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 April 24, 2024)
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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
Download Paper
Keywords
Fast multipole method, Chebyshev system, generalized Gaussian quadrature
Citation
Created July 9, 2020, Updated July 10, 2020