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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Conservative high-order data transfer method on generalized polygonal meshes

A conservative data transfer (remap) between two meshes is an important step of arbitrary Lagrangian-Eulerian (ALE) hydrodynamics simulations. High-order numerical methods for ALE simulations require both high-order (curvilinear) meshes and high-order remap algorithms. Here we develop a conservative and bounds-preserving method for accurate remapping of discrete fields on generalized polygonal meshes with curvilinear edges. The properties of the proposed method are studied theoretically and numerically for various (smooth and non-smooth) mesh deformations and discrete fields that represent smooth and discontinuous functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems.

Brandt, A.↗
NASA NTRS1986

Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems.

Brandt, A.↗
NASA NTRS1997

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Kvernadze, George↗
NASA NTRS2007

GIFTS SM EDU Data Processing and Algorithms

The Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS) Sensor Module (SM) Engineering Demonstration Unit (EDU) is a high resolution spectral imager designed to measure infrared (IR) radiances using a Fourier transform spectrometer (FTS). The GIFTS instrument employs three Focal Plane Arrays (FPAs), which gather measurements across the long-wave IR (LWIR), short/mid-wave IR (SMWIR), and visible spectral bands. The raw interferogram measurements are radiometrically and spectrally calibrated to produce radiance spectra, which are further processed to obtain atmospheric profiles via retrieval algorithms. This paper describes the processing algorithms involved in the calibration stage. The calibration procedures can be subdivided into three stages. In the pre-calibration stage, a phase correction algorithm is applied to the decimated and filtered complex interferogram. The resulting imaginary part of the spectrum contains only the noise component of the uncorrected spectrum. Additional random noise reduction can be accomplished by applying a spectral smoothing routine to the phase-corrected blackbody reference spectra. In the radiometric calibration stage, we first compute the spectral responsivity based on the previous results, from which, the calibrated ambient blackbody (ABB), hot blackbody (HBB), and scene spectra can be obtained. During the post-processing stage, we estimate the noise equivalent spectral radiance (NESR) from the calibrated ABB and HBB spectra. We then implement a correction scheme that compensates for the effect of fore-optics offsets. Finally, for off-axis pixels, the FPA off-axis effects correction is performed. To estimate the performance of the entire FPA, we developed an efficient method of generating pixel performance assessments. In addition, a random pixel selection scheme is designed based on the pixel performance evaluation.

Tian, Jialin↗
NASA NTRS2005

Kurtosis Approach Nonlinear Blind Source Separation

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Duong, Vu A.↗
NASA NTRS2005

Kurtosis Approach for Nonlinear Blind Source Separation

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

kurtosis↗
DOE OSTI2026

An efficient level set method for tracking many materials

Here, we present an efficient level set method to track an arbitrary number of materials. The algorithm is optimal in the sense that it only needs to store a single unsigned distance-like function and a single integer indicator function, independent of the number of materials or distinct regions being tracked. Furthermore, for smooth velocity fields and smooth interface shape, arbitrarily high order solutions can be demonstrated. For interfaces that are or become kinked, the solution is limited to second-order convergence rates in the L 1 norm and first-order in the L ∞ norm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions

We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical “best” convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

Implicit determination of multispectral scanner data variation over extended areas.

Description of a method by which variations in aerial multispectral scanner data can be accounted for when there is insufficient ground truth information. The data are suitably filtered and smoothed along the flight line, and the reduced results are presented in a form such that the investigator can readily determine the preprocessing that should be used and the spatial extent to which it should be applied. An algorithm is developed for the detection of cloud-shadowed areas.

Kriegler, F. J.↗
NASA NTRS1987

Numerical studies of the thermal design sensitivity calculation for a reaction-diffusion system with discontinuous derivatives

The aim of this study is to find a reliable numerical algorithm to calculate thermal design sensitivities of a transient problem with discontinuous derivatives. The thermal system of interest is a transient heat conduction problem related to the curing process of a composite laminate. A logical function which can smoothly approximate the discontinuity is introduced to modify the system equation. Two commonly used methods, the adjoint variable method and the direct differentiation method, are then applied to find the design derivatives of the modified system. The comparisons of numerical results obtained by these two methods demonstrate that the direct differentiation method is a better choice to be used in calculating thermal design sensitivity.

Hou, Jean W.↗
NASA NTRS1998

A New and Fast Method for Smoothing Spectral Imaging Data

The Airborne Visible Infrared Imaging Spectrometer (AVIRIS) acquires spectral imaging data covering the 0.4 - 2.5 micron wavelength range in 224 10-nm-wide channels from a NASA ER-2 aircraft at 20 km. More than half of the spectral region is affected by atmospheric gaseous absorption. Over the past decade, several techniques have been used to remove atmospheric effects from AVIRIS data for the derivation of surface reflectance spectra. An operational atmosphere removal algorithm (ATREM), which is based on theoretical modeling of atmospheric absorption and scattering effects, has been developed and updated for deriving surface reflectance spectra from AVIRIS data. Due to small errors in assumed wavelengths and errors in line parameters compiled on the HITRAN database, small spikes (particularly near the centers of the 0.94- and 1.14-micron water vapor bands) are present in this spectrum. Similar small spikes are systematically present in entire ATREM output cubes. These spikes have distracted geologists who are interested in studying surface mineral features. A method based on the "global" fitting of spectra with low order polynomials or other functions for removing these weak spikes has recently been developed by Boardman (this volume). In this paper, we describe another technique, which fits spectra "locally" based on cubic spline smoothing, for quick post processing of ATREM apparent reflectance spectra derived from AVIRIS data. Results from our analysis of AVIRIS data acquired over Cuprite mining district in Nevada in June of 1995 are given. Comparisons between our smoothed spectra and those derived with the empirical line method are presented.

