FFT-based Method Research Articles

Investigation on the longitudinal compressive strength of unidirectional carbon fiber/nanoparticles reinforced polymer composites using FFT-based method

The longitudinal compressive properties of carbon fiber/nanoparticles reinforced polymer unidirectional composites are investigated by experiments and a series of numerical simulations based on fast Fourier transforms (FFT) method taking into consideration matrix plastic behavior and initial fiber waviness. The efficient and accurate FFT-based method is convenient and has the low computation cost to discuss the effects of material and geometric parameters on the longitudinal compressive strength in details. The proper filling nanoparticles can significantly increase the longitudinal compressive strength. The computational results for failure mechanisms and strength show a good consistency with our experimental results. The present study provides reliable guidance for designing the fiber reinforced polymer composites with better damage tolerance.

Fast implicit solvers for phase-field fracture problems on heterogeneous microstructures

We study fast and memory-efficient FFT-based implicit solution methods for small-strain phase-field crack problems for microstructured brittle materials. A fully implicit first order formulation of the problem coupling elasticity and damage permits using comparatively few, but large, time steps compared to semi-explicit schemes. We investigate memory-efficient FFT-based solution techniques, and identify the heavy ball scheme as particularly powerful. We discuss the memory-efficient implementation and present demonstrative numerical examples.

Target detection for linear frequency‐modulated continuous‐wave radar via reduced‐dimension approximate message passing

A two-stage target detection approach, jointly performing traditional and approximate message passing (AMP) algorithms, is proposed for linear frequency-modulated continuous-wave radar. In the first stage, fast Fourier transform (FFT) and target pre-detection are carried out. Based on the pre-detection results, a reduced-dimension signal observation model is established. In the second stage, AMP is used to reconstruct true targets, and then target detection is implemented. Performances of the proposed approach are provided by numerical experiments and compared with those of AMP and the traditional FFT-based methods. Results indicate the effectiveness of the proposed approach.

Rapid wavelet-based bathymetry inversion method for nearshore X-band radars

A wavelet based method for bathymetry retrieval from X-band radar images is proposed. The method combines traditional Fast Fourier Transform techniques for retrieving peak frequency maps by evaluating the spectral peaks in the time domain, and a localized 2D Continuous Wavelet Transform for retrieving the corresponding peak wavenumbers. The main improvements of the new method compared to conventional FFT-based methods are as follows: a) the wavelet-based approach is localized - naturally fitting the inhomogeneous conditions typically found in the nearshore environment; b) it is continuous and uses wave phase information providing smooth bathymetry maps with good accuracy (RMSE in the range 2.6–6.6% of the maximum water depth); c) it requires relatively small number of successive images without the limitation of requiring a uniform time step.In order to verify the proposed method, 2D simulations of wave shoaling and refraction were performed for different sea conditions and over several bottom topographies. A radar image model including tilt and shadowing modulations together with speckle noise was applied to the simulated surface elevations to provide synthetic radar images. The method's ability to reconstruct the original bathymetry is shown to be robust in intermediate to shallow water depths (kph < 1) for all cases. The method was also applied to real data acquired in Sylt island (Germany). A comparison between a bathymetric survey held prior to a storm and a radar reconstructed one during the storm shows very good agreement. These results reassure the high capability of this new method to be used in operational settings.

A comparison of fast Fourier transform-based homogenization method to asymptotic homogenization method

This paper provides a comparison study on the homogenization methods based on asymptotic approach and fast Fourier transform (FFT), respectively. Their essential ideas, numerical implementation, efficiency, applicability as well as the deformation modes of unit cell are reviewed and compared. Numerical examples show that the effective mechanical properties obtained by FFT-based homogenization are smaller than those of asymptotic homogenization with the same mesh but within an acceptable error margin with a finer mesh. Because a conjugate gradient algorithm is used, the FFT-based homogenization method can obtain the results much faster than asymptotic homogenization which is based on finite element analysis. We find FFT-based can be used for porous structures with infinite contrast in Young’s modulus of solid material and void material. We propose an algorithm to calculate the node displacement of unit cell for FFT-based homogenization and note it can generate deformation patterns which came more reasonably reflect periodic boundary conditions than asymptotic homogenization.

FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials

This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.

