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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

On polynomial preconditioning for indefinite Hermitian matrices

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Freund, Roland W.↗
NASA NTRS2020

Recommendations for Using Noise Monitors to Estimate Noise Exposure During X-59 Community Tests

A low fidelity simulation approach is used to explore how to place and use noise monitors during X-59 QueSST community tests, where people’s annoyance to the noise produced by the X-59 aircraft will be gathered. Several recommendations are provided including: 1) the desired number of sparsely spaced noise monitor sites within the survey area, 2) whether to group and average measurements across multiple noise monitors located at a site, 3) what spacing should be used if grouped noise monitors are used, 4) an approach to mitigate ambient noise contamination at the measurement sites, 5) a method to combine empirical and predicted dose estimates to provide a single dose estimate for respondents, and 6) assessing how changes in turbulence intensity and array configuration affect dose uncertainty. To make these recommendations, the error that is expected when fitting contrived, smoothly varying sonic boom “reference exposure surfaces” is studied when a spatially sparse and scattered set of samples is used as responses for the fit. The reference exposure surfaces mimic the sonic boom exposure at ground level that might be expected in the X-59 survey area in the absence of atmospheric turbulence, ambient noise, and other localized effects. The spatial extent of these surfaces varies and is representative of the different survey area sizes that might be expected during future X-59 community overflight tests. These contrived reference surfaces are sampled, and those reference samples are then perturbed to mimic atmospheric turbulence, ambient noise and other localized effects that might affect noise monitor measurements within overflown communities. Two different surface fitting methods are investigated when fitting these perturbed samples to approximate the reference surface. The first method uses interpolation between the perturbed data at the scattered sites to compute the fit. The second method fits a polynomial surface model to the perturbed data using ordinary least squares regression analysis. For both fitting methods, the root mean square fit error is computed from the pointwise difference between the fit surface and the reference surface as the count and configuration of the sites is varied while also averaging the error across many different realizations of both the smooth variation of the reference exposure surface and the random, localized perturbations at the sample sites. Different site configurations are compared using this error statistic to make the recommendations noted above. Additionally, the two fitting approaches (interpolation vs linear regression) are compared based on the fit error observed in these simulations. These analyses, comparisons, and recommendations should inform future decisions on the noise monitor placement and the methods used to analyze the noise monitor data that is collected during X-59 community overflights.

sonic boom↗
NASA NTRS1966

Computation research

Least squares method used in linearizing roots of polynomial and to derive approximations

APPROXIMATION METHOD↗
NASA NTRS1992

Measurement and calibration of static distortion of position data from 3D trackers

Three-dimensional trackers are becoming increasingly important as user inputs in interactive computer systems. These trackers output the three-dimensional position, and often the orientation, of a sensor in space. The three-dimensional tracking is often, however, highly distorted and inaccurate. The purpose of this paper is to discuss methods for the measurement and characterization of the static distortion of the position data. When the distortion is constant, various methods can be used to calibrate the data from the tracker to increase accuracy. Several preliminary methods are discussed in this paper, including polynomial and weighted lookup methods. The measurement and calibration methods are applied to the Polhemus electromagnetic tracking system, but are applicable to tracking systems based on other technologies.

Bryson, Steve↗
NASA NTRSDate not supplied

Efficient Parametric Uncertainty Analysis of an Earth Entry Vehicle Concept Using Least Angle Regression

The objective of this work was to outline and apply an efficient and accurate parametric un-certainty propagation approach to the analysis of convective heating on an Earth entry vehicle concept. The described approach was based on Least Angle Regression used to solve a sparse and underdetermined linear system in the point-collocation non-intrusive polynomial chaos surrogate method. This approach involved an iterative process to computing the non-zero terms of the underlying polynomial chaos model using only enough samples to converge uncertainty interval predictions and Sobol index values based global nonlinear sensitivity estimates. The Earth entry vehicle was analyzed at three points along a representative trajectory for a Mars return mission. 329 sources of uncertainty were identified in the computational fluid dynamics model used to predict the forebody convective heating. These included uncertainty in flow field chemical rates, collision integrals, heats of formation, surface finite rate char model reaction rates, wall roughness height, and the turbulent Schmidt number. Results from this study showed that convective heating uncertainty as high as 50% of the nominal was predicted with only about 50 evaluations of the computational model. This was far fewer than would be required for a sampling-based approach or a full basis polynomial chaos model, which would have required over 50,000 samples. Additionally, results showed that over 90% of the total convective heating uncertainty was due to uncertainty in the N2catalytic rate on the surface, while the remainder of the uncertainty was attributed to the turbulent Schmidt number and the wall roughness uncertainties.

