三维泊松方程基于Richardson外推的高精度多重网格解法  

High-precision multi-mesh method for solution of three-dimensional Poisson equation based on Richardson extrapo-lation

作　　者：李小纲[1] 袁冬芳[2] 葛永斌[2] 

机构地区：[1]宁夏大学新华学院,银川750021 [2]宁夏大学应用数学和力学研究所,银川750021

出　　处：《兰州理工大学学报》2011年第6期131-135,共5页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11061025);教育部科学技术研究重点项目(210239);霍英东教育基金会高等院校青年教师基金(121105)

摘　　要：基于三维泊松方程的四阶紧致差分格式,利用Richardson外推法、算子插值法和多重网格算法,使已有四阶紧致差分格式的计算精度整体提高二阶,精度达到六阶.数值实验验证六阶格式的精确性和多重网格方法的有效性,并与四阶紧致差分格式多重网格方法的计算结果进行比较.Based on the fourth-order compact difference format of three-dimensional Poisson equation and by using the Richardson extrapolation, operator insertion, multi-mesh algorithm, the computation accuracy of above-mentioned difference format was improved by two orders, amounting to sixth-order. The nu- merical experiments verified the accuracy of the sixth-order format and the effectiveness of multi-mesh method. Its computation result was compared with that of the fourth-order difference format and multimesh method.

关 键 词：泊松方程 高阶紧致格式 RICHARDSON外推 算子插值 多重网格方法 

分 类 号：O241.82[理学—计算数学]