Related papers: Spectrally accurate Ewald summation for the Yukawa…
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…
The Ewald summation technique is generalised to power-law 1/|r|^k potentials in three-, two- and one-dimensional geometries with explicit formulae for all the components of the sums. The cases of short-range, long-range and "marginal"…
Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in…
We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e. sums involving a large number of free space Green's functions. We consider sums involving stokeslets, stresslets and rotlets that appear…
We present a fast and spectrally accurate method for efficient computation of the three dimensional Coulomb potential with periodicity in one direction. The algorithm is FFT-based and uses the so-called Ewald decomposition, which is…
Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The…
When evaluating the electrostatic potential, periodic boundary conditions in one, two or three of the spatial dimensions are often needed for different applications. The triply periodic Ewald summation formula is classical, and Ewald…
We derive a Ewald decomposition for the Stokeslet in planar periodicity and a novel PME-type O(N log N) method for the fast evaluation of the resulting sums. The decomposition is the natural 2P counterpart to the classical 3P decomposition…
We derive analytic solutions for the potential and field in a one-dimensional system of masses or charges with periodic boundary conditions, in other words Ewald sums for one dimension. We also provide a set of tools for exploring the…
Yukawa potentials are often used as effective potentials for systems as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential ; in this small screening limit, or…
Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions. We show how Ewald summation, and accompanying truncation…
A unified treatment for fast and spectrally accurate evaluation of electrostatic potentials subject to periodic boundary conditions in any or none of the three spatial dimensions is presented. Ewald decomposition is used to split the…
In this note, we derive Ewald sums for Yukawa potential for three dimensional systems with two dimensional periodicity. This sums are derived from the Ewald sums for Yukawa potentials with three dimensional periodicity [G. Salin and J.-M.…
A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for…
We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using…
We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…
Yukawa potentials may be long ranged when the Debye screening length is large. In computer simulations, such long ranged potentials have to be taken into account with convenient algorithms to avoid systematic bias in the sampling of the…
Ab initio computation of two-dimensional electronic spectra is an expanding field, whose goal is improving upon simple, few-dimensional models often employed to explain experiments. Here, we propose an accurate and computationally…
The electrostatic potential and energy of point charges in a real crystal, in the presence of thermal vibrations, is obtained as a special case of the Fourier method. Incorporating the role of thermal vibrations in electrostatic energy…
We establish Strichartz estimates (both reversed and some direct ones), pointwise decay estimates, and weighted decay estimates for the linear wave equation in dimension two with an almost scaling-critical potential, in the case when there…