The Ewald sums for singly, doubly and triply periodic electrostatic systems
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.
KeywordsElectrostatic potential Periodicity Ewald summation
Mathematics Subject Classification (2010)65Z05 40C99 35J05 31C20 70E55
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