Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Fourier”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Fourier-informed knot placement schemes for B-spline approximation

Fitting B-splines to scientific data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently approximated with B-splines by analyzing the Fourier spectrum of the data. Our method uses a collection of spectral filters to compute high-order derivatives, smoothed versions of noisy data, and the locations of jump discontinuities. Further, these quantities are then combined to choose knots that capture the qualitative features of the data, leading to accurate B-spline approximations with few knots. The method we introduce is direct and does not require any intermediate B-spline fitting before choosing the final knot distribution. Aside from fast Fourier transforms to transfer to and from Fourier space, the method runs in linear time with very little communication. We assess performance on several test cases in one and two dimensions, including data sets with jump discontinuities and noise. These tests show the method fits discontinuous data without spurious oscillations and remains effective in the presence of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading

Fourier pseudo-spectral methods for nonlinear partial differential equations are of wide interest in many areas of advanced computational science, including direct numerical simulation of three-dimensional (3-D) turbulence governed by the Navier-Stokes equations in fluid dynamics. This paper presents a new capability for simulating turbulence at a new record resolution up to 35 trillion grid points, on the world's first exascale computer, Frontier, comprising AMD MI250x GPUs with HPE's Slingshot interconnect and operated by the US Department of Energy's Oak Ridge Leadership Computing Facility (OLCF). Key programming strategies designed to take maximum advantage of the machine architecture involve performing almost all computations on the GPU which has the same memory capacity as the CPU, performing all-to-all communication among sets of parallel processes directly on the GPU, and targeting GPUs efficiently using OpenMP offloading for intensive number-crunching including 1-D Fast Fourier Transforms (FFT) performed using AMD ROCm library calls. With 99% of computing power on Frontier being on the GPU, leaving the CPU idle leads to a net performance gain via avoiding the overhead of data movement between host and device except when needed for some I/O purposes. Memory footprint including the size of communication buffers for MPI_ALLTOALL is managed carefully to maximize the largest problem size possible for a given node count. Detailed performance data including separate contributions from different categories of operations to the elapsed wall time per step are reported for five grid resolutions, from 2048 3 on a single node to 32768 3 on 4096 or 8192 nodes out of 9408 on the system. Both 1D and 2D domain decompositions which divide a 3D periodic domain into slabs and pencils respectively are implemented. The present code suite (labeled by the acronym GESTS, GPUs for Extreme Scale Turbulence Simulations) achieves a figure of merit (in grid points per second) exceeding goals set in the Center for Accelerated Application Readiness (CAAR) program for Frontier. The performance attained is highly favorable in both weak scaling and strong scaling, with notable departures only for 2048 3 where communication is entirely intra-node, and for 32768 3 , where a challenge due to small message sizes does arise. Communication performance is addressed further using a lightweight test code that performs all-to-all communication in a manner matching the full turbulence simulation code. Performance at large problem sizes is affected by both small message size due to high node counts as well as dragonfly network topology features on the machine, but is consistent with official expectations of sustained performance on Frontier. Overall, although not perfect, the scalability achieved at the extreme problem size of 32768 3 (and up to 8192 nodes — which corresponds to hardware rated at just under 1 exaflop/sec of theoretical peak computational performance) is arguably better than the scalability observed using prior state-of-the-art algorithms on Frontier's predecessor machine (Summit) at OLCF. New science results for the study of intermittency in turbulence enabled by this code and its extensions are to be reported separately in the near future.

3D fast Fourier transform↗
DOE OSTI2025

A generalizable machine learning-assisted fast Fourier transform algorithm to simulate the large strain phenomena in polycrystalline materials

Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient Super-Resolution of Near-Surface Climate Modeling Using the Fourier Neural Operator

