Search NASA⌕ Search

SEARCH · Search NASA

Results for “spectral methods”

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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Quarteroni, Alfio↗
NASA NTRS1986

Preconditioned conjugate residual methods for the solution of spectral equations

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Wong, Y. S.↗
NASA NTRS2002

Spectral (Finite) Volume Method for One Dimensional Euler Equations

Consider a mesh of unstructured triangular cells. Each cell is called a Spectral Volume (SV), denoted by Si, which is further partitioned into subcells named Control Volumes (CVs), indicated by C(sub i,j). To represent the solution as a polynomial of degree m in two dimensions (2D) we need N = (m+1)(m+2)/2 pieces of independent information, or degrees of freedom (DOFs). The DOFs in a SV method are the volume-averaged mean variables at the N CVs. For example, to build a quadratic reconstruction in 2D, we need at least (2+1)(3+1)/2 = 6 DOFs. There are numerous ways of partitioning a SV, and not every partition is admissible in the sense that the partition may not be capable of producing a degree m polynomial. Once N mean solutions in the CVs of a SV are given, a unique polynomial reconstruction can be obtained.

Wang, Z. J.↗
NASA NTRS1983

Preconditioned Minimal Residual Methods for Chebyshev Spectral Caluclations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗
NASA NTRS1985

Preconditioned minimal residual methods for Chebyshev spectral calculations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗
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↗
NASA NTRS1973

Spectral ratio imaging methods for geological remote sensing from aircraft and satellites

The author has identified the following significant results. The production of ratio images from multispectral scanner data is described and several examples of ratio images from aircraft and ERTS-1 data are given for visible, reflective infrared, and thermal infrared wavelengths. The application of photogrammetric techniques to ratio images, defined for this paper as ratio scannergrammetry, is considerably aided by the lesser dependence of ratio images on atmospheric and solar illumination variations, compared with single channel scanner imagery or aerial photos. Ratio scannergrammetry is further aided by the proportionality between ratios of a target deduced from ratio images and ratios of reflectances calculated from laboratory spectra of samples from the target area. Consequently, ratios calculated from laboratory data can be used to predict which ratios are best for discriminating a given rock or mineral, to predict what other rocks or minerals will be confused with it, and finally, to place ratio scannergrammetry on an absolute basis, within an estimated standard error on the order of 5% to 10%. Examples of relative agreement between laboratory data and ratio images are given from two iron oxides, hematite and magnetite.

Vincent, R. K.↗
NASA NTRS1973

Spectral ratio imaging methods for geological remote sensing from aircraft and satellites

An improved photogrammetric technique (scannergrammetry) for the production of ratio images from multispectral scanner data is described. The multispectral technique is less affected by variations in atmospheric and solar illumination levels than single-channel scanner imagery of aerial photographs. Another advantage of the multispectral technique is the proportionality between ratios of a target deduced from ratio images, on the one hand, and ratios of reflectances calculated from laboratory spectra of samples from the target area, on the other hand. Several representative ratio images from aircraft and satellite data in the visible, reflective IR, and thermal IR regions are included. The geological applications suggested for ratio scannergrammetry include exploration of construction materials, soils, stratigraphy, volcanic ash flows, beaches, and sand dunes.

Vincent, R. K.↗
NASA NTRS1977

A method of determining spectral dye densities in color films

A mathematical analysis technique called characteristic vector analysis, reported by Simonds (1963), is used to determine spectral dye densities in multiemulsion film such as color or color-IR imagery. The technique involves examining a number of sets of multivariate data and determining linear transformations of these data to a smaller number of parameters which contain essentially all of the information contained in the original set of data. The steps involved in the actual procedure are outlined. It is shown that integral spectral density measurements of a large number of different color samples can be accurately reconstructed from the calculated spectral dye densities.

Friederichs, G. A.↗
NASA NTRS1982

Method for evaluating moisture tensions of soils using spectral data

A method is disclosed which permits evaluation of soil moisture utilizing remote sensing. Spectral measurements at a plurality of different wavelengths are taken with respect to sample soils and the bidirectional reflectance factor (BRF) measurements produced are submitted to regression analysis for development therefrom of predictable equations calculated for orderly relationships. Soil of unknown reflective and unknown soil moisture tension is thereafter analyzed for bidirectional reflectance and the resulting data utilized to determine the soil moisture tension of the soil as well as providing a prediction as to the bidirectional reflectance of the soil at other moisture tensions.

Peterson, John B.↗
DOE OSTI2024

Enhancing Thomson scattering polychromator performance with multi-pass spectral filters

In photon-deficient, noncollective Thomson scattering diagnostics, filter polychromators are typically employed in the spectral analysis of Thomson-scattered signals to achieve acceptable signal-to-noise performance. Currently, the most common polychromator filter configuration employs a set of single-passband optical filters that define individual spectral channels. Here, we introduce a new spectral analysis method for Thomson scattering based on spectral filters with multiple passbands, referred to as Thomson scattering spectral multiplexing. Implementing multi-bandpass spectral filters on polychromators increases the achievable range of electron temperature measurement for a given number of filters employed. In addition, Thomson scattering spectral multiplexing reduces systematic measurement uncertainty, with fewer required spectral channels, thereby decreasing light loss from reduced optical element interactions. A multi-bandpass filter set, optimized by a genetic algorithm, has been successfully installed and tested on the Helically Symmetric eXperiment (HSX), demonstrating the benefits of the Thomson scattering spectral multiplexing method.

Instruments & Instrumentation↗