Related papers: On FFT-based convolutions and correlations, with a…
Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…
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…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…
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…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
We propose a Fast Fourier Transform based Periodic Interpolation Method (FFT-PIM), a flexible and computationally efficient approach for computing the scalar potential given by a superposition sum in a unit cell of an infinitely periodic…
We describe an implementation to solve Poisson's equation for an isolated system on a unigrid mesh using FFTs. The method solves the equation globally on mesh blocks distributed across multiple processes on a distributed-memory parallel…
A common problem in cosmology is to integrate the product of two or more spherical Bessel functions (sBFs) with different configuration-space arguments against the power spectrum or its square, weighted by powers of wavenumber. Naively…
The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation…
Although the classical density functional theory (DFT) of inhomogeneous fluids was formulated more than four decades ago, its application to broken symmetry phases of molecular systems remained a challenge. Approximate free energy…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
The solution of the Poisson equation is a ubiquitous problem in computational astrophysics. Most notably, the treatment of self-gravitating flows involves the Poisson equation for the gravitational field. In hydrodynamics codes using…
A system of soft ellipsoid molecules confined between two planar walls is studied using classical Density Functional Theory (DFT). Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different…
In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the fast Fourier transform (FFT), the fast multipole method (FMM), the geometric multigrid (GMG), and…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
We present a fast and accurate algorithm to solve Poisson problems in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson problems with interfaces across which the solution is…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…