Downscaling methods are critical in efficiently generating high-resolution atmospheric data. However, state-of-the-art statistical or dynamical downscaling techniques either suffer from the high computational cost of running a physical model or require high-resolution data to develop a downscaling tool. Here, we demonstrate a recently proposed zero-shot super-resolution method, the Fourier neural operator (FNO), to efficiently perform downscaling without the need for high-resolution data. Because the FNO learns dynamics in Fourier space, FNO is a resolution-invariant emulator; it can be trained at a coarse resolution and produces emulation at any high resolution. We applied FNO to downscale a 4-km resolution Weather Research and Forecasting (WRF) Model simulation of near-surface heat-related variables over the Great Lakes region. The FNO is driven by the atmospheric forcings, and topographic features used in the WRF model at the same resolution. We incorporated a physics-constrained loss in FNO by using the Clausius-Clapeyron relation to better constrain the relations among the emulated states. Trained on merely 600 WRF snapshots at 4-km resolution, the FNO shows comparable performance with a widely used convolutional network, U-Net, achieving averaged modified Kling-Gupta Efficiency of 0.88 and 0.94 on the test dataset for temperature and pressure, respectively. We then employed the FNO to produce 1-km emulations to reproduce the fine climate features. Further, by taking the WRF simulation as ground truth, we show consistent performances at the two resolutions, suggesting the reliability of FNO in producing high-resolution dynamics. Our study demonstrates the potential of using FNO for zero-shot super-resolution in generating first-order estimation on atmospheric modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Direct measurement of storage and loss behavior in AFM force–distance experiments using the modified Fourier transformation

Force–distance curve experiments are commonly performed in atomic force microscopy (AFM) to obtain the viscoelastic characteristics of materials, such as the storage and loss moduli or compliances. The classic methods used to obtain these characteristics consist of fitting a viscoelastic material model to the experimentally obtained AFM data. Here, we demonstrate a new method that utilizes the modified discrete Fourier transform to approximate the storage and loss behavior of a material directly from the data, without the need for a fit. Additionally, one may still fit a model to the resulting storage and loss behavior if a parameterized description of the material is desired. In contrast to fitting the data to a model chosen a priori, departing from a model-free description of the material's frequency behavior guides the selection of the model, such that the user may choose the one that is most appropriate for the particular material under study. To this end, we also include modified Fourier domain descriptions of commonly used viscoelastic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Fourier Analysis and Design of a Shielded 120kW Inductive Wireless System

High-power inductive wireless power transfer (WPT) systems for EVs are designed to meet specifications such as stray field, power level, efficiency, misalignment tolerance, and ground clearance. These metrics are all heavily influenced by the coil geometry. Herein this paper proposes a coil design method based on the Fourier Analysis Method (FAM) which is an analytical method for directly designing coil geometries to meet stray field and power level requirements through an optimization of Fourier basis function coefficients. In this work, two 120 kW WPT proof-of-concept demonstrators with low stray field and high efficiency are built from FAM optimization results to validate the models and show the impact of the FAM design process. Experimental validation of the Gen. 2 demonstrator at 120 kW output power resulted in a measured DC/DC efficiency of 97.2% at alignment with a 125 mm airgap. At the 120 kW test point, the stray fields 80 cm away from the center of the airgap between the coil assemblies were 3.4 µT(rms) on the X-axis and 3.5 µT(rms) on the Y-axis, much lower than the 27 µT(rms) ICNIRP limit.

42 ENGINEERING↗
DOE OSTI2024

Rotational Millimeter-Wave Shoe Scanner Using the Discrete Fourier Transform for Backprojection-Based Image Reconstruction

An active 3D microwave / millimeter-wave shoe scanner was previously developed at the Pacific Northwest National Laboratory (PNNL) using two linear arrays scanned over a rectilinear aperture. The radar system chirps a frequency sweep from 10-40 GHz. These frequencies allow imaging through optically opaque material such as leather, rubber, plastics, and other dielectrics. The system was designed to detect concealed items in the soles of shoes while allowing people to leave their shoes on through a security checkpoint. To shrink the footprint of the system, a new iteration of the design has been developed that scans the two linear arrays over a circular aperture. This new footprint opens the possibility of it being installed in the floor of a cylindrical millimeter-wave body scanner. The backprojection-based multilayer dielectric image reconstruction developed at PNNL can easily handle arbitrary spatial sampling, accommodating the new rotational shoe scanner design. Commonly, the fast Fourier transform (FFT) is used to efficiently compute the range response from the data collected by the system as a preprocessing step to the backprojection algorithm. It was found that converting to range using the discrete Fourier transform (DFT) directly has some advantages over the FFT. For example, nonlinear and non-uniform frequency sweeps can easily be compensated for during the computation of the DFT and only the range bins of interest need to be computed and their spacing can be chosen arbitrarily. Because the range conversion step of the image reconstruction is the fastest part of the process there is very little speed penalty for using the DFT over the FFT and it can even increase the speed of image reconstruction when the ranges of interest are fewer than the total span that is calculated in the FFT.