A Method for Retrieving Wave Parameters From Synthetic X-Band Marine Radar Images

The research on retrieving wave parameters from X-band marine radar images based on the spectral analysis method is investigated in this paper. Since the sea wave field is not always homogeneous and stationary in the spatial and temporal domain, especially in the coastal shallow water area, the two-dimensional continuous wavelet transform (2D CWT) is currently utilized to retrieve wave spectrum and wave parameters for improving the inversion accuracy. Although the wavelet is concentrated around the given wavenumber, the CWT of the original image is spread out over a region. By deeply investigating the CWT and its application on radar image, a novel method based on the synchrosqueezed wavelet transform (SWT) is proposed to effectively extract wave parameters from the radar images. The effectiveness of the proposed algorithm is verified based on the simulated radar image. The experimental results demonstrate that the proposed SWT method has better performance than the traditional three-dimensional fast Fourier transform (3D FFT) method and the wavelet-based method for retrieving wave height. The performance of retrieving wave direction and wave period is close to that of both the 3D FFT-based method and the CWT-based method.

Computing the Kolmogorov-Smirnov Distribution When the Underlying CDF is Purely Discrete, Mixed, or Continuous

The distribution of the Kolmogorov-Smirnov (KS) test statistic has been widely studied under the assumption that the underlying theoretical cumulative distribution function (CDF), F (x), is continuous. However, there are many real-life applications in which fitting discrete or mixed distributions is required. Nevertheless, due to inherent difficulties, the distribution of the KS statistic when F (x) has jump discontinuities has been studied to a much lesser extent and no exact and efficient computational methods have been proposed in the literature. In this paper, we provide a fast and accurate method to compute the (complementary) CDF of the KS statistic when F (x) is discontinuous, and thus obtain exact p values of the KS test. Our approach is to express the complementary CDF through the rectangle probability for uniform order statistics, and to compute it using fast Fourier transform (FFT). Secondly, we provide a C++ and an R implementation of the proposed method, which fills the existing gap in statistical software. We give also a useful extension of the Schmid's asymptotic formula for the distribution of the KS statistic, relaxing his requirement for F (x) to be increasing between jumps and thus allowing for any general mixed or purely discrete F (x). The numerical performance of the proposed FFT-based method, implemented both in C++ and in the R package KSgeneral, available from https://CRAN.R-project.org/package=KSgeneral, is illustrated when F (x) is mixed, purely discrete, and continuous. The performance of the general asymptotic formula is also studied.

Transmissivity assessment of plasmonic-dielectric waveguide interconnects via modified FFT-BPM

We present remedies to two fundamental difficulties facing the applicability of the traditional FFT-based beam propagation method (FFT-BPM) when investigating the propagation and transmission of transverse magnetic (TM) optical beams in subwavelength step-index waveguiding structures. To the best of our knowledge, the FFT-BPM is introduced for the first time to assess the plasmonic-dielectric waveguide interconnects. At the junction plane, we modified the FFT-BPM algorithm by including a combined spatial-spectral reflection operator formalism to calculate the reflected field. As a test, we calculated the optical power transmission efficiency between plasmonic and dielectric waveguide interconnect. A comparison between our results, and those obtained by full-modal matching using finite-difference frequency-domain (FDFD), reveals good agreement. Such interconnecting structure is crucial in many applications as biosensors, optical near-field probes, and interfacing elements involving high-contrast refractive index materials. We believe that rehabilitating the classical FFT-BPM to handle nanoscale waveguiding structures, which include metal-dielectric interfaces, will be of prime importance in the development, analysis and assessment of nano-photonics devices.

Parallel Algorithm for Supercomputing Simulation of Dust-Gaseous Gravitating Systems Using Particle-In-Cell and SPH Methods

We present a supercomputer numerical model for simulating 3D dynamics of dust-gas gravitating circumstellar disk. The model combines SPH method for solving gas dynamical equations, particle-in-cell (PIC) method for solving Vlasov equation, and convolution FFT-based grid method for solving Poisson equation. The approach is based on 3D domain decomposition, sorting of particles with regard to grid cell, and transferring necessary amount of particles between subdomains. The algorithm is aimed to be run on supercomputers with distributed memory and on hybrid supercomputers.

Extension of an FFT-Based Beam Propagation Method to Plasmonic and Dielectric Waveguide Discontinuities and Junctions

We adapted a fast Fourier transform-based Beam Propagation Method (FFT-BPM) to investigate waveguide discontinuities in plasmonic waveguides. The adaptation of the FFT-BPM to treat transverse magnetic (TM) fields requires the circumvention of two major difficulties: the mixed derivatives of the magnetic field and waveguide refractive index profile in the TM wave equation and the step-like index change at the transverse metal-dielectric boundary of the plasmonic guide and the transverse boundaries of the dielectric waveguide as well. An equivalent-index method is adopted to transform TM fields to transverse electric (TE) ones, thus enabling the benefit of the full power and simplicity of the FFT-BPM. Moreover, an appropriate smoothing function is used to approximate the step-like refractive index profile in the transverse direction. At the junction plane, we used an accurate combined spatial-spectral reflection operator to calculate the reflected field. To validate our proposed scheme, we investigated the modal propagation in a silicon waveguide terminated by air (like a laser facet in two cases: with and without a coating layer). Then we considered a subwavelength plasmonic waveguide (metal-insulator-metal MIM) butt-coupled with a dielectric waveguide, where the power transmission efficiency has been calculated and compared with other numerical methods. The comparison reveals good agreement.