Gao, Bo-Cai↗
DOE OSTI2026

Locally purified maximally mixed states at scale: Entanglement pruning and symmetries

Locally Purified Density Operators (LPDOs) are state-of-the-art tensor network ansatze candidates that efficiently represent mixed quantum states at scale. However, given their non-uniqueness, their representational complexity is generally sub-optimal in practical computations. Here, in this work we perform a comprehensive numerical and analytical analysis and resolve this issue in the experimentally relevant limit where noise depolarizes the density operator into a maximally mixed state. To resolve the sub-optimality issue, we analyze two numerical tools, one analytic method, and detail the relations between them. The numerical tools used are fidelity-preserving truncations and isometric gauge transformations leveraging Riemannian optimizations over entropic objective functions. In addition, by invoking the injectivity and symmetry constraints of the maximally mixed LPDO, we also present analytical closed-form expressions for the disentangler and discuss their relation to numerical optimizers. Further, away from the maximally mixed state, our simulations highlight how the truncation threshold smoothly interpolate, as a function of depolarization, between established matrix product results and our new results. Our work shows how, by minimizing the resources required to represent key states of practical interest in experiment, the efficiency of tensor network algorithms can be substantially increased. This paves the path for uncovering tensor network’s fundamental scalability limits and latent potential in representing the wide locus of mixed quantum states that are accessible on near-term quantum devices.

Gangapuram, Amit Jamadagni [Oak Ridge National Lab↗
NASA NTRS1988

Spectral element multigrid. Part 2: Theoretical justification

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from tha approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

Maday, Yvon↗
NASA NTRS1989

Numerical simulation of flow over a hypersonic aircraft using an explicit upwind PNS solver

A hypersonic flow field over a generic airplane configuration is simulated by solving the Parabolized Navier-Stokes (PNS) equations. The finite difference solution of the PNS equations is calculated using a noniterative space marching, explicit, upwind scheme recently developed by the authors. Special gridding techniques are used which allowed the sharp changes in surface geometry of the airplane configuration to be modelled without smoothing of corners. Comparisons of the PNS results to a solution of the Navier-Stokes equations demonstrates a good agreement of the numerical results in approximately 1/6 of the cpu time. This paper demonstrates that the explicit upwind algorithm for solving the PNS equations is an efficient method for simulating hypersonic flow fields about complete airplane configurations and should be considered as an alternative to solving the Navier-Stokes equations for flow fields where the PNS equations are valid.

Korte, John J.↗
NASA NTRS1991

A simulation of the collapse and fragmentation of cooling molecular clouds

The application of the Smoothed Particle Hydrodynamics method to the fragmentation of rotating cloud and disk systems is described, allowing for molecular cooling due to H2 and CO. A novel approach to solving Poisson's equation for disklike structures which exploits the multigrid algorithm is also described. Numerical studies are presented which investigate the evolution of both rotating clouds and Maclaurin disks, in each case with both an isothermal equation of state and with molecular cooling. The results establish the influence of molecular cooling on the fragmentation of molecular clouds. The isothermal sequences, if they fragment at all, do so into far fewer lumps than the cooling sequences. This is not due to a cooling instability as such, but rather to the reduced thermal support. One of the sequences shows a remarkable similarity to the W49A star-forming region.

Monaghan, Joe J.↗
NASA NTRS1997

Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton- Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the reader can understand the algorithms and code them up for applications.

Shu, Chi-Wang↗
NASA NTRS2011

Enchanced interference cancellation and telemetry reception in multipath environments with a single paraboic dish antenna using a focal plane array

An Advanced Focal Plane Array ("AFPA") for parabolic dish antennas that exploits spatial diversity to achieve better channel equalization performance in the presence of multipath (better than temporal equalization alone), and which is capable of receiving from two or more sources within a field-of-view in the presence of multipath. The AFPA uses a focal plane array of receiving elements plus a spatio-temporal filter that keeps information on the adaptive FIR filter weights, relative amplitudes and phases of the incoming signals, and which employs an Interference Cancelling Constant Modulus Algorithm (IC-CMA) that resolves multiple telemetry streams simultaneously from the respective aero-nautical platforms. This data is sent to an angle estimator to calculate the target's angular position, and then on to Kalman filters FOR smoothing and time series prediction. The resulting velocity and acceleration estimates from the time series data are sent to an antenna control unit (ACU) to be used for pointing control.

Mukai, Ryan↗