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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier analysis is that it can be used to minimize an estimate of the spectral radius of a stationary iteration, or the condition number of a preconditioned system, in terms of a symbol representation of the algorithm. In practice, this is a “minimax” problem, minimizing with respect to solver parameters the appropriate measure of work, which involves maximizing over the Fourier frequency. Often, several algorithmic parameters may be determined by local Fourier analysis in order to obtain efficient algorithms. Analytical solutions to minimax problems are rarely possible beyond simple problems; the status quo in local Fourier analysis involves grid sampling, which is prohibitively expensive in high dimensions. In this paper, we propose and explore optimization algorithms to solve these problems efficiently. Finally, several examples, with known and unknown analytical solutions, are presented to show the effectiveness of these approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A High-Order Nonlinear Diffusion Acceleration for the SN Equations Discretized with the Discontinuous FEM II: Fourier Analysis

In this paper, a Fourier Analysis (FA) of a new high order Nonlinear Diffusion Acceleration Method (NDA) for the $S_N$ equations discretized with the Discontinuous Finite Element Method (DFEM) is presented. In contrast to coarse mesh finite difference methods (CMFD), the associated diffusion system is discretized using DFEM with a function space identical to the $S_N$ equations. The utilized $S_N$ solver is the latest addition to the Rattlesnake\cite{Wang2013} radiation transport code that is based on the MOOSE\cite{Gaston2009} framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Convergence Study of LR-NDA Using Fourier Analysis

Numerical solution of neutron transport equations is challenging. It often requires acceleration techniques to improve computational efficiency. In the last two decades, various acceleration methods have been developed. Among those methods, the coarse-mesh nonlinear diffusion acceleration (CM-NDA) technique, or commonly known as coarse-mesh finite difference (CMFD), becomes one of the most popular methods due to its effectiveness and simplicity in recent years. However, CM-NDA will lose its effectiveness and could become unstable when the mesh optical thickness becomes large. There exists a number of stabilization techniques to improve the stability of CM-NDA, such as pCMFD and most recent odCMFD. Wang et al., proposed a new CM-NDA scheme, LR-NDA, which employs local refinement on the coarse mesh. The new scheme can significantly improve the effectiveness and stability of CM-NDA. In this paper, we perform a convergence study of LR-NDA using Fourier analysis. The spectral radius calculated from Fourier analysis is consistent with the numerical results for a 1-D fixed source model problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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

Fourier Analysis and Loss Modeling for Inductive Wireless Electric Vehicle Charging with Reduced Stray Field

With the growth of electric vehicle (EV) popularity, different charging options to increase user convenience and reduce charging times are being considered and researched. Among these, inductive wireless power transfer (WPT) systems for EVs are being designed to meet specifications such as stray field, power level, efficiency, misalignment tolerance, and ground clearance, which are all heavily influenced by the coil geometry. The proposed Fourier Analysis Method (FAM) is an analytical method to directly design coil geometries to meet stray field and power level requirements through an optimization of Fourier basis function coefficients. The outputs of the optimization are complex, planar coil geometries that meet the power level and stray field constraints with minimized loss factors. Contours of these potentials determine the coil conductor paths and loss models predict the system efficiency and performance over misalignment. The Fourier representation of the geometry is used to conveniently calculate the coupling over misalignment, external proximity effect loss, and ferrite loss. A 6.6 kW prototype WPT system with low stray field and high efficiency is built from the optimization results to validate the models and showcase the usefulness of the FAM design approach.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2019

Characterizing filamentary magnetic structures in counter-streaming plasmas by Fourier analysis of proton images

Proton imaging is a powerful tool for probing electromagnetic fields in a plasma, providing a path-integrated map of the field topology. However, in cases where the field structure is highly inhomogeneous, inferring spatial properties of the underlying field from proton images can be difficult. This problem is exemplified by recent experiments, which used proton imaging to probe the filamentary magnetic field structures produced by the Weibel instability in collisionless counterstreaming plasmas. In this paper, we perform analytical and numerical analyses of proton images of systems containing many magnetic filaments. We find that, in general, the features observed on proton images do not directly correspond to the spacing between magnetic filaments (the magnetic wavelength) as has previously been assumed and that they instead correspond to the filament size. Furthermore, we demonstrate this result by Fourier analysis of synthetic proton images for many randomized configurations of magnetic filaments. Our results help guide the interpretation of experimental proton images of filamentary magnetic structures in plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Fourier Analysis Method for Wireless Power Transfer Coil Design

