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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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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm

We consider numerical methods for initial value problems that employ a two stage approach consisting of solution on a relatively coarse discretization followed by solution on a relatively fine discretization. Examples include adaptive error control, parallel-in-time solution schemes, and efficient solution of adjoint problems for computing a posteriori error estimates. We describe a general formulation of two stage computations then perform a general a posteriori error analysis based on computable residuals and solution of an adjoint problem. The analysis accommodates various variations in the two stage computation and in formulation of the adjoint problems. We apply the analysis to compute “dual-weighted” a posteriori error estimates, to develop novel algorithms for efficient solution that take into account cancellation of error, and to the Parareal Algorithm. We test the various results using several numerical examples.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Halo orbit station keeping for International Sun-Earth Explorer-C /ISEE-C/

The ISEE-C spacecraft must be kept close to an unstable 'halo' orbit with a series of discrete orbital maneuvers set at intervals at least one month apart. A numerical algorithm has been developed to compute a velocity correction at any point on the trajectory which will minimize the distance between the satellite orbit and the nominal halo path. This algorithm is used to generate a number of station keeping histories with fixed time intervals between maneuvers to ascertain bounds on fuel cost, tightness of fit to nominal path and expected duration between thrust applications. The difference between a third order analytic representation of the halo orbit and a numerically improved nominal path as a reference orbit in the station keeping scheme is investigated as well as the distinction between a tight control and a loose control. A simulation of an operational approach to station keeping is also presented which shows that intermittant propulsive maneuvers can be used to control the spacecraft with very modest fuel expenditure.

Heuberger, H.↗
DOE OSTI2021

A survey of numerical linear algebra methods utilizing mixed-precision arithmetic

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this study, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1981

Computation of separated flows by a vortex-tracing algorithm

Numerical solutions for two-dimensional, time-dependent, separated flows around bodies are obtained, using a new version of the vortex method. This method provides an efficient representation of flows involving large regions of separation. The modifications incorporated in the new version, which improve its accuracy, versatility, and computing speed, are described. The computer cost is only of the order of the 3/2 power on N, instead of N-squared, for each step with N vortices. Arbitrary shapes can be treated; a conformal mapping is not required. Special attention is paid to the viscous character of the solution and to the accurate computation of the pressure distribution at the body surface. The vortex solution for the outer flow is coupled to an inner solution for the attached part of the boundary layer. Numerical results are presented for several bluff bodies exhibiting dependence on Reynolds number, for stationary airfoils under steady or transient conditions and for oscillating airfoils, including dynamic stalls. These results are compared with other available results, analytical or experimental, and demonstrate the enhanced reliability and accuracy of the improved method.

Spalart, P. R.↗
NASA NTRS1992

Computational methods in the prediction of advanced subsonic and supersonic propeller induced noise: ASSPIN users' manual

This document describes the computational aspects of propeller noise prediction in the time domain and the use of high speed propeller noise prediction program ASSPIN (Advanced Subsonic and Supersonic Propeller Induced Noise). These formulations are valid in both the near and far fields. Two formulations are utilized by ASSPIN: (1) one is used for subsonic portions of the propeller blade; and (2) the second is used for transonic and supersonic regions on the blade. Switching between the two formulations is done automatically. ASSPIN incorporates advanced blade geometry and surface pressure modelling, adaptive observer time grid strategies, and contains enhanced numerical algorithms that result in reduced computational time. In addition, the ability to treat the nonaxial inflow case has been included.

Dunn, M. H.↗
DOE OSTI2020

Moment preserving constrained resampling with applications to particle-in-cell methods

The Moment Preserving Constrained Resampling (MPCR) algorithm for particle resampling is introduced and applied to particle-in-cell (PIC) methods to increase simulation accuracy, reduce compute cost, and/or avoid numerical instabilities. The general algorithm partitions the system space into smaller subsets and resamples the distribution within each subset. Further, the algorithm is designed to conserve any number of particle and grid moments with a high degree of accuracy (i.e. machine accuracy). The effectiveness of MPCR is demonstrated with several numerical tests, including a use-case study in gyrokinetic fusion plasma simulations. Finally, the computational cost of MPCR is negligible compared to the cost of particle evolution in PIC methods, and the tests demonstrate that periodic particle resampling yields a significant improvement in the accuracy and stability of the results.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

The calculation of efficient high precision orbits by optimum matching of the formulation and numerical integrator

The development of improved computer algorithms is considered for calculating earth satellite orbital trajectories by optimum selection of the analytical method that minimizes the number of perturbative acceleration computations for a given accuracy. A variation of parameter algorithm considering the equation of motion for a satellite proved superior for the geosynchronous orbit.

