二次插值;线性插值;中心差分方法;非对称椭圆型方程

ABSTRACT

　　　In this paper, non-symmetric elliptic equation is discreted by taking central difference method. The coarse grid and fine grid are formed by selecting different steps as ‘h’ and ‘h/4’. Then the exact solution is used on coarse grid. A better initial value is provided for the fine grid by using linear interpolation (or quadratic interpolation).A new cascadic two-level method is constructed for non-symmetric elliptic equation. Numerical experiments show that the new method is more efficient.

Keywords: cascadic two- level method; quadratic interpolation; linear interpolation; central difference method; non-symmetric elliptic equation

目录

摘要

ABSTRACT

第一章 引言

第二章 准备知识

2.1 椭圆型方程的差分离散

2.2 迭代法

2.2.1 Jacobi迭代法

2.2.2 Gauss-Seidel迭代法

2.3 瀑布型多重网格法

第三章 新瀑布型两层网格法

3.1 Lagrange线性插值的构造

3.2 Lagrange二次插值的构造

3.3 新瀑布型两层网格法

第四章 数值实验及结论

参考文献

致谢