Wireless power transfer (WPT) systems for Electric Vehicles (EVs) are designed to meet specifications such as stray field, power transfer, efficiency, and ground clearance. Typical design approaches include iterative analysis of predetermined coil geometries to identify candidates that meet these constraints. This work instead directly generates WPT coil shapes and magnetic fields to meet specifications and constraints through the optimization of Fourier basis function coefficients. The proposed Fourier Analysis Method (FAM) applies to arbitrary planar coil geometries and does not rely on iterative finite-element analysis (FEA) simulations. This flexibility allows for rapid design evaluation across a larger range of coil geometries and design specifications. A prototype coil is built to compare FAM outputs to experimental measurements and FEA simulations. The FAM is then used to illustrate the tradeoff of coil current and stray field for a given power level showing that the method is capable of generating optimized coil shapes to meet arbitrary field constraints.

Foote, Andrew↗
DOE OSTI2016

Fourier Analysis of the Multilevel QD Method with {alpha}-Approximation For Time-Dependent Radiative Transfer Problems

Thermal radiation transfer (TRT) problems describe interaction of photon radiation with matter. They are defined by the time-dependent radiative transfer (RT) equation for the specific intensity I coupled with the energy balance (EB) equation. This class of problems is characterised by high dimensionality, multiple scales and strong nonlinearity. In this paper we analyze the multilevel quasi-diffusion (QD) method for solving TRT problems. This is a nonlinear method of moments with exact closures. The QD method enables one to reduce dimensionality of the original radiative transfer problem. It is formulated by a nonlinear system of equations consisting of (i) the high-order RT (HORT) equation for the intensity of photon radiation and (ii) low-order equations for the angular and energy moments of the intensity. The nonlinear closures are formulated by means of stable factors. The low-order problem brings the radiative transfer model to the level of multi-physics equations. The multilevel QD (MLQD) method possesses attractive features for efficient multi-physics coupling. To calculate the high-order RT solution we apply the {alpha}-approximation which assumes that the intensity changes exponentially in time over a time step. The {alpha}-approximation leads to the steady-state RT equation with a modified opacity and enables one to avoid storing the high-dimensional solution from the previous time step. The rate of change is evaluated by the solution of the time-dependent low-order QD (LOQD) equations for moments. We note that the HORT equation in the {alpha}-approximation contains an extra nonlinear term. It affects the iterative behaviour of the MLQD method. The obtained computational results indicated that the rate of convergence is slower compared to the rate when the time-dependent HORT is used to calculate the intensity. In this paper we perform an iterative stability analysis of the MLQD method in a discretized form and analyze convergence of outer (transport) iterations on a time step. We consider multigroup TRT problems in 1D slab geometry. The fully implicit scheme is used to discretize equations in time. The HORT equation is approximated with the method of step characteristics. A finite volume method is applied for spatial discretization of multigroup LOQD equations. The grey (one-group) LOQD equations are algebraically consistent with the multigroup LOQD equations. To perform Fourier analysis a model TRT problem in an infinite homogeneous medium is considered. The system of nonlinear equations of the MLQD method is linearized near an equilibrium solution at some given temperature. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Extraction of the Muon Revolution Frequency Distribution via the Fourier Analysis of the Fast Rotation Signal in the Muon g-2 Experiment

The Muon g-2 experiment at Fermi National Accelerator Laboratory aims to measure the anomalous magnetic moment a of the muon to an unprecedented precision of 0.14 ppm, obtaining a near four-fold increase in precision over the previous experiment at Brookhaven National Laboratory (BNL). The value of a from BNL diers from the Standard Model prediction by 3.4 standard deviations, suggesting a tantalizing hint of new physics and so motivating a new measurement. The Fermilab experiment follows the measurement principle from the BNL experiment. A beam of positive muons is stored in the ring, where a combination of magnetic and electric elds helps to focus the beam. The combination of these elds and the stored beam properties directly impact the nal extraction of of a. The muon anomaly relies on the measurement of the spin precession frequency !a about the momentum of the muon. Due to a muon beam momentum spread of approximately 0:1%, !a must be corrected for the eect of a radial electric eld. The correction is estimated by means of a modied Fourier analysis of the so-called fast rotation signal. We explore the application of this analysis to the case of a beam with longitudinal spread and to the case of late-time beam detection. We also consider the numerical extension of the method, and apply it to data from the recent commissioning run.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Nonlinear Fourier analysis for discontinuous conductivities: Computational results

Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global uniqueness proofs for Calderón problem exposed in Nachman (1996) [43] and Astala and Päivärinta (2006) [6]: the Astala–Päivärinta theory-based low-pass transport matrix method implemented in Astala et al. (2011) [3] and the shortcut method which considers ingredients of both theories. The latter method is formally similar to the Nachman theory-based regularized EIT reconstruction algorithm studied in Knudsen et al. (2009) [34] and several references from there. New numerical results are presented using parallel computation with size parameters larger than ever, leading mainly to two conclusions as follows. First, both methods can approximate piecewise constant conductivities better and better as the cutoff frequency increases, and there seems to be a Gibbs-like phenomenon producing ringing artifacts. Second, the transport matrix method loses accuracy away from a (freely chosen) pivot point located outside of the object to be studied, whereas the shortcut method produces reconstructions with more uniform quality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

FOURIER ANALYSIS OF BLAZAR VARIABILITY: KLEIN–NISHINA EFFECTS AND THE JET SCATTERING ENVIRONMENT

The strong variability of blazars can be characterized by power spectral densities (PSDs) and Fourier frequency-dependent time lags. In previous work, we created a new theoretical formalism for describing the PSDs and time lags produced via a combination of stochastic particle injection and emission via the synchrotron, synchrotron self-Compton, and external Compton (EC) processes. This formalism used the Thomson cross section and simple δ-function approximations to model the synchrotron and Compton emissivities. Here we expand upon this work, using the full Compton cross section and detailed and accurate emissivities. Our results indicate good agreement between the PSDs computed using the δ-function approximations and those computed using the accurate expressions, provided the observed photons are produced primarily by electrons with energies exceeding the lower limit of the injected particle population. Breaks are found in the PSDs at frequencies corresponding to the cooling timescales of the electrons primarily responsible for the observed emission, and the associated time lags are related to the difference in electron cooling timescales between the two energy channels, as expected. If the electron cooling timescales can be determined from the observed time lags and/or the observed EC PSDs, then one could in principle use the method developed here to determine the energy of the external seed photon source for EC, which is an important unsolved problem in blazar physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Fourier analysis of conductive heat transfer for glazed roofing materials

For low-rise buildings, roof is the most exposed surface to solar radiation. The main mode of heat transfer from outdoor via the roof is conduction. The rate of heat transfer and the thermal impact is dependent on the thermophysical properties of roofing materials. Thus, it is important to analyze the heat distribution for the various types of roofing materials. The objectives of this paper are to obtain the Fourier series for the conductive heat transfer for two types of glazed roofing materials, namely polycarbonate and polyfilled, and also to determine the relationship between the ambient temperature and the conductive heat transfer for these materials. Ambient and surface temperature data were collected from an empirical field investigation in the campus of Universiti Teknologi MARA Shah Alam. The roofing materials were installed on free-standing structures in natural ventilation. Since the temperature data are generally periodic, Fourier series and numerical harmonic analysis are applied. Based on the 24-point harmonic analysis, the eleventh order harmonics is found to generate an adequate Fourier series expansion for both glazed roofing materials. In addition, there exists a linear relationship between the ambient temperature and the conductive heat transfer for both glazed roofing materials. Based on the gradient of the graphs, lower heat transfer is indicated through polyfilled. Thus polyfilled would have a lower thermal impact compared to polycarbonate.