Velez, C. E.↗
DOE OSTI2016

Tokamak-independent software analysis suite for multi-spectral line-polarization MSE diagnostics

A tokamak-independent analysis suite has been developed to process data from Motional Stark Effect (mse) diagnostics. The software supports multi-spectral line-polarization mse diagnostics which simultaneously measure emission at the mse σ and π lines as well as at two "background" wavelengths that are displaced from the mse spectrum by a few nanometers. This analysis accurately estimates the amplitude of partially polarized background light at the σ and π wavelengths even in situations where the background light changes rapidly in time and space, a distinct improvement over traditional "time-interpolation" background estimation. The signal amplitude at many frequencies is computed using a numerical-beat algorithm which allows the retardance of the mse photo-elastic modulators (pem's) to be monitored during routine operation. It also allows the use of summed intensities at multiple frequencies in the calculation of polarization direction, which increases the effective signal strength and reduces sensitivity to pem retardance drift. The software allows the polarization angles to be corrected for calibration drift using a system that illuminates the mse diagnostic with polarized light at four known polarization angles within ten seconds of a plasma discharge. As a result, the software suite is modular, parallelized, and portable to other facilities.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2012

Physics of Acoustic Radiation from Jet Engine Inlets

Numerical simulations of acoustic radiation from a jet engine inlet are performed using advanced computational aeroacoustics (CAA) algorithms and high-quality numerical boundary treatments. As a model of modern commercial jet engine inlets, the inlet geometry of the NASA Source Diagnostic Test (SDT) is used. Fan noise consists of tones and broadband sound. This investigation considers the radiation of tones associated with upstream propagating duct modes. The primary objective is to identify the dominant physical processes that determine the directivity of the radiated sound. Two such processes have been identified. They are acoustic diffraction and refraction. Diffraction is the natural tendency for an acoustic wave to follow a curved solid surface as it propagates. Refraction is the turning of the direction of propagation of sound waves by mean flow gradients. Parametric studies on the changes in the directivity of radiated sound due to variations in forward flight Mach number and duct mode frequency, azimuthal mode number, and radial mode number are carried out. It is found there is a significant difference in directivity for the radiation of the same duct mode from an engine inlet when operating in static condition and in forward flight. It will be shown that the large change in directivity is the result of the combined effects of diffraction and refraction.

Tam, Christopher K. W.↗
DOE OSTI2018

Solving numerically nonlinear systems of balance laws by multivariate sigmoidal functions approximation

A numerical method for solving systems of nonlinear one-dimensional balance laws, based on multivariate sigmoidal functions approximation, is developed. Constructive approximation theorems are first established in both, uniform and L{sup p} norms. A priori as well as a posteriori error estimates are derived for the numerical solutions, when various kinds of sigmoidal functions, such as unit step, logistic and Gompertz functions, are chosen. The residual of the numerical method is also estimated. Numerical examples are given to test the performance of the algorithm, a comparison with the Godunov method is made concerning accuracy and computational cost. Finally, the numerical stability of the method is analyzed.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

ICASE

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in the areas of (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving Langley facilities and scientists; and (4) computer science.

Source record↗
DOE OSTI2021

A scalable algorithm for the optimization of neural network architectures

In this work, we propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers that is at least as performant as neural networks of the same structure identified by other hyperparameter search algorithms in terms of accuracy and computational cost. Numerical results performed on benchmark datasets show that, for these datasets, our method outperforms state-of-the-art hyperparameter optimization algorithms in terms of attainable predictive performance by the selected neural network architecture, and time-to-solution for the hyperparameter optimization to complete.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus

Abstract Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider the Adaptive, Problem-Tailored Variational Quantum Eiegensolver (ADAPT-VQE) ansätze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction accomplishes two things: First, it provides an initialization strategy that can yield solutions with over an order of magnitude smaller error compared to random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still “burrow” toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to barren plateaus and random initialization. Even if such barren plateaus appear in the parameter landscape, our analysis suggests that ADAPT-VQE avoids such regions by design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Molecular properties of excited electronic state: Formalism, implementation, and applications of analytical second energy derivatives within the framework of the time-dependent density functional theory/molecular mechanics

This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

NIMROD Development AND Applications for Advanced Simulations of Tokamak Plasmas

Operation in a regime of zero off-normal events is an important goal for ITER, and after that DEMO. Edge Localized Modes (ELMs) are off-normal events of particular concern due to their ubiquity in the highest performing discharges and their localized energy deposition on vessel walls. To avoid damage from these events, ITER has invested in costly coils in addition to exploring other mitigation techniques. A more attractive approach is to find an operational regime that has the requisite high performance while avoiding ELMs entirely. DIII-D experimentalists have found such a regime, wherein the ELMs are prevented from occurring by the existence of a saturated instability. Although this regime is attractive, how this saturated instability occurs and how to extrapolate to ITER is not well understood. NIMROD is well suited for studying this mode, and significant progress has already been made in modeling the equilibria that give rise to this instability. Another off-normal event of concern to ITER is the sawtooth mode in the presence of energetic particles. These modes are ubiquitous in near-steady-state tokamaks, and their behavior in the presence of the energetic particles that will be found in burning plasma experiments is poorly understood. The internal kink is notorious for requiring all extended MHD effects (two-fluid, closures, vacuum regime, energetic particles) in a production level simulation. NIMROD has matured to the point where it can now address this problem, though significant expertise in the MHD physics, numerical algorithms, and large-scale computation will be required. The expertise of Tech-X in attacking the most difficult NIMROD problems has already resulted in significant improvements to the NIMROD code that benefit the larger fusion community, and we expect further improvements as we attack these challenging problems. To maximize the community benefits, Tech-X provided community outreach and code management efforts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Tokamak-independent Software Analysis Suite for Multi-Spectral Line-Polarization MSE diagnostics

A tokamak-independent analysis suite has been developed to process data from Motional Stark Effect (MSE) diagnostics. The software supports multi-spectral line-polarization MSE diagnostics which simultaneously measure emission at the MSE sigma and pi lines as well as at two `background' wavelengths that are displaced from the MSE spectrum by a few nanometers. This analysis accurately estimates the amplitude of partially-polarized background light at the sigma and pi wavelengths even in situations where the background light changes rapidly in time and space. The signal amplitude at many frequencies is computed using a numerical-beat algorithm which allows the retardance of the MSE photo-elastic modulators (PEMs) to be monitored during routine operation. It also allows the use of summed intensities at multiple frequencies in the calculation of polarization direction, which increases the effective signal strength and reduces sensitivity to PEM retardance drift. The software allows the polarization angles to be corrected for calibration drift using a system that illuminates the MSE diagnostic with polarized light at four known polarization angles within ten seconds of a plasma discharge The software suite is modular, parallelized, and portable to other facilities. (2016-06-06)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Tokamak-independent Software Analysis Suite for Multi-Spectral Line-Polarization MSE diagnostics

A tokamak-independent analysis suite has been developed to process data from Motional Stark Effect (MSE) diagnostics. The software supports multi-spectral line-polarization MSE diagnostics which simultaneously measure emission at the MSE sigma and pi lines as well as at two `background' wavelengths that are displaced from the MSE spectrum by a few nanometers. This analysis accurately estimates the amplitude of partially-polarized background light at the sigma and pi wavelengths even in situations where the background light changes rapidly in time and space. The signal amplitude at many frequencies is computed using a numerical-beat algorithm which allows the retardance of the MSE photo-elastic modulators (PEMs) to be monitored during routine operation. It also allows the use of summed intensities at multiple frequencies in the calculation of polarization direction, which increases the effective signal strength and reduces sensitivity to PEM retardance drift. The software allows the polarization angles to be corrected for calibration drift using a system that illuminates the MSE diagnostic with polarized light at four known polarization angles within ten seconds of a plasma discharge The software suite is modular, parallelized, and portable to other facilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