Thomas K West IV↗
NASA NTRS1974

Multiple zeros of polynomials

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.

Wood, C. A.↗
NASA NTRS1988

Recursive algorithms for vector extrapolation methods

Three classes of recursion relations are devised for implementing some extrapolation methods for vector sequences. One class of recursion relations can be used to implement methods like the modified minimal polynomial extrapolation and the topological epsilon algorithm; another allows implementation of methods like minimal polynomial and reduced rank extrapolation; while the remaining class can be employed in the implementation of the vector E-algorithm. Operation counts and storage requirements for these methods are also discussed, and some related techniques for special applications are also presented. Included are methods for the rapid evaluations of the vector E-algorithm.

Ford, William F.↗
NASA NTRS2014

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

corona↗
DOE OSTI2026

Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution

The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.

Wu, Chenghao [Northeast Electric Power University]↗
NASA NTRS1989

Closure of the cubic tensor polynomial failure surface

An analytical method has been developed to ensure closure of the cubic form of the tensor polynomial strength criterion. The intrinsic complexity of the cubic function is such that special conditions must be met to close the failure surface in three-dimensional stress space. These requirements are derived in terms of non-intersecting conditions for asymptotes and an asymptotic plane. To demonstrate the validity of this approach, closed failure surfaces were derived for two graphite/epoxy material systems (3M SP288-T300 and IM7 8551-7). The agreement of test data with this model clearly shows that it is possible to use a higher order cubic failure theory with confidence.

Jiang, Zhiqing↗
DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

An enrichment wall modeling framework for spectral element methods

In the present work, a first-of-its-kind enrichment wall-model is developed within the spectral element method (SEM) framework for large-eddy simulations (LES) of wall-bounded turbulent flows. The method augments the polynomial solution in the wall-adjacent elements with an analytical law-of-the-wall enrichment function representing the mean velocity near the wall. In the solution representation, this enrichment function captures the large gradients in the boundary layer, which allows the polynomial modes to represent the turbulent fluctuations. The enriched solution is able to resolve the shear stress at the wall without any modification to the no-slip wall boundary conditions, which allows for greater accuracy in the near-wall region compared to traditional methods. The enrichment wall modeling approach is implemented in a high-order SEM computational fluid dynamics solver, Nek5000, and its performance is assessed in turbulent channel flow wall-modeled LES for a range of Reynolds numbers. It is demonstrated that the enrichment wall-model improves solution accuracy on under-resolved near-wall grids as compared to traditional shear stress wall-models.

42 ENGINEERING↗
DOE OSTI2025

Many-Body Basis Set Amelioration Method for Incremental Full Configuration Interaction

Incremental full configuration interaction (iFCI) is a polynomial-cost electronic structure method that systematically approaches the FCI limit by employing the method of increments to solve the Schrödinger equation through a many-body expansion. This article introduces the many-body basis set amelioration (MBBSA) method, which is designed to allow iFCI to be applicable to larger atomic orbital basis sets. MBBSA uses a series of inexpensive iFCI calculations to approximate the correlation energy that would be found using a more expensive, highly accurate iFCI calculation. Here, when compared to standard iFCI computations on smaller molecules in triple-zeta and larger basis sets, MBBSA provides approximations to the total and relative energies within chemical accuracy. MBBSA exhibits a reduced cost of between 60-92% when compared to standard iFCI calculations, with larger systems experiencing the largest benefit. Tests of MBBSA on two reactions that involve highly correlated systems, the automerization of cyclobutadiene and a Criegee intermediate reaction, show that MBBSA has practical utility for studying realistic chemistries.

