中文摘要：

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．

英文摘要：

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.