On double-boundary non-crossing probability for a class of compound processes with applications

We develop an efficient method for computing the probability that a non-decreasing, pure jump (compound) stochastic process stays between arbitrary upper and lower boundaries (i.e., deterministic functions, possibly discontinuous) within a finite time period. The compound process is composed of a process modelling the arrivals of certain events (e.g., demands for a product in inventory systems, customers in queuing, or claims/capital gains in insurance/dual risk models), and a sequence of independent and identically distributed random variables modelling the sizes of the events. The events arrival process is assumed to belong to the wide class of point processes with conditional stationary independent increments which includes (non-)homogeneous Poisson, binomial, negative binomial, mixed Poisson and doubly stochastic Poisson (i.e., Cox) processes as special cases. The proposed method is based on expressing the non-exit probability through Chapman–Kolmogorov equations, re-expressing them in terms of a circular convolution of two vectors which is then computed applying fast Fourier transform (FFT). We further demonstrate that our FFT-based method is computationally efficient and can be successfully applied in the context of inventory management (to determine an optimal replenishment policy), ruin theory (to evaluate ruin probabilities and related quantities) and double-barrier option pricing or simply computing non-exit probabilities for Brownian motion with general boundaries.

Staggered Grid Scheme for the FFT‐Based Methods

A staggered grid scheme is proposed to reduce both the total memory requirement and the CPU time of generating the corrected near matrix in the FFTbased methods. Two sets of Cartesian grids are used to project the source points and the field points, respectively. The proposed method does not lower the efficiency of computing far matrix-vector products, compared with the traditional uniform Cartesian grid scheme. Some numerical experiments are provided to demonstrate both the correctness and the efficiency of the proposed method.

CoDockPP: A Multistage Approach for Global and Site-Specific Protein-Protein Docking.

Protein-protein docking technology is an effective approach to study the molecular mechanism of essential biological processes mediated by complex protein-protein interactions. The fast Fourier transform (FFT) correlation approach makes a good balance between the exhaustive global sampling and the computational efficiency for protein-protein docking. However, it is difficult to integrate the precise knowledge-based scoring function and site constraint information into the FFT-based approach. New docking strategies with the capability of combining both global sampling and precise scoring are strongly needed. We propose a multistage protein-protein docking strategy called CoDockPP. This program takes full advantage of the sampling efficiency of the FFT-based method to choose the valid ligand protein poses with good surface complementarity. The retained poses are transformed to the real Cartesian space for the implementation of site constraints and atomic scoring. Site constraints and a rapid table lookup scoring are applied to gradually reduce the candidate poses to a tractable number. To enhance the accuracy of docking prediction, the best fast-scoring states are expanded the local sampling points and then these neighbor poses are further evaluated by the precise knowledge-based scoring function. By testing on protein-protein docking benchmark 5.0, CoDockPP remarkably improves the success rate and hit count in both ab initio docking and site-specific docking, especially in difficult cases. The server is free and open to all users with no login requirement at http://codockpp.schanglab.org.cn .

An FFT-Based CLEAN Deconvolution Method for Interferometric Microwave Radiometers With Spatially Variable Beam Pattern

A modification to the extended CLEAN deconvolution method for passive microwave interferometric radiometers is presented to account for the interferometer beam patterns that vary depending on the source position within the interferometer field of view. This method is developed for the newly proposed multisatellite rotating microwave interferometric radiometer concept for geostationary atmospheric sounding, which is found to have a spatially varying beam pattern. The proposed method is implemented by the piecewise application of Fast Fourier Transform (FFT)-based convolution, i.e., the image is divided into discrete segments, where the beam pattern is assumed to be constant within each segment. This approach allows the proposed method to exploit the speed advantage of the FFT. Applying this method to the proposed multisatellite interferometer shows a twofold improvement in the radiometric accuracy of the restored brightness temperature map, as compared with the constant beam pattern CLEAN.

Effect of heterogeneous interphase on the mechanical properties of unidirectional fiber composites studied by FFT-based method

Based on representative volume element (RVE) with interphase region between fiber and matrix, the microscopic mechanical behavior of transversely randomly distributed unidirectional (UD) carbon fiber reinforced polymer composites is studied by using fast Fourier transforms (FFT) simulation. The change of mechanical properties across interphase region can be described by an exponential function. By using FFT method, the effect of fiber volume fraction and interphase properties distribution on the effective material properties and the damage development mechanism of the composites are investigated. The effect of heterogeneous behaviors of carbon fiber with core/shell like behavior and interphase is also discussed. Compared to the traditional finite element model with zero-thickness interface, the stress-strain results obtained by the present computational approach are in good agreement with experimental data. This study can be helpful for interface design and manufacturing of fiber reinforced composites.

