Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


A Fourier method for the numerical solution of Poisson's equation

Author: Gunilla Sköllermo
Journal: Math. Comp. 29 (1975), 697-711
MSC: Primary 65N10
MathSciNet review: 0371096
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A method for the solution of Poisson's equation in a rectangle, based on the relation between the Fourier coefficients for the solution and those for the right-hand side, is developed. The Fast Fourier Transform is used for the computation and its influence on the accuracy is studied. Error estimates are given and the method is shown to be second order accurate under certain general conditions on the smoothness of the solution. The accuracy is found to be limited by the lack of smoothness of the periodic extension of the inhomogeneous term. Higher order methods are then derived with the aid of special solutions. This reduces the problem to a case with sufficiently smooth data. A comparison of accuracy and efficiency is made between our Fourier method and the Buneman algorithm for the solution of the standard finite difference formulae.

References [Enhancements On Off] (What's this?)

  • [1] O. BUNEMAN, A Compact Non-Iterative Poisson Solver, Rep. 294, Stanford University, Institute for Plasma Research, Stanford, Calif., 1969.
  • [2] B. L. Buzbee, G. H. Golub, and C. W. Nielson, On direct methods for solving Poisson’s equations, SIAM J. Numer. Anal. 7 (1970), 627–656. MR 0287717 (44 #4920)
  • [3] J. W. COOLEY, P. A. W. LEWIS & P. D. WELCH, "The fast Fourier transform and its applications," IEEE Trans. Education, v. E-12, 1969, pp. 27-34.
  • [4] R. W. HOCKNEY, "The potential calculation and some applications," Methods in Computational Physics, v. 9, 1970, pp. 135-211.
  • [5] J. B. ROSSER, Fourier Series in The Computer Age, Mathematics Research Center, Technical Summary Report #1401, University of Wisconsin, Madison, Wis., Feb. 1974.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65N10

Retrieve articles in all journals with MSC: 65N10

Additional Information

PII: S 0025-5718(1975)0371096-4
Keywords: Poisson's equation, Fast Fourier Transform
Article copyright: © Copyright 1975 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia