A fast simple algorithm for computing the potential of charges on a line

07/08/2019

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by   Zydrunas Gimbutas, et al.

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We present a fast method for evaluating expressions of the form u_j = ∑_i = 1,i = j^n α_i/x_i - x_j, for j = 1,...,n, where α_i are real numbers, and x_i are points in a compact interval of R. This expression can be viewed as representing the electrostatic potential generated by charges on a line in R^3. While fast algorithms for computing the electrostatic potential of general distributions of charges in 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.