Basis sets↗
NASA NTRS1994

Separation of lithospheric, external, and core components of the south polar geomagnetic field at satellite altitudes

We present a new approach to producing scalar Magsat magnetic anomaly maps based on correlation coefficient filtering and the use of almost all of the available orbits. Our method differs from earlier techniques with respect to the following: (1) Passes are selected based on their variance properties rather than planetary indices such as Kp. (2) The core field model is least squares fit to individual passes and subsequently removed instead of substracting the model directly. This technique replaces band pass filtering or polynomial trend removal methods. (3) Each selected pass is sorted geographically and by local time, placed into one of four different altitude bands, and correlation coefficient filtered with the two adjacent passes. The filtering is the second step toward isolating the static lithospheric signal from the more dynamic external field signals. (4) Least squares collocation is used to grid the correlated passes; subsequently, the dawn and dusk maps are also correlation filtered providing another step toward removal of external fields. (5) The four resultant total field maps are continued to a common altitude and again correlation filtered for the static lithospheric anomalies. (6) The filtered results are then averaged together to provide a new total field map of the lithosphere south of 40 deg S latitude. Our total field map differs from previous efforts over the crustal blocks of West Antarctica. We obtained a positive anomaly over Edward VII Peninsula, extending into the Byrd subglacial basin and obtained a negative anomaly over the Ellsworth Mountains and parts of the Byrd subglacial basin. Also, a positive anomaly extending from the Ross Sea to offshore Wilkes Land is present in our map; however, this feature is absent in other maps. Positive anomalies marking the Weddell Sea in previous efforts are not present in our map. Prominent external field anomalies in the quadrant offshore of Wilkes Land are present in all previous efforts; however, these signatures are reduced in our total field map. This map significantly advances efforts for the identification and interpretation of magnetic anomalies of the south polar lithosphere.

Alsdorf, Douglas E.↗
DOE OSTI2025

Decayheatml

This code is designed to predict and analyze the decay heat generated in molten salt reactors (MSRs) using a hybrid approach that combines machine learning and segmented polynomial fitting. The accurate prediction of decay heat is essential for reactor safety and the optimization of spent fuel storage. The code operates through several key components: 1) Data Architecture: It incorporates a modular data architecture that handles various MSR-specific operational parameters such as power density, humidity content, and air ingress. These parameters are sampled using Sobol sequences to ensure comprehensive coverage of operational uncertainties. 2) Machine Learning Framework: The code employs a diverse set of machine learning models, including polynomial regression, decision trees, random forests, gradient boosting, support vector regression, k-nearest neighbors, multi-layer perceptrons, and symbolic regression. These models are trained to predict decay heat over a wide temporal range, from immediate shutdown up to 10,000 years. 3) Region-Optimized Training: The temporal domain is divided into multiple regions, each modeled separately to capture distinct decay heat characteristics across different time scales. This approach significantly improves the accuracy and interpretability of predictions. 4) Segmented Polynomial Interpretation (SPI): The SPI method translates machine learning predictions into piecewise polynomial equations. These equations are physically interpretable and can be directly integrated into existing engineering workflows and safety analyses. 5) Front-End Interfaces: The code includes both a Jupyter notebook interface for research development and a Streamlit web application for operational deployment. These interfaces allow users to interactively explore decay heat predictions, adjust operational parameters, and visualize results in real-time. 6) Applications: The framework supports various applications, including safety system validation and spent fuel container optimization. It enables real-time evaluation of worst-case decay heat scenarios, informing the design of passive safety systems and optimizing container designs for long-term storage. Overall, this code provides a robust, accurate, and user-friendly tool for predicting decay heat in MSRs, enhancing reactor safety, and optimizing spent fuel management.

Retamales, Mauricio Eduardo Tano [Idaho National L↗
NASA NTRS1992

A new model for estimating total body water from bioelectrical resistance

Estimation of total body water (T) from bioelectrical resistance (R) is commonly done by stepwise regression models with height squared over R, H(exp 2)/R, age, sex, and weight (W). Polynomials of H(exp 2)/R have not been included in these models. We examined the validity of a model with third order polynomials and W. Methods: T was measured with oxygen-18 labled water in 27 subjects. R at 50 kHz was obtained from electrodes placed on the hand and foot while subjects were in the supine position. A stepwise regression equation was developed with 13 subjects (age 31.5 plus or minus 6.2 years, T 38.2 plus or minus 6.6 L, W 65.2 plus or minus 12.0 kg). Correlations, standard error of estimates and mean differences were computed between T and estimated T's from the new (N) model and other models. Evaluations were completed with the remaining 14 subjects (age 32.4 plus or minus 6.3 years, T 40.3 plus or minus 8 L, W 70.2 plus or minus 12.3 kg) and two of its subgroups (high and low) Results: A regression equation was developed from the model. The only significant mean difference was between T and one of the earlier models. Conclusion: Third order polynomials in regression models may increase the accuracy of estimating total body water. Evaluating the model with a larger population is needed.

Siconolfi, S. F.↗