Ewald summation based on nonuniform fast Fourier transform

Hedman, Fredrik; Laaksonen, Aatto

doi:10.1016/j.cplett.2006.04.106

Cited by 22 publications

(55 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a first implementation [56,57], we used the libraries FFTW [58] and NFFT [54]. Details of the accuracy and scaling properties can be found in reference papers.…”

Section: Implementation and Resultsmentioning

confidence: 99%

Non-Uniform FFT and Its Applications in Particle Simulations

Wang¹,

Hedman²,

Porcu³

et al. 2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a first implementation [56,57], we used the libraries FFTW [58] and NFFT [54]. Details of the accuracy and scaling properties can be found in reference papers.…”

Section: Implementation and Resultsmentioning

confidence: 99%

Non-Uniform FFT and Its Applications in Particle Simulations

Wang¹,

Hedman²,

Porcu³

et al. 2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…7] for an overview. Indeed, in [46] we point out that the building blocks of the fast summation for nonperiodic boundary conditions and the NFFT-based fast Ewald summation [23] for periodic boundary conditions are very similar. Especially, both algorithms employ the NFFT in order to achieve a fast algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…A broad variety of mathematical algorithms and applications depends on the calculation of the nonequispaced discrete Fourier transform (NDFT), which is a generalization of the discrete Fourier transform to nonequispaced nodes. Especially, its fast approximate realization called nonequispaced fast Fourier transform (NFFT) [8,3,55,59,52,20,31] led to the development of a large number of fast numerical algorithms, e.g., in computerized tomography [16,9], particle simulation [50,23], and spectral methods on adaptive grids, just to name a few examples. An extensive list of applications can be found e.g., in [20].…”

mentioning

confidence: 99%

Parallel Three-Dimensional Nonequispaced Fast Fourier Transforms and Their Application to Particle Simulation

Pippig

Potts²

2013

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract.Starting from an approved serial algorithm, we develop a new parallel algorithm for calculating nonequispaced fast Fourier transforms on massively parallel distributed memory architectures. We demonstrate how to deal with the inherent load imbalance of the serial algorithm due to the use of oversampled FFT. This algorithm has been implemented in a new open source software library called PNFFT. Furthermore, we derive a new parallel distributed memory algorithm for the fast computation of fully Coulomb interactions in a charged particle system with nonperiodic boundary conditions based on a particle-mesh approximation scheme. We show that an appropriate adjustment of the underlying parallel nonequispaced fast Fourier transform circumvents severe load imbalance due to particle scaling. To prove the high scalability of our algorithms we provide performance results on a BlueGene/P system using up to 65536 cores.Key words. parallel nonequispaced fast Fourier transform, parallel fast summation, parallel particle-mesh methods, NFFT AMS subject classifications. 65T50, 65Y05 DOI. 10.1137/120888478 1. Introduction. A broad variety of mathematical algorithms and applications depends on the calculation of the nonequispaced discrete Fourier transform (NDFT), which is a generalization of the discrete Fourier transform to nonequispaced nodes. Especially, its fast approximate realization called nonequispaced fast Fourier transform (NFFT) [8,3,55,59,52,20,31] led to the development of a large number of fast numerical algorithms, e.g., in computerized tomography [16,9], particle simulation [50,23], and spectral methods on adaptive grids, just to name a few examples. An extensive list of applications can be found e.g., in [20].Roughly speaking, the NFFT consists of three steps. First, a deconvolution in frequency domain. Second, a fast Fourier transform (FFT) and, finally, a discrete convolution in spatial domains. The deconvolution and convolution is performed with a window function that is well localized in frequency and spatial domains. Therefore, these two convolution steps can be performed approximately in a fast way. Another advantage of the good localization is that parallel implementations of the convolution steps only require next neighbor communication.The FFT plays a central role in the modular structure of the NFFT algorithm and is a perfect example for the important interplay between the development of fast algorithms and sustainable software engineering in order to produce high performance software. Without a doubt, the FFTW software library [18,19] is an outstanding implementation of the FFT and one of the most important software packages in scientific computing. It offers support of shared memory parallelism and also distributed memory parallelism based on a one-dimensional decomposition of the input

show abstract

“…Also approximations via a Gaussian have already been considered, see Lindbo and Tornberg [5]. The particle-particle NFFT (P 2 NFFT) approach, which was suggested in Hedman and Laaksonen [9] and Pippig and Potts [7], is based on the FFT for nonequispaced data (NFFT) and allows the usage of various types of approximating window functions, as for example also (Kaiser-)Bessel functions besides B-splines and Gaussian. In this context we remark that in a variety of applications the results strongly depend on which window function is applied.…”

Section: Introductionmentioning

confidence: 99%

Parameter Tuning for the NFFT Based Fast Ewald Summation

Nestler

2016

Front. Phys.

View full text Add to dashboard Cite

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P 2 NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well-known particle-particle particle-mesh (P 3 M) algorithm. The publicly available P 2 NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.

show abstract

Ewald summation based on nonuniform fast Fourier transform

Cited by 22 publications

References 32 publications

Non-Uniform FFT and Its Applications in Particle Simulations

Non-Uniform FFT and Its Applications in Particle Simulations

Parallel Three-Dimensional Nonequispaced Fast Fourier Transforms and Their Application to Particle Simulation

Parameter Tuning for the NFFT Based Fast Ewald Summation

Contact Info

Product

Resources

About