Millimeter-wave imaging, microwave imaging, shoe s↗
DOE OSTI2020

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

Atomic force microscopy (AFM) is an important tool for measuring a variety of nanoscale surface properties, such as topography, viscoelasticity, electrical potential and conductivity. Some of these properties are measured using contact methods (static contact or intermittent contact), while others are measured using noncontact methods. Some properties can be measured using different approaches. Conductivity, in particular, is mapped using the contact-mode method. However, this modality can be destructive to delicate samples, since it involves continuously dragging the cantilever tip on the surface during the raster scan, while a constant tip–sample force is applied. In this paper we discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than contact-mode imaging. To explore its feasibility, we derive the analytical form of the tip–sample current that would be obtained for attractive (noncontact) and repulsive (intermittent-contact) dynamic AFM characterization, and compare it with results obtained from numerical simulations. Although significant instrumentation challenges are anticipated, the modelling results are promising and suggest that Fourier-based higher-harmonics current measurement may enable the development of a reliable intermittent-contact conductive AFM method.

14 SOLAR ENERGY↗
DOE OSTI2024

Detection and Signal Processing for Near-Field Nanoscale Fourier Transform Infrared Spectroscopy

Researchers from a broad spectrum of scientific and engineering disciplines are increasingly using scattering-type near-field infrared spectroscopic techniques to characterize materials non-destructively with nanoscale spatial resolution. However, a sub-optimal understanding of a technique's implementation can complicate data interpretation and act as a barrier to entering the field. Here the key detection and processing steps involved in producing scattering-type near-field nanoscale Fourier transform infrared spectra (nano-FTIR) are outlined. The self-contained mathematical and experimental work derives and explains: i) how normalized complex-valued nano-FTIR spectra are generated, ii) why the real and imaginary components of spectra qualitatively relate to dispersion and absorption respectively, iii) a new and generally valid equation for spectra which can be used as a springboard for additional modeling of the scattering processes, and iv) an algebraic expression that can be used to extract an approximation to the sample's local extinction coefficient from nano-FTIR. The algebraic model for weak oscillators is validated with nano-FTIR and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectra on samples of polystyrene and Kapton and further provides a pedagogical pathway to cementing some of the technique's key qualitative attributes.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Microstructural characterization and assessment of mechanical properties of concrete based on combined elemental analysis techniques and Fast-Fourier transform-based simulations

This paper presents a pixel-based modeling approach of concrete which combines an experimental characterization of concrete and the Fast-Fourier transform simulations. High-resolution phase maps created from experimental characterization by micro X-ray fluorescence, energy dispersive X-ray analysis, and X-ray diffraction contain 9 different phases, including 22.17 vol.% of hydrated cement paste, 54.21 vol.% of minerals, and 23.62 vol.% of interfaces. These phases provide the input for determining the effective elastic properties, coupled with Fast-Fourier transform-based simulation. The simulation results show that the effective range of Young’s modulus of concrete is comparable with the range of experimental values ~ 37 ± 4 GPa with the assumption of realistic properties of interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Fourier-based three-dimensional multistage transformer for aberration correction in multicellular specimens

High-resolution tissue imaging is often compromised by sample-induced optical aberrations that degrade resolution and contrast. Although wavefront sensor-based adaptive optics (AO) can measure these aberrations, such hardware solutions are typically complex, expensive to implement and slow when serially mapping spatially varying aberrations across large fields of view. Here we introduce AOViFT (adaptive optical vision Fourier transformer)—a machine learning-based aberration sensing framework built around a three-dimensional multistage vision transformer that operates on Fourier domain embeddings. AOViFT infers aberrations and restores diffraction-limited performance in puncta-labeled specimens with substantially reduced computational cost, training time and memory footprint compared to conventional architectures or real-space networks. We validated AOViFT on live gene-edited zebrafish embryos, demonstrating its ability to correct spatially varying aberrations using either a deformable mirror or postacquisition deconvolution. By eliminating the need for the guide star and wavefront sensing hardware and simplifying the experimental workflow, AOViFT lowers technical barriers for high-resolution volumetric microscopy across diverse biological samples.

