Advances in Computational Mathematics

, Volume 42, Issue 1, pp 227–248 | Cite as

The Ewald sums for singly, doubly and triply periodic electrostatic systems

  • Anna-Karin Tornberg


When evaluating the electrostatic potential, periodic boundary conditions in one, two or three of the spatial dimensions are often required for different applications. The triply periodic Ewald summation formula is classical, and Ewald summation formulas for the other two cases have also been derived. In this paper, derivations of the Ewald sums in the doubly and singly periodic cases are presented in a uniform framework based on Fourier analysis, which also yields a natural starting point for FFT-based fast summation methods.


Electrostatic potential Periodicity Ewald summation 

Mathematics Subject Classification (2010)

65Z05 40C99 35J05 31C20 70E55 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Numerical Analysis, Department of Mathematics/Swedish e-Science Research CentreRoyal Institute of Technology (KTH)StockholmSweden

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