Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems
Dag Lindbo,Anna-Karin Tornberg +1 more
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In this paper, a spectral representation in terms of both Fourier series and integrals is presented for the 2P Ewald sum. But the spectral representation is not suitable for large-scale computations.Abstract:
A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series and integrals. This allows us to concisely derive both the 2P Ewald sum and a fast PME-type method suitable for large-scale computations. The primary results are: (i) close and illuminating connections between the 2P problem and the standard Ewald sum and associated fast methods for full periodicity; (ii) a fast, O(N log N), and spectrally accurate PME-type method for the 2P k-space Ewald sum that uses vastly less memory than traditional PME methods; (iii) errors that decouple, such that parameter selection is simplified. We give analytical and numerical results to support this.read more
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References
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Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems
TL;DR: An N⋅log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms.
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TL;DR: In this paper, a simulation program for particle-mesh force calculation is presented, based on a one-dimensional plasma model and a collisionless particle model, which is used to simulate collisionless particle models.
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On the Lambert W function
TL;DR: A new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing W are presented.
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Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems.
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