Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fast Fourier transform (FFT)”

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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Grain size effects on slip band development

Crystallographic slip localizations, known as slip bands, concentrate stress in polycrystals, often leading to the nucleation of damage. Slip band development has been experimentally shown to be sensitive to grain size, tending to develop more frequently and with a greater intensity in large grains. In this work, we investigate the influence of grain size on the propensity for crystallographic slip band development. To this end, we employ the slip band-fast Fourier transform method (SB-FFT). SB-FFT is a 3D, full-field crystal plasticity model that permits the incremental development of discrete crystallographic slip bands according to microstructure and material properties. We present a model Inconel 718 tricrystal to isolate the effect of grain size. Our findings show that slip bands in large grains develop at lower applied strain levels and at a faster rate than slip bands in small grains. The grain size effect is due to a backstress produced by the interaction of the slip band and its neighboring grain. The backstress is most intense at small grain sizes, impeding slip activity within a developing slip band and immediately surrounding the slip band.

36 MATERIALS SCIENCE↗
DOE OSTI2021

encore : an O ( N g2) estimator for galaxy N -point correlation functions

ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ${\sim}100$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Microprocessor implementation of an FFT for ionospheric VLF observations

A fast Fourier transform algorithm is implemented on a CMOS microprocessor for application to very low-frequency electric fields (less than 10 kHz) sensed on high-altitude scientific balloons. Two FFT's are calculated simultaneously by associating them with conjugate symmetric and conjugate antisymmetric results. One goal of the system was to detect spectral signatures associated with fast time variations present in natural signals such as whistlers and chorus. Although a full evaluation of the system was not possible for operational reasons, a measure of the system's success has been defined and evaluated.

Elvidge, J.↗
DOE OSTI2025

kokkos-fft: A shared-memory FFT for the Kokkos ecosystem

kokkos-fft provides a unified, performance-portable interface for Fast Fourier Transforms (FFTs) within the Kokkos ecosystem (C. Trott et al., 2021). It seamlessly integrates with leading local FFT libraries including FFTW, cuFFT, rocFFT, and oneMKL. Designed for simplicity and efficiency, kokkos-fft offers a user experience akin to numpy.fft for in-place and out-of-place transforms, while leveraging the raw speed of vendor-optimized libraries. A demonstration solving 2D Hasegawa-Wakatani turbulence with the Fourier spectral method illustrates how kokkos-fft can deliver significant speedups over Python-based alternatives without drastically increasing code complexity, empowering researchers to perform high-performance FFTs simply and effectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Chapter 4: Physically informed deep learning networks for simulating microstructure evolution of 3D polycrystals

As discussed in the previous chapter, high energy diffraction microscopy (HEDM) is used to study the micromechanical evolution of a material during in situ loading. HEDM experiments have been used to verify crystal plasticity (CP) simulations [119, 91, 90, 120], for experimental planning, material design, and to further analyze experimental results. However, Fast Fourier transform-based CP (CP-FFT) or finite element-based CP (CP-FE) methods are often too slow to be used in real-time during an experiment. CP-FFT is faster than CP-FE simulations due to the absence of meshing, but can still take hours to simulate the response of a single volume depending on the size and number of strain steps [127]. Reducing computation time would create a larger exploration space in planning and design, and enable faster analysis of experimental results and real-time feedback during an experiment. This research expands upon previous works to develop a workflow for predicting the full-field evolution of a 3D polycrystal. The workflow is simplified from previous works to predict only orientation and elastic strain tensors (from which stress tensors are calculated). The network is physically informed through loss functions and network architecture for a more robust model. The orientation predictions are informed about the cubic crystal symmetry of the material by incorporating disorientation and misorientation information into the network architecture and loss. The Von Mises stress is used to enforce the correct stress-strain trends in the strain tensor predictions. Additional total strain steps from the elastic and elastoplastic region are included to better capture the stress-strain evolution at smaller total strain steps. Material and hardening parameters are additional inputs into the networks to further inform the network and to study the network’s ability to predict different materials other than those used for training.

