泊松方程的傅里叶拟谱方法（英文）  

A Fourier Pseudospectral Method for the Poisson Equation

作　　者：吕忠全[1,2,3] 龚跃政 

机构地区：[1]南京航空航天大学理学院,江苏南京210016 [2]南京林业大学理学院,江苏南京210037 [3]“大规模复杂系统数值模拟”江苏省重点实验室,南京师范大学数学科学学院,江苏南京210023

出　　处：《南京师大学报（自然科学版）》2015年第1期8-12,共5页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：Supported by the Postdoctoral Foundation of Jiangsu Province of China(1301030B);Open Fund Project of Jiangsu Key Laboratory for NSLSCS(201301);the Project of Graduate Education Innovation of Jiangsu Province(KYLX0691);Fund Project for Highly Educated Talents of Nanjing Forestry University(GXL201320)

摘　　要：本文基于二阶傅里叶拟谱微分矩阵来近似二阶导数,得到一个泊松方程的全离散傅里叶拟谱格式.运用FFT理论分析了该数值格式,推导了快速方法,最后进行了数值试验.数值试验显示数值方法求解速度快、方便实施,且高精度,说明该数值方法为泊松方程的研究提供了一个有效的新工具.In this paper,based on second-order Fourier spectral differentiation matrix D2 to approximate the second derivative,we obtain a standard Fourier pseudospectral full-discretization for the Poisson equation. According to the relationship between the spectral differentiation matrix and discrete Fourier transform,we provide a fast algorithm for solving the discrete equations. Some numerical results are presented. By using the FFT algorithm,numerical experiments show that the new scheme is very effective for calculation speed and easy to practice,and it has the high accuracy,these imply that the Fourier pseudospectral method provides a new useful tool for the study of the Poisson equation.

关 键 词：Fourier拟谱 泊松方程 FFT 

分 类 号：O241[理学—计算数学]