In this paper a method is presented for evaluating the convolution of the Green's function for the Laplace operator with a specified function $\rho(\vec x)$ at all grid points in a rectangular domain $\Omega \subset {\mathrm R}^{d}$ ($d = 1,2,3$), i.e. a solution of Poisson's equation in an infinite domain. 4th and 6th order versions of the method achieve high accuracy when $\rho ( \vec x )$ possesses sufficiently many continuous derivatives. The method utilizes FFT's for computational efficiency and has a computational cost that is $\rm O (N \log N)$ where $\rm N$ is the total number of grid points in the rectangular domain.
翻译:本文介绍了一种方法,用于评价在矩形域$\rho(\vecxx)所有网格点上具有特定功能的Laplace操作员Green函数的演变情况。 在矩形域$\rho(\vecxx)$\vecxx)的所有网格点,该方法的计算成本为$\rft(N\logN)$=1,230美元,即Poisson方程式在无限域中的解决方案。当 $\rho(\vecx)$(\vecx)拥有足够多的连续衍生物时,该方法的第四和第六顺序版本的精确度很高。该方法使用FFT的计算效率,计算成本为$\rm O(N\logN),其中$\rm N$是矩形域的网格点总数。