Non-Uniform FFT and Its Applications in Particle Simulations

Wang, Yong‐Lei; Hedman, Fredrik; Porcu, Mariano; Mocci, Francesca; Laaksonen, Aatto

doi:10.4236/am.2014.53051

Cited by 12 publications

(17 citation statements)

References 69 publications

(93 reference statements)

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“…With given Fourier coefficientsf , the Fourier samples f can be transformed with suitable FFT algorithms in both directions. More in-depth discussion and technical details can be found in publications [20,23,24,26,[48][49][50] and references therein. [20,24,26] which is similar to the other particle-mesh based schemes in handling the long-ranged part of electrostatic interactions.…”

Section: Discrete Fourier Transforms For Nonequispaced Datamentioning

confidence: 99%

“…[8,20,24] Later, the ENUF method was implemented in the dissipative particle dynamics (DPD) framework to calculate electrostatic interactions between charge density distributions at mesoscopic level. [24][25][26] The ENUF and ENUF-DPD methods were adopted to explore the dependence of conformational properties of polyelectrolytes on charge fraction, ion concentration and counterion valency of added salts, [26] to investigate specific binding structures of dendrimers on bilayer membranes and the corresponding permeation mechanisms, [27] and to study heterogeneous structures and dynamics in ionic liquids (ILs) and how electrostatic interactions between charged particles affect these properties at extended spatiotemporal scales. [8] In addition, great endeavors have been made in recent years to accelerate scientific computation using, for example, dedicated and specialized hardware and high-performance accelerator processors.…”

Section: Introductionmentioning

confidence: 99%

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TheENUFmethod—Ewald summation based onnonuniformfast Fourier transform: Implementation, parallelization, and application

Yang

Zhu

et al. 2020

J Comput Chem

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Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between charged particles constitute a prominent factor in determining structures and states of model systems. How to efficiently calculate electrostatic interactions in simulation systems subjected to partial or full periodic boundary conditions has been a grand challenging task. In the past decades, a large variety of computational schemes has been proposed, among which the Ewald summation method is the most reliable route to accurately deal with electrostatic interactions between charged particles in simulation systems. In addition, extensive efforts have been done to improve computational efficiencies of the Ewald summation based methods. Representative examples are approaches based on cutoffs, reaction fields, multi‐poles, multi‐grids, and particle‐mesh schemes. We sketched an ENUF method, an abbreviation for the Ewald summation method based on the nonuniform fast Fourier transform technique, and have implemented this method in particle‐based simulation packages to calculate electrostatic energies and forces at micro‐ and mesoscopic levels. Extensive computational studies of conformational properties of polyelectrolytes, dendrimer‐membrane complexes, and ionic fluids demonstrated that the ENUF method and its derivatives conserve both energy and momentum to floating point accuracy, and exhibit a computational complexity of scriptO)(NlogN with optimal physical parameters. These ENUF based methods are attractive alternatives in molecular simulations where high accuracy and efficiency of simulation methods are needed to accelerate calculations of electrostatic interactions at extended spatiotemporal scales.

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Section: Discrete Fourier Transforms For Nonequispaced Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

TheENUFmethod—Ewald summation based onnonuniformfast Fourier transform: Implementation, parallelization, and application

Yang

Zhu

et al. 2020

J Comput Chem

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“…In the development of effective potentials with the NI and IBI methods, the electrostatic interactions should be explicitly incorporated in iteration processes. In subsequent CGMD simulations, the long range electrostatic interactions should also be calculated explicitly with proper methods [136][137][138] to improve the reliability of dynamical properties of model IL systems at wide temperature range.…”

