[1]吕忠全,龚跃政.泊松方程的傅里叶拟谱方法[J].南京师大学报(自然科学版),2015,38(01):8.
 Lv Zhongquan,Gong Yuezheng.A Fourier Pseudospectral Method for thePoisson Equation[J].Journal of Nanjing Normal University(Natural Science Edition),2015,38(01):8.
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泊松方程的傅里叶拟谱方法()
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《南京师大学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第38卷
期数:
2015年01期
页码:
8
栏目:
数学
出版日期:
2015-06-30

文章信息/Info

Title:
A Fourier Pseudospectral Method for thePoisson Equation
作者:
吕忠全123龚跃政3
(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)
Author(s):
Lv Zhongquan123Gong Yuezheng3
(1.College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)(2.College of Science,Nanjing Forestry University,Nanjing 210037,China)(3.Jiangsu Key Laboratory for NSLSCS,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)
关键词:
Fourier拟谱泊松方程FFT
Keywords:
Fourier pseudospectral methodPoisson equationFFT
分类号:
O241
文献标志码:
A
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.
Abstract:
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.

参考文献/References:

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[8]Haidvogel D B,Zang T A. The accurate solution of Poisson’s equation by expansion in Chebyshev polynomials[J]. J Comput Phys,1979,30:167-180.
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相似文献/References:

[1]吕忠全,王雨顺.泊松方程的一个多辛积分方法(英文)[J].南京师大学报(自然科学版),2011,34(04):9.
 Lv Zhongquan,Wang Yushun.A Multi-Symplectic Integration Method for the Poisson Equation[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(01):9.

备注/Memo

备注/Memo:
Received data:2014-04-16.
Foundation item: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)and Fund Project for Highly Educated Talents of Nanjing Forestry University(GXL201320).
Corresponding author:Lv Zhongquan,associate professor,majored in numerical solution of partial differential equations. E-mail:zhqlv@njfu.edu.cn
更新日期/Last Update: 2015-03-30