36 MATERIALS SCIENCE↗
NASA NTRS2010

Use of Modal Acoustic Emission to Monitor Damage Progression in Carbon Fiber/Epoxy and Implications for Composite Structures

Broad-band modal acoustic emission (AE) data was used to characterize micromechanical damage progression in uniaxial IM7 and T1000 carbon fiber-epoxy tows and an IM7 composite overwrapped pressure vessel (COPV) subjected to an intermittent load hold tensile stress profile known to activate the Felicity ratio (FR). Damage progression was followed by inspecting the Fast Fourier Transforms (FFTs) associated with acoustic emission events. FFT analysis revealed the occurrence of cooperative micromechanical damage events in a frequency range between 100 kHz and 1 MHz. Evidence was found for the existence of a universal damage parameter, referred to here as the critical Felicity ratio, or Felicity ratio at rupture (FR*), which had a value close to 0.96 for the tows and the COPV tested. The implications of using FR* to predict failure in carbon/epoxy composite materials and related composite components such as COPVs are discussed. Trends in the FFT data are also discussed; namely, the difference between the low and high energy events, the difference between early and late-life events, comparison of IM7 and T1000 damage progression, and lastly, the similarity of events occurring at the onset of significant acoustic emission used to calculate the FR.

Waller, J. M.↗
DOE OSTI2022

Benchmarking a Proof-of-Concept Performance Portable SYCL-based Fast Fourier Transformation Library

ABSTRACT In this paper, we present an early version of a SYCL-based FFT library, capable of running on all major vendor hardware, including CPUs and GPUs from AMD, ARM, Intel and NVIDIA. The current limitations of our library is it supports single-dimension FFTs up to 211 in length and base-2 input sequences. Although preliminary, the aim of this work is to seed further developments for a rich set of features for calculating FFTs. The library has the advantage over existing portable FFT libraries in that it is single-source, and there- fore removes the complexities that arise due to abundant use of pre-processor macros and auto-generated kernels to target different architectures. We exercise two SYCL-enabled compilers, Codeplay ComputeCpp and Intel's open-source LLVM project, to evaluate performance portability of our SYCL-based FFT on various hetero- geneous architectures.We provide studies comparing our portable library with highly optimized vendor-specific FFT libraries, and discuss potential sources hindering performance.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Numerical comparisons of a modified Rayleigh approach with other rough surface EM scattering solutions.

A modification of the classical Rayleigh technique utilizing the fast Fourier transform, developed into the so-called Rayleigh-FFT method for electromagnetic scattering, is shown to obtain valid scattering results from arbitrary irregular periodic structures composed of a rough layer over a rough half-space. The considerable usefulness of the Rayleigh approach is thus established, and Beckmann's (1968) contention (that the convergence of the method is reasonably rapid only if the roughness is very slight) is refuted.

Jiracek, G. R.↗
DOE OSTI2024

A parallel and performance portable implementation of a full-field crystal plasticity model

We have developed a parallel implementation of an Elasto-Viscoplastic Fast Fourier Transform-based (EVPFFT) micromechanical solver to enable computationally efficient crystal plasticity modeling for polycrystalline materials. Our primary focus lies in achieving performance portability, allowing a single EVPFFT implementation to run optimally on various homogeneous architectures, including multi-core Central Processing Units (CPUs), as well as on heterogeneous computer architectures comprising multi-core CPUs and Graphics Processing Units (GPUs) from different vendors. To accomplish this goal, we have leveraged MATAR, a C++ software library that simplifies the creation and utilization of multidimensional dense or sparse matrix and array data structures. These data structures are designed to be portable across diverse architectures through the use of Kokkos, a performance-portable library. Additionally, we have employed the Message Passing Interface (MPI) to efficiently distribute the computational workload among processors. The heFFTe (Highly Efficient FFT for Exascale) library is used to facilitate the performance portability of the fast Fourier transforms (FFTs) computation. The computational performance of EVPFFT is evaluated and presented in terms of parallel scalability and simulation runtime on different high-performance computing (HPC) architectures. As a result, the utility of the developed framework to efficiently simulate the micro-mechanical fields in polycrystalline microstructures in engineering applications is discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2010

