[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):9-12.
　Lv Zhongquan,Wang Yushun.A Multi-Symplectic Integration Method for the Poisson Equation[J].Journal of Nanjing Normal University(Natural Science Edition),2011,34(04):9-12.
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泊松方程的一个多辛积分方法(英文)()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第34卷
期数:
2011年04期
页码:
9-12
栏目:
数学
出版日期:
2011-12-20

文章信息/Info

Title:
A Multi-Symplectic Integration Method for the Poisson Equation
作者:
吕忠全1; 2; 王雨顺1
( 1．“大规模复杂系统数值模拟”江苏省重点实验室，数学研究所，南京师范大学数学科学学院，江苏南京210046) ( 2． 南京林业大学理学院，江苏南京210037)
Author(s):
Lv Zhongquan1; 2; Wang Yushun1
1.Jiangsu Key Laboratory for NSLSCS,Institute of Mathematics,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,China
关键词:
多辛; Fourier 拟谱方法; 泊松方程
Keywords:
multi-symplectic; Fourier pseudo-spectral method; Poisson equation
分类号:
O241.82
摘要:
分析了泊松方程的多辛结构,推导了泊松方程的多辛拟谱格式,并得出相关守恒律,最后进行了数值试验.数值模拟的高精度说明多辛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，we analyze the multi-symplectic structure and the relevant conservation laws for the Poisson equation． A multi-symplectic pseudo-spectral scheme of the Poisson equation is derived and some numerical results are presented． The high accuracy of the new-derived scheme implies that the multi-symplectic methods provide a new useful tool to study the Poisson equation．

参考文献/References:

［1］ Sun L，Ma D J，Qin F H，et al． A two-step predictive-corrective scheme for 2D poisson equation［J］． Mechanics in Engineering， 2010，32( 1) : 37-40．
［2］ Ma J F，Shen X R，Zhang B Z，et al． A new pseudo-spectral method for solving Poisson equation in polar coordinate system ［J］． Acta Aerodynamica Sinica，2006，24( 2) : 243-245．
［3］ Liao C，Zhu D J，Liu S G． Parallel algorithm research on solving poisson equations based on five point difference format［J］． Journal of University of Electronic Science and Technology of China，2008，37( 1) : 81-83．
［4］ Ida M B Nielsen，Curtis L Janssen． A novel pseudo-spectral Fourier method for solving Poisson’s equation for a solute in a non-uniform dielectric［J］． Computer Physics Communications，2001，136: 29-36．
［5］ John P Boyd，Fu Yu． Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials． Logan-Shepp ridge polynomials，Chebyshev-Fourier Series，cylindrical Robert functions，Bessel-Fourier expansions，square-to-disk conformal mapping and radial basis functions［J］． Journal of Computational Physics，2011，230: 1 408-1 438．

备注/Memo

备注/Memo:
Foundation item: Supported by the National Basic Research Program of China( 2010AA012304) ， the National Natural Science Foundation of China ( 10971102 ＆ 10871099) ， the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China( 200720) and“333 Project” Foundation of Jiangsu Province of China． Corresponding author: Lv Zhongquan，Ph． D student，lecturer，majored in structure-preserving algorithms． E-mail: zhqlv@ njfu． edu． cn
更新日期/Last Update: 2013-03-21