摘要
本文提出平面上拉普拉斯算子在一类平行六边形网格上的成对4点差分格式.这种差分格式虽然只有一阶的局部截断误差,但实际具有二阶的收敛性.基于平行六边形网格可以被分解为两套三向三角形网格,我们给出成对4点格式的二阶收敛性的证明,并且提出相应的预条件子快速解法.文末给出的数值算例符合我们的结论.
In this paper we propose so-called coupled 4-point difference schemes for the Laplacian operator over a class of parallel hexagon partitions of the plane. The scheme exhibits global second order accuracy, despite its first order local truncation error. Based on the fact the parallel hexagonal grid can be decoupled into two sets of 3-direction triangular grids, a detailed proof for the second order behavior is given and the corresponding fast solver for Helmholtz equation is also studied. Numerical examples are provided to varify our analysis.
出处
《计算数学》
CSCD
北大核心
2005年第4期437-448,共12页
Mathematica Numerica Sinica
基金
国家自然科学基金重点项目"偏微分方程数值求解中的自适应网格方法研究"(10431050)973项目"高性能科学计算研究"课题"大规模并行计算研究"(2005CB321702)资助.