A High-Throughput, Adaptive FFT Architecture for FPGA-Based Space-Borne Data Processors

Historically, computationally-intensive data processing for space-borne instruments has heavily relied on ground-based computing resources. But with recent advances in functional densities of Field-Programmable Gate-Arrays (FPGAs), there has been an increasing desire to shift more processing on-board; therefore relaxing the downlink data bandwidth requirements. Fast Fourier Transforms (FFTs) are commonly used building blocks for data processing applications, with a growing need to increase the FFT block size. Many existing FFT architectures have mainly emphasized on low power consumption or resource usage; but as the block size of the FFT grows, the throughput is often compromised first. In addition to power and resource constraints, space-borne digital systems are also limited to a small set of space-qualified memory elements, which typically lag behind the commercially available counterparts in capacity and bandwidth. The bandwidth limitation of the external memory creates a bottleneck for a large, high-throughput FFT design with large block size. In this paper, we present the Multi-Pass Wide Kernel FFT (MPWK-FFT) architecture for a moderately large block size (32K) with considerations to power consumption and resource usage, as well as throughput. We will also show that the architecture can be easily adapted for different FFT block sizes with different throughput and power requirements. The result is completely contained within an FPGA without relying on external memories. Implementation results are summarized.

Nguyen, Kayla↗
DOE OSTI2020

Analysis of FFT Run-Times on LANL Computers

This paper gives results of a timing study for computing fast Fourier transforms (FFTs) on LANL based computing platforms. The platforms considered will be a node on Snow and a standard LANL HP laptop. The run-time for 1D FFTs will be measured for different sizes of data and the results are reported in FFTs/s.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Ordered fast Fourier transforms on a massively parallel hypercube multiprocessor

The present evaluation of alternative, massively parallel hypercube processor-applicable designs for ordered radix-2 decimation-in-frequency FFT algorithms gives attention to the reduction of computation time-dominating communication. A combination of the order and computational phases of the FFT is accordingly employed, in conjunction with sequence-to-processor maps which reduce communication. Two orderings, 'standard' and 'cyclic', in which the order of the transform is the same as that of the input sequence, can be implemented with ease on the Connection Machine (where orderings are determined by geometries and priorities. A parallel method for trigonometric coefficient computation is presented which does not employ trigonometric functions or interprocessor communication.

Tong, Charles↗
DOE OSTI2024

Dimensionally Aligned Signal Projection Algorithms Library

Dimensionally aligned signal projection (DASP) algorithms are used to analyze fast Fourier transforms (FFTs) and generate visualizations that help focus on the harmonics for specific signals. At a high level, these algorithms extract the FFT segments around each harmonic frequency center, and then align them in equally sized arrays ordered by increasing distance from the base frequency. This allows for a focused view of the harmonic frequencies, which, among other use cases, can enable machine learning algorithms to more easily identify salient patterns. This work seeks to provide an effective open-source implementation of the DASP algorithms proposed by Vann et al. (2018) as well as functionality to help explore and test how these algorithms work with an interactive dashboard and signal-generation tool. The DASP library is implemented in Python and contains four types of algorithms for implementing these feature engineering techniques: fixed harmonically aligned signal projection (HASP), decimating HASP, interpolating HASP, and frequency aligned signal projection (FASP). Each algorithm returns a numerical array, which can be visualized as an image. The HASP algorithms are variations of the algorithms originally presented by Vann et al. (2018). For consistency, FASP, which is the terminology used for the short-time Fourier transform (STFT), has been implemented as part of the library to provide a similar interface to the STFT of the raw signal. Additionally, the library contains an algorithm to generate artificial signals with basic customizations such as the base frequency, sample rate, duration, number of harmonics, noise, and number of signals. Finally, the library provides multiple interactive visualizations, each of which is implemented using IPyWidgets and works in a Jupyter environment. A dashboard-style visualization is provided, which contains some common signal-processing visual components (signal, FFT, spectogram) updating in unison with the HASP functions (see Figure 1 below). Separate from the dashboard, an independent visualization is provided for each of the DASP algorithms as well as for the artifical signal generator. These visualizations are included in the library to aid in developing an intuitive understanding how the algorithms are affected by different input signals and parameter selections.

