A comparison of Ewald summation techniques for planar surfaces

Widmann, Albert H.; Adolf, David B.

doi:10.1016/s0010-4655(97)00090-8

Cited by 55 publications

(57 citation statements)

References 23 publications

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“…For this geometry Ewald based formulas are only slowly convergent, have mostly O(N 2 ) scalings and no "a priori" error estimates exist [36]. Recently Arnold [37,38] developed a method which is based on convergent factors, whose errors are well controlled, and which uses a factorization approach resulting in an O(N 5/3 ) scaling (MMM2D).…”

Section: Methods For Long Range Interactionsmentioning

confidence: 99%

Computer Simulations of Charged Systems

Holm

Kremer

2001

Electrostatic Effects in Soft Matter and Biophysics

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Abstract. In this brief contribution to the Proceedings of the NATO-ASI on "Electrostatic Effects in Soft Matter and Biophysics" [1], which took place in Les Houches from Oct. 1-13, 2000, we summarize in short aspects of the simulations methods to study charged systems. After describing some basics of Monte Carlo and Molecular dynamics techniques, we describe a few methods to compute long range interactions in periodic systems. After a brief detour to mean-field models, we describe our results obtained for flexible polyelectrolytes in good and bad solvents. We follow with a description of the inhomogeneity of the counterion distribution around finite chains, and continue then with infinitely long, rodlike systems. The last part is devoted to the phenomenon of overcharging for colloidal particles and its explanation in terms of simple electrostatic arguments.

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Section: Methods For Long Range Interactionsmentioning

confidence: 99%

Computer Simulations of Charged Systems

Holm

Kremer

2001

Electrostatic Effects in Soft Matter and Biophysics

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“…For this geometry Ewald based formulas are only slowly convergent, have mostly O(N 2 ) scalings and no "a priori" error estimates exist [10]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [10] a comparison was made with respect to speed and accuracy of the three most popular versions, the traditional 2d-Ewald method developed by Heyes, Barber, and Clarke (HBC) [11], the one due to Hautmann-Klein (HK) [12], and the approach attributed to Nijboer and de Wette (NdW) [13,14]. Another variant is due to Smith [15], which combines HBC and NdW, resulting in a good scaling, but still slow convergence.…”

Section: Introductionmentioning

confidence: 99%

MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries

Arnold

Holm

2002

Computer Physics Communications

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We present a new method, in the following called MMM2D, to accurately calculate the electrostatic energy and forces on charges being distributed in a two dimensional periodic array of finite thickness. It is not based on an Ewald summation method and as such does not require any fine-tuning of an Ewald parameter for convergence. We transform the Coulomb sum via a convergence factor into a series of fast decaying functions which can be easily evaluated. Rigorous error bounds for the energies and the forces are derived and numerically verified. Already for small systems our method is much faster than the traditional 2D-Ewald methods, but for large systems it is clearly superior because its time demand scales like O(N 5/3 ) with the number N of charges considered. Moreover it shows a rapid convergence, is very precise and easy to handle.

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“…A comparison of three versions of EW2D method can be found in Ref. [11].Unfortunately, the practical use of the EW2D sum is hampered by the occurrence of a reciprocal space term. The resulting Fourier space sum does not allow for a product decomposition as it is done in the three-dimensional periodic Ewald method and therefore the method has a scaling of O(N 2 ).…”

Section: Ewald Methods For 2dp1df Boundary Conditions Called Ew2d Hmentioning

confidence: 99%

A particle-particle, particle-density algorithm for the calculation of electrostatic interactions of particles with slablike geometry

Ghasemi

Neelov

Goedecker

2007

The Journal of Chemical Physics

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We present a fast and accurate method to calculate the electrostatic energy and forces of interacting particles with the boundary conditions appropriate to surfaces, i.e periodic in the two directions parallel to the surface and free in the perpendicular direction. In the spirit of the Ewald method the problem is divided into a short range and long range part. The charge density responsible for the long range part is represented by plane waves in the periodic directions and by finite elements in the non-periodic direction. Our method has computational complexity of O(N g log(N g )) with a very small prefactor, where N g is the number of grid points.

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A comparison of Ewald summation techniques for planar surfaces

Cited by 55 publications

References 23 publications

Computer Simulations of Charged Systems

Computer Simulations of Charged Systems

MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries

A particle-particle, particle-density algorithm for the calculation of electrostatic interactions of particles with slablike geometry

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