Section: Coarsementioning

confidence: 99%

4. Multigranular modeling of ionic liquids

Wang¹,

Sarman²,

Laaksonen³

et al. 2019

Ionic Liquids

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Ionic liquids (ILs) are a special category of molten salts with melting points near ambient temperatures (or by convention below 100°C). Owing to their numerous valuable physicochemical properties as bulk liquids, solvents, at surfaces and in confined environments, ILs have attracted increasing attention in both academic and industrial communities in a variety of application areas involving physics, chemistry, material science and engineering. Due to their nearly limitless number of combinations of cation-anion pairs and mixtures with cosolvents, a molecular level understanding of their hierarchical structures and dynamics, requiring strategies to connect several length and time scales, is of crucial significance for rational design of ILs with desired properties, and thereafter refining their functional performance in applications. As an invaluable compliment to experiments from synthesis to characterization, computational modeling and simulations have significantly increased our understanding on how physicochemical and structural properties of ILs can be controlled by their underlying chemical and molecular structures. In this chapter, we will give examples from our own modeling work based on selected IL systems, with focus on imidazolium-based and tetraalkylphosphonium-orthoborate ILs, studied at several spatio-temporal scales in different environments and with particular attention to applications of high technological interest. We start by describing studies performed using ab initio methods on force field development for tetraalkylphosphonium-orthoborate ILs, and computational studies on thermal decomposition of these ILs. The delicate interplay between hydrogen bonding and π-type interactions in an imidazolium-orthoborate IL was studied by performing ab initio molecular dynamics simulations. On the atomistic level, atomistic simulations were performed with constructed force field parameters to study intrinsic molecular interactions between residual water molecules and tetraalkylphosphoniumorthoborate ionic species. For a typical trihexyltetradecylphosphonium bis(oxalato) borate IL at varied concentrations, microstructures and dynamics were systematically analyzed as water concentration increases. The liquid viscosities of typical trihexyltetradecylphosphonium-based ILs were estimated through equilibrium atomistic simulations using Green-Kubo relation with charge scaling factors on ionic species.Additionally, atomistic simulations were combined with X-ray scattering experiments to investigate phase behavior and ionic structures in IL mixtures with varied concentrations. Peculiar features of X-ray scattering spectra of IL mixtures with organic solvent are also discussed with an example dealing with ethyl ammonium nitrate and acetonitrile mixtures. On the mesoscopic level, a united-atom model for trihexyltetradecylphosphonium cation and coarse-grained models for butylmethy-limidazolium hexafluorophosphate were proposed, and effective interactions between coarse-grained beads were validated against experimental...

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“…Particularly, the ENUF method, which refers to Ewald summation method based on nonequispaced fast Fourier transform or nonuniform fast Fourier transform (NFFT) technique developed by Laaksonen and coworkers, is an easy‐to‐implement, and efficient method for calculating long‐range electrostatic interactions. The NFFT is a generalization of the FFT, and can be applied to nonequispaced points for Fourier transform. Several similar approaches have been proposed and some examples can be found in Refs.…”

Section: Introductionmentioning

confidence: 99%

Accelerating electrostatic interaction calculations with graphical processing units based on new developments of ewald method using non‐uniform fast fourier transform

et al. 2015

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We present new algorithms to improve the performance of ENUF method (F. Hedman, A. Laaksonen, Chem. Phys. Lett. 425, 2006, 142) which is essentially Ewald summation using Non-Uniform FFT (NFFT) technique. A NearDistance algorithm is developed to extensively reduce the neighbor list size in real-space computation. In reciprocal-space computation, a new algorithm is developed for NFFT for the evaluations of electrostatic interaction energies and forces. Both real-space and reciprocal-space computations are further accelerated by using graphical processing units (GPU) with CUDA technology. Especially, the use of CUNFFT (NFFT based on CUDA) very much reduces the reciprocal-space computation. In order to reach the best performance of this method, we propose a procedure for the selection of optimal parameters with controlled accuracies. With the choice of suitable parameters, we show that our method is a good alternative to the standard Ewald method with the same computational precision but a dramatically higher computational efficiency.

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Non-Uniform FFT and Its Applications in Particle Simulations

Abstract: ABSTRACT

Cited by 12 publications

References 69 publications

TheENUFmethod—Ewald summation based onnonuniformfast Fourier transform: Implementation, parallelization, and application

TheENUFmethod—Ewald summation based onnonuniformfast Fourier transform: Implementation, parallelization, and application

4. Multigranular modeling of ionic liquids

Accelerating electrostatic interaction calculations with graphical processing units based on new developments of ewald method using non‐uniform fast fourier transform

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