平面三向交错网格上Cauchy-Riemann方程的数值离散及快速解法  

DISCRETIZATION AND FAST METHOD OF CAUCHY-RIEMANN EQUATIONS ON THREE-DIRECTIONAL STAGGERED GRID

作　　者：杨超[1] 孙家昶[1] 

机构地区：[1]中国科学院软件研究所并行计算实验室,北京100080

出　　处：《数值计算与计算机应用》2008年第1期25-38,共14页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金重点项目(10431050;60573023)资助.

摘　　要：Cauchy-Riemann方程在复变函数、流体力学、偏微分方程组理论等方面具有重要的研究价值和应用背景.现有的关于Cauchy-Riemann方程快速数值解法的研究主要局限于张量积区域.本文利用平面上三向坐标改写了Cauchy-Riemann方程,并设计了一类三向交错网格以及相应的差分格式.本文证明了这种差分格式虽然只具有局部一阶的截断误差,但实际有二阶整体收敛性.最后还给出相应的谱预条件子快速解法和一些数值例子.We propose a new irregular staggered grid consisted by an arbitrary three-directional triangular grid and its dual hexagonal grid. A three-colored finite difference scheme for Cauchy-Riemann equations on the staggered grid is constructed. This scheme has second order accuracy despite its first order truncation error. Based on grid decoupling, we give a detailed proof for this phenomenon, as well as a fast solving algorithm. Some numerical tests are also listed to show the accuracy of the scheme and test our fast method.

关 键 词：Cauchy—Riemann方程 三向交错网格 离散谱预条件子 HFFT 

分 类 号：O241.8[理学—计算数学]