A novel, FFT-based one-dimensional blood flow solution method for arterial network

In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for the vessel skin friction through the use of Womersley solution. To incorporate nonlinear effects, a novel approximation method is proposed to enable calculation of nonlinear corrections. Unlike similar methods available in the literature, the set of algebraic equations required for every harmonic is constructed automatically. The result is a generalized, robust and fast method to accurately capture the increasing pulse wave velocity downstream as well as steepening of the pulse front. The proposed method is shown to be appropriate for incorporating correct convection and diffusion coefficients. We show that the proposed method is fast and accurate and it can be an effective tool for 1D modelling of blood flow in human arterial networks.

Low-Complexity Joint Extrapolation-MUSIC-Based 2-D Parameter Estimator for Vital FMCW Radar

In this paper, a low-complexity joint extrapolation-multiple signal classification (MUSIC)-based 2-D parameter estimator is proposed for vital frequency-modulated continuous-wave (FMCW) radar. Recently, an FMCW radar, which can detect the distance and vital Doppler information, has been considered for vital non-contact radar. In the conventional FMCW radar system, fast Fourier transform (FFT)-based algorithms with low complexity are used to extract multiple parameters. However, the resolution and accuracy of an FFT-based parameter estimator are considerably low. Thus, 2-D high-resolution algorithms, such as the 2-D estimation of signal parameters via rotational invariance techniques and 2-D MUSIC, have been suggested as an alternative method. However, a large computation power is required compared with the FFT-based methods. Therefore, this paper proposes a 2-D parameter estimator that combines extrapolated FFT and MUSIC to reduce the computational load for vital detection. The proposed method uses an extrapolated FFT to overcome the disadvantages of the low-resolution FFT for the distance information, and then, the 1-D MUSIC algorithm is applied to the Doppler domain direction only for the extracted magnitude and phase information of the target’s extrapolated FFT results. Hence, the proposed algorithm combines the advantages of FFT and MUSIC. The performance of the proposed estimation is compared with that of other algorithms using Monte Carlo simulation results. The root-mean-square error of the proposed method is compared with that of 2-D MUSIC with various parameters. To verify the performance of the proposed combination method, the FMCW radar was used, and its performance was verified in an indoor environment.

FFT-based homogenization of hypoelastic plasticity at finite strains

Fast Fourier Transform (FFT) based methods are becoming increasingly popular for modeling the texture evolution and local mechanical response of polycrystalline materials within the representative volume element (RVE). Originally, the FFT-based method was formulated through the Lippman–Schwinger (L–S) equation in terms of a homogeneous elastic reference medium. More recently, the Fourier–Galerkin method was proposed to discretize the RVE weak form independently of the reference medium using trigonometric polynomials. The Fourier–Galerkin method, albeit efficient and robust, has not been extended to solve crystal plasticity (CP) problems with spatial heterogeneity and fine resolution. Also, its algorithmic homogenization has not yet been investigated, which is essential for concurrent multiscale modeling. In this paper, a general framework is proposed that connects the FFT-based method and objective rate constitutive models, in particular a generalized implementation of crystal plasticity. Consistent linearization is achieved by pulling back the tangent stiffness from unrotated configuration to reference configuration, which improves the convergence behavior of the Newton–Krylov solver. Applying the inexact Newton method further improves the numerical efficiency. Also, the algorithmic homogenized tangent stiffness for the Fourier–Galerkin method is derived to enable mixed boundary conditions and concurrent multiscale modeling. Lastly, the Fourier–Galerkin method’s accuracy and efficiency for solving CP problems are studied in a parallelized environment, and significant speedup is observed versus the finite element method and L–S based FFT method.

Phase Matching of Coincident Pulses for Range-Doppler Estimation of Multiple Targets

Range-Doppler estimation algorithms that use the phase of the returned signal face the 2 $\pi$ phase ambiguity problem. In this letter, we eliminate phase wrapping by using two coincident opposite polarity chirps but equal starting frequencies. The returns for both chirps from the same target have near equal phases. The phase wrap is present in both returns but they are the same. Therefore, the differential phase matching used to pair the returns from the same target cancels out the phase wrap. No phase unwrapping is needed. The proposed method has no inherent maximum unambiguous range or velocity, works in multitarget theaters, requires a much lower sampling rate, is not affected by range migration, decouples the Doppler cycle from the pulse repetition frequency and is computationally more efficient than FFT-based methods.