42 ENGINEERING↗
DOE OSTI2014

Fourier analysis of blazar variability

Blazars display strong variability on multiple timescales and in multiple radiation bands. Their variability is often characterized by power spectral densities (PSDs) and time lags plotted as functions of the Fourier frequency. We develop a new theoretical model based on the analysis of the electron transport (continuity) equation, carried out in the Fourier domain. The continuity equation includes electron cooling and escape, and a derivation of the emission properties includes light travel time effects associated with a radiating blob in a relativistic jet. The model successfully reproduces the general shapes of the observed PSDs and predicts specific PSD and time lag behaviors associated with variability in the synchrotron, synchrotron self-Compton, and external Compton emission components, from submillimeter to γ-rays. We discuss applications to BL Lacertae objects and to flat-spectrum radio quasars (FSRQs), where there are hints that some of the predicted features have already been observed. We also find that FSRQs should have steeper γ-ray PSD power-law indices than BL Lac objects at Fourier frequencies ≲ 10{sup –4} Hz, in qualitative agreement with previously reported observations by the Fermi Large Area Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

TH-E-17A-08: Estimation of Image Quality of 4-Dimensional Computed Tomography (4DCT) Via Fourier Analysis of Corresponding 1D Breathing Surrogate

Purpose: Motion artifacts are common in patient 4DCT, leading to an illdefined tumor volume with variation up to 110% or setting up a poor foundation with low imaging fidelity for tumor motion study. We developed a method to estimate 4DCT image quality by establishing a correlation between the severity of motion artifacts in 4DCT images and the periodicity of corresponding 1D respiratory wave-function (1DRW) surrogate used for 4DCT reconstruction. Methods: Fast Fourier Transformation (FFT) was applied to analyze 1DRW periodicity, defined as the sum of the 5 largest Fourier coefficients, ranging in 0–1. Distortional motion artifacts of cine-scan 4DCT at the junctions of adjacent couchposition scans around the diaphragm were identified in 3 categories: incomplete, overlapping and duplicate. To quantify these artifacts, the discontinuity of the diaphragm at the junctions was measured in distance and averaged along 6 directions in 3 orthogonal views. Mean and sum artifacts per junction (APJ) across the entire diaphragm were calculated in each breathing phase. To make the APJ inter-patient comparable, patientspecific motion was removed from APJ by dividing patient-specific diaphragmatic velocity (displacement divided by the mean period, from FFT analysis of the 1DRW) and the normalized APJ was defined as motion artifact severity (MAS). Twenty-five patients with free-breathing 10-phase 4DCT and corresponding 1DRW surrogate datasets were studied. Results: A mild correlation of 0.56 was found between 1DRW periodicity and 4DCT artifact severity. Higher MAS tends to appear around mid inhalation and mid exhalation and the lowest MAS tends to be around full exhalation. The breathing periodicity of >0.8 possesses minimal motion artifacts. Conclusion: The 1D-4D correlation provides a fast means to estimate 4DCT image quality. Using 1DRW signal, we can retrospectively screen out high-quality 4DCT images for clinical research (periodicity>0.8) and prospectively identify poor breathers as candidates of breath coaching prior to 4DCT scan. This research is in part supported by NIH (U54CA137788/132378). MC would like to thank MSKCC summer medical student research program supported by National Cancer Institute and hosted by Department of Medical Physics at MSKCC.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Mass Transport in Membrane Systems: Flow Regime Identification by Fourier Analysis

The numerical calculation of local mass distributions in membrane systems by computational fluid dynamics (CFD) offers indispensable benefits. However, the concept to calculate such distributions in response to separate variations of operation conditions (OCs) makes it difficult to address overall, flow-physics-related questions, which require the consideration of the collective interaction of OCs. It is shown that such understanding-related relationships can be obtained by the analytical solution of the advection–diffusion equation considered. A Fourier series model (FSM) is presented, which provides exact solutions of an advection–diffusion equation for a wide range of OCs. On this basis, a new zeroth-order model is developed, which is very simple and as accurate as the complete FSM for all conditions of practical relevance. Advection-dominated blocked and diffusion-dominated unblocked flow regimes are identified (depending on a Péclet number which compares the flow geometry with a length scale imposed by the flow), which implies relevant requirements for the use of lab results for pilot- and full-scale applications. Analyses reveal the equivalence of variations of OCs, which offers a variety of options to accomplish desired flow regime changes.

Heinz, Stefan (ORCID:0000000248712416)↗