Gimbutas, Z.
, Marshall, N.
and Rokhlin, V.
(2020),
A fast simple algorithm for computing the potential of charges on a line, Applied and Computational Harmonic Analysis, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=928101
(Accessed October 14, 2025)
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A fast simple algorithm for computing the potential of charges on a line
Published
Author(s)
, Nicholas F. Marshall, Vladimir Rokhlin
Abstract
We present a fast method for evaluating expressions of the form $$ u_j = \sum_{i = 1,i \not = j}^n \frac{\alpha_i}{x_i - x_j}, \quad \text{for} \quad j = 1,\ldots,n, $$ where $\alpha_i$ are real numbers, and $x_i$ are points in a compact interval of $\mathbb{R}$. This expression can be viewed as representing the electrostaticpotential generated by charges on a line in $\mathbb{R}^3$. While fast algorithms for computing the electrostatic potential of general distributions of charges in $\mathbb{R}^3$ exist, in a number of situations in computational physics it is useful to have a simple and extremely fast method for evaluating the potential of charges on a line; we present such a method in this paper, and report numerical results for several examples.
Citation
Applied and Computational Harmonic Analysis
Pub Type
Journals
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Keywords
Fast multipole method, Chebyshev system, generalized Gaussian quadrature
Citation
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Created July 9, 2020, Updated July 10, 2020