harmonics↗
NASA NTRS1995

Extracting Periodic Signals From Irregularly Sampled Data

Successive approximations formed in Fourier space. Algorithm extracts periodic signals from sparse, irregularly sampled sets of measurement data. Pertains to data processed via fast Fourier transforms (FFTs). Data represents signal components with initially unknown frequencies spanning large spectral range and includes frequencies not integer multiples of minimum FFT frequency.

Wilcox, Jaroslava Z.↗
NASA NTRS1984

LANDSAT instruments characterization

Work performed for the LANDSAT instrument characterization task in the areas of absolute radiometry, coherent noise analysis, and between-date smoothing is reported. Absolute radiometric calibration for LANDSAT-5 TM under ambient conditions was performed. The TM Radiometric Algorithms and Performance Program (TRAPP) was modified to create optional midscan data files and to match the TM Image Processing System (TIPS) algorithm for pulse determination. Several data reduction programs were developed, including a linear regression and its plotted result. A fast Fourier transformation study was conducted on the resequenced TM data. Subscenes of homogeneous water within scenes over Pensacola, Florida were used for testing the FFT on the resequenced data. Finally, a gain and pulse height stability study of LANDSAT 5 TM spectral bands was performed.

Lee, Y.↗
NASA NTRS1978

A fast D.F.T. algorithm using complex integer transforms

Winograd (1976) has developed a new class of algorithms which depend heavily on the computation of a cyclic convolution for computing the conventional DFT (discrete Fourier transform); this new algorithm, for a few hundred transform points, requires substantially fewer multiplications than the conventional FFT algorithm. Reed and Truong have defined a special class of finite Fourier-like transforms over GF(q squared), where q = 2 to the p power minus 1 is a Mersenne prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 61. In the present paper it is shown that Winograd's algorithm can be combined with the aforementioned Fourier-like transform to yield a new algorithm for computing the DFT. A fast method for accurately computing the DFT of a sequence of complex numbers of very long transform-lengths is thus obtained.

Reed, I. S.↗
DOE OSTI2022

New large-strain FFT-based formulation and its application to model strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials

This paper presents a new robust large-strain (LS) elasto-viscoplastic (EVP) formulation based on Fast Fourier Transforms (FFTs) for the prediction of the micro-mechanical response and microstructure evolution of polycrystalline and multiphase materials, with emphasis on the effect of strong crystallographic and/or morphologic anisotropy on localization of plastic deformation. In this work, the novel LS-EVPFFT formulation allows treatment of complex initial geometries and large deformations considering three grids of material points: a regular grid in the reference configuration, where FFTs can be performed; an irregular grid in the initial configuration, created by applying a stress-free displacement field to the reference regular grid; and an irregular grid in the current configuration, undergoing large strains and rotations as the material is loaded. Further numerical stability of the new formulation also required the use of a novel expression for the discrete modified Green’s operator, which reduces spurious field oscillations. After presenting and validating the new formulation by comparison with preexisting implementations and analytical solutions, LS-EVPFFT is applied to the prediction of slip and kink bands formation in polycrystalline columnar ice, and kink bands in single crystal zinc wires, showing good agreement with classic experiments. Finally, the model is used to study kink band formation during compression of Cu–Nb nano-metallic laminates (NMLs), in which accurate treatment of the complex geometry associated with the tortuosity of interfaces and large deformations become critical, showing consistency with corresponding micropillar experiments.

36 MATERIALS SCIENCE↗