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High Order Accurate Solution of Poisson's Equation in Infinite Domains for Smooth Functions

2021/08/26 by Christopher R. Anderson, Anderson, Christopher R.
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2108.11871

15 pages, 3 Figures, 1 Table

arxiv created 2021/08/26 · openalex publication_date 2021/08/26 · arxiv updated 2021/08/27 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

In this paper a method is presented for evaluating the convolution of the Green's function for the Laplace operator with a specified function ρ( x) at all grid points in a rectangular domain Ω⊂ \mathrm Rd (d = 1,2,3), i.e. a solution of Poisson's equation in an infinite domain. 4th and 6th order versions of the method achieve high accuracy when ρ( x ) possesses sufficiently many continuous derivatives. The method utilizes FFT's for computational efficiency and has a computational cost that is \rm O (N log N) where \rm N is the total number of grid points in the rectangular domain.

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