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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A Fourier method for the numerical solution of Poisson’s equation
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by Gunilla Sköllermo PDF
Math. Comp. 29 (1975), 697-711 Request permission

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
    O. BUNEMAN, A Compact Non-Iterative Poisson Solver, Rep. 294, Stanford University, Institute for Plasma Research, Stanford, Calif., 1969.
  • 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 287717, DOI 10.1137/0707049
    • 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. R. W. HOCKNEY, "The potential calculation and some applications," Methods in Computational Physics, v. 9, 1970, pp. 135-211. J. B. ROSSER, Fourier Series in The Computer Age, Mathematics Research Center, Technical Summary Report #1401, University of Wisconsin, Madison, Wis., Feb. 1974.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Math. Comp. 29 (1975), 697-711
  • MSC: Primary 65N10
  • DOI: https://doi.org/10.1090/S0025-5718-1975-0371096-4
  • MathSciNet review: 0371096