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Related papers: Fast Ewald Summation using Prolate Spheroidal Wave…

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Prolate spheroidal wave functions (PSWFs) play an important role in various areas, from physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). One of the principal reasons for the importance of…

Functional Analysis · Mathematics 2012-06-21 Andrei Osipov

The ENUF method, i.e., Ewald summation based on the Non-Uniform FFT technique (NFFT), is implemented in Dissipative Particle Dynamics (DPD) simulation scheme to fast and accurately calculate the electrostatic interactions at mesoscopic…

Computational Physics · Physics 2013-03-20 Yong-Lei Wang , Aatto Laaksonen , Zhong-Yuan Lu

We present an efficient algorithm for the all-electron periodic Coulomb matrix based on the Ewald summation combined with the Fourier-transformed Coulomb method. The short-range contributions involving compact densities are evaluated in…

Chemical Physics · Physics 2025-09-23 Hieu Q. Dinh , Adam Rettig , Xintian Feng , Joonho Lee

For fixed $c,$ Prolate Spheroidal Wave Functions (PSWFs), denoted by $\psi_{n, c},$ form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith $c$. They have been largely studied and used after…

Classical Analysis and ODEs · Mathematics 2017-05-03 Aline Bonami , Abderrazek Karoui

Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…

Numerical Analysis · Mathematics 2025-02-05 Zecheng Gan , Xuanzhao Gao , Jiuyang Liang , Zhenli Xu

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…

Numerical Analysis · Mathematics 2017-09-13 Davoud Saffar Shamshirgar , Anna-Karin Tornberg

Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…

Data Analysis, Statistics and Probability · Physics 2015-07-08 Elya Courtney , Michael Courtney

Prolate spheroidal wave functions (PSWFs) play an important role in various areas, from physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). Even though the significance of PSWFs was realized…

Classical Analysis and ODEs · Mathematics 2012-12-14 Andrei Osipov

In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even…

Computational Physics · Physics 2015-06-17 Nail A. Gumerov , Ramani Duraiswami

Dielectrically confined Coulomb systems are widely employed in molecular dynamics (MD) simulations. Despite extensive efforts in developing efficient and accurate algorithms for these systems, rigorous and accurate error estimates, which…

Numerical Analysis · Mathematics 2025-03-25 Xuanzhao Gao , Qi Zhou , Zecheng Gan , Jiuyang Liang

In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order $\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both a weighted concentration integral operator,…

Numerical Analysis · Mathematics 2018-02-13 Jing Zhang , Huiyuan Li , Li-Lian Wang , Zhimin Zhang

Fast convolution algorithms, including Winograd and FFT, can efficiently accelerate convolution operations in deep models. However, these algorithms depend on high-precision arithmetic to maintain inference accuracy, which conflicts with…

Machine Learning · Computer Science 2024-07-04 Liulu He , Yufei Zhao , Rui Gao , Yuan Du , Li Du

The Fast Fourier Transform (FFT) is widely used in applications such as MRI, CT, and interferometry; however, because of its dependence on uniformly sampled data, it requires the use of gridding techniques for practical implementation. The…

Numerical Analysis · Mathematics 2025-12-22 Federico Achini , Paola Causin , Sara Vanini , Ke Chen , Simone Scacchi

The smooth particle mesh Ewald (SPME) method is the standard method for computing the electrostatic interactions in the molecular simulations. In this work, the multiple staggered mesh Ewald (MSME) method is proposed to boost the accuracy…

Computational Physics · Physics 2016-07-15 Han Wang , Xingyu Gao , Jun Fang

Accurately estimating the point spread function (PSF) of an optical system requires solving free-space wave propagation, which entails evaluating a diffraction integral. This integral is traditionally computed numerically using Fast Fourier…

Image and Video Processing · Electrical Eng. & Systems 2026-05-22 Nicholas Ganino , Qi Guo

To evaluate electrostatics interactions, Molecular dynamics (MD) simulations rely on Particle Mesh Ewald (PME), an O(Nlog(N)) algorithm that uses Fast Fourier Transforms (FFTs) or, alternatively, on O(N) Fast Multipole Methods (FMM)…

Numerical Analysis · Mathematics 2023-05-29 Igor Chollet , Louis Lagardère , Jean-Philip Piquemal

Particle Mesh Ewald (PME) methods accelerated through Fast Fourier Transforms (FFTs) for their reciprocal part are widely used to solve N -body problems over periodic structures with Laplace-like kernels. The FFT dependence of classical PME…

Numerical Analysis · Mathematics 2026-01-28 Igor Chollet

The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…

Numerical Analysis · Mathematics 2017-08-14 Santhosh Karnik , Zhihui Zhu , Michael B. Wakin , Justin Romberg , Mark A. Davenport

Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…

Quantitative Methods · Quantitative Biology 2019-01-30 Christopher K. Kovach , Phillip E. Gander

Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…

Numerical Analysis · Mathematics 2017-03-08 Marco Caliari , Simone Zuccher