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The Ewald method is used for simulations with periodic boundary conditions.
Imagine that the density distribution is a superposition of delta functions
and mutually-cancelling Gaussians:
where
and  The position of the periodic box that contains an identical image of particles as the active box is r_n. The particle positions in the active box are r_i and r_j .
Using Fourier transforms,
where  is the box volume and k is a vector wavenumber.
The force on particle i from the imaginary, or wave-part, of this distribution of density is
This sum requires discrete Fourier transforms, or a  operation using the WINE chip with the exp operation done by the function evaluator.
For each particle i, enter wavenumber k to WINE and stream the j particles by. (Note that this expression is independent of the box positions, r_n).
The force on particle i from the real component of the density distribution is
This expression requires a direct sum with function evaluators using MD-GRAPE2.
For each particle i, stream particles j and boxes n by inside MD-GRAPE2. For small eta, this expression converges for the sum over the box count, n.
Attribute: rapid convergence of k and n sums for an infinitely large (i.e., periodic) system.
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