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A Multi-Symplectic Integration Method for the Poisson Equation(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2011年04期
Page:
9-12
Research Field:
数学
Publishing date:

Info

Title:
A Multi-Symplectic Integration Method for the Poisson Equation
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
Keywords:
multi-symplectic; Fourier pseudo-spectral method; Poisson equation
PACS:
O241.82
DOI:
-
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．

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．

Memo

Memo:
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Last Update: 2013-03-21