Alshaabi, Thayer [Howard Hughes Medical Institute,↗
DOE OSTI2020

RIFTA: A Robust Iterative Fourier Transform-based dwell time Algorithm for ultra-precision ion beam figuring of synchrotron mirrors

With the rapid evolution of synchrotron X-ray sources, the demand for high-precision X-ray mirrors has greatly increased. Single nanometer profile error is required to keep imaging capability at the diffraction limit. Ion Beam Figuring (IBF), as a highly deterministic surfacing technique, has been used for ultra-precision finishing of mirrors. One crucial step that guides the IBF process is dwell time calculation. A valid dwell time solution should be non-negative and duplicate the shape of the desired removal map. Another important aspect is to minimize the total dwell time. In this study, we propose a Robust Iterative Fourier Transform-based dwell time Algorithm (RIFTA) that automatically fulfills these requirements. First, the thresholded inverse filtering in Fourier transform-based deconvolution is stabilized and automated by optimizing the threshold value using the Nelder-Mead simplex algorithm. Second, a novel two-level iterative scheme is proposed to guarantee the minimized total dwell time with its non-negativity at each dwell point. Third, a bicubic resampling is employed to flexibly adapt the calculated dwell time map to any IBF process intervals. The performance of RIFTA is first studied with simulation, followed by a comparison with the other state-of-the-art dwell time algorithms. We then demonstrate with an experiment that, using the dwell time calculated by the RIFTA, the total dwell time is shortened by a factor of two and the RMS in a 5 × 50 mm clear aperture was reduced from 3.4 nm to 1.1 nm after one IBF run, which proves the effectiveness and the efficiency of the proposed algorithm.

42 ENGINEERING↗
DOE OSTI2020

Correlations between azimuthal anisotropy Fourier harmonics in PbPb collisions at sNN =2.76 TeV in the HYDJET++ model and in the multiphase transport model

Correlations between azimuthal anisotropy Fourier harmonics vn (n=2,3,4) are studied using the events from PbPb collisions at sNN=2.76 TeV generated by the HYDJET++ and multiphase transport (AMPT) models, and compared to the corresponding experimental results obtained by the ATLAS Collaboration. The Fourier harmonics vn are measured over a wide centrality range using the two-particle azimuthal correlation method. The slopes of the v2-v3 correlation from both models are in a good agreement with the ATLAS data. The HYDJET++ model predicts a stronger slope for the v2-v4 and v3-v4 correlations than the ones experimentally measured, while the results from the AMPT model are in a rather good agreement with the experimental results. In contrast to the HYDJET++ predictions, the AMPT model predicts a boomeranglike shape in the structure of the correlations as found in the experimental data. © 2020 American Physical Society.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Perturbation theory models for LSST-era galaxy clustering: Tests with subpercent mock catalog measurements in Fourier and configuration space

Here, we analyze the clustering of galaxies using the z = 1.006 snapshot of the CosmoDC2 simulation, a high-fidelity synthetic galaxy catalog designed to validate analysis methods for the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). We present sub-percent measurements of the galaxy auto-correlation and galaxy-dark matter cross correlations in Fourier space and configuration space for a magnitude-limited galaxy sample. At these levels of precision, the statistical errors of the measurement are comparable to the systematic effects present in the simulation and measurement procedure; nevertheless, using a hybrid-PT model, we are able to model non-linear galaxy bias with 0.5% precision up to scales of k max = 0.5 h/Mpc and r min = 4 Mpc/h. While the linear bias parameter is measured with 0.01% precision, other bias parameters are determined with considerably weaker constraints and sometimes bimodal posterior distributions. We compare our fiducial model with lower dimensional models where the higher-order bias parameters are fixed at their co-evolution values and find that leaving these parameters free provides significant improvements in our ability to model small scale information. We also compare bias parameters for galaxy samples defined using different magnitude bands and find agreement between samples containing equal numbers of galaxies. Finally, we compare bias parameters between Fourier space and configuration space and find moderate to significant tension between the two approaches. Although our model is often unable to fit the CosmoDC2 galaxy samples within the 0.1% precision of our measurements, our results suggest that the hybrid-PT model used in this analysis is capable of modeling non-linear galaxy bias within the percent level precision needed for upcoming galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Asymptotic behavior of the Fourier coefficients and the analytic structure of the QCD equation of state

In this paper we study the universal properties of the baryon chemical potential Fourier coefficients in quantum chromodynamics. We show that by following a well-defined strategy, the Fourier coefficients can be used to locate Yang-Lee edge singularities associated with chiral phase transition (and by extension with the Roberge-Weiss) in the complex chemical potential plane. We comment on the viability of performing this analysis using lattice QCD data. Published by the American Physical Society 2024

Astronomy & Astrophysics↗