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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations

The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.

Sidi, Avram↗
NASA NTRS1996

Flight data results of estimate fusion for spacecraft rendezvous navigation from shuttle mission STS-69

A recently developed rendezvous navigation fusion filter that optimally exploits existing distributed filters for rendezvous and GPS navigation to achieve the relative and inertial state accuracies of both in a global solution is utilized here to process actual flight data. Space Shuttle Mission STS-69 was the first mission to date which gathered data from both the rendezvous and Global Positioning System filters allowing, for the first time, a test of the fusion algorithm with real flight data. Furthermore, a precise best estimate of trajectory is available for portions of STS-69, making possible a check on the performance of the fusion filter. In order to successfully carry out this experiment with flight data, two extensions to the existing scheme were necessary: a fusion edit test based on differences between the filter state vectors, and an underweighting scheme to accommodate the suboptimal perfect target assumption made by the Shuttle rendezvous filter. With these innovations, the flight data was successfully fused from playbacks of downlinked and/or recorded measurement data through ground analysis versions of the Shuttle rendezvous filter and a GPS filter developed for another experiment. The fusion results agree with the best estimate of trajectory at approximately the levels of uncertainty expected from the fusion filter's covariance matrix.

Carpenter, J. Russell↗
NASA NTRS1996

Collision Strengths for Electron Impact Excitation of Inelastic Transitions in Ar II

We have calculated collision strengths for electron impact excitation of inelastic transitions in Ar II using the R-matrix method in two independent nine- and 19-state close-coupling approximations. In the nine-state calculation the 3s(sup 2)3p(sup 5)2p(sup 0), 3S(sup 3)p(sup 6)S-2, 3p(sup 4)(P-3)4s(sup 2)P, 3p(sup 4)(P-3)3d(sup 2)P, 3p(sup 4)(D-1)4s(sup 2)D, 3p(sup 4)(P-3)3d(sup 2)D, 3p(sup 4)(S-1)4s(sup 2)S, 3p(sup 4)(D-1)3d(sup 2)S and 3p(sup 4)(D-1)4d(sup 2)S states are included, while in the 19-state calculation these states plus an additional ten states 3p(sup 4)(P-3)3d(sup 2)F, 3p(sup 4)(P-3)4p(sup 2)D(sup 0), 2p(sup 0), 2S(sup 0), 3p(sup 4)(D-1)4p(sup 2)P(sup 0), 2D(sup O), 2F(sup 0), 3p(sup 4)(D-1)3d(sup 2)D, p-2 and 3p(sup 4)(S-1)4p(sup 2)P(sup 0) are considered. These target states are represented by fairly extensive configuration-interaction wavefunctions which yield excitation energies and oscillator strengths that are generally in good agreement with the available most accurate calculations and the experimental values. Rydberg series of resonances converging to the excited state thresholds are included in the calculation. The effective collision strengths are obtained assuming a Maxwellian distribution of electron energies which are tabulated over the temperature range (0.5-20) x 10(exp 4) K.

Tayal, S. S.↗
NASA NTRS2004

Hot Structure Control Surface Progress for X-37 Technology Development Program

The NASA Marshall Space Flight Center (MSFC) has been leading the development of technologies that will enable the development, fabrication, and flight of the automated X-37 Orbital Vehicle (OV). With the Administration s recent announcement of the Vision for Space Exploration, NASA placed the X-37 OV design on hold while developing detailed requirements for a Crew Exploration Vehicle, but has continued funding the development of high-risk, critical technologies for potential future space exploration vehicle applications. Hot Structure Control Surfaces (HSCS) technology development is one of the high-priority areas being funded at this time. The goal of HSCS research is to mitigate risk by qualifying the lightest possible components that meet the stringent X-37 OV weight and performance requirements, including Shuttle-type reen- try environments with peak temperatures of 2800 OF. The small size of the X-37 OV (25.7-feet long and 14.9-foot wingspan) drives the need for advanced HSCS because the vehicle's two primary aerodynamic surfaces, the flaperons and ruddervators, have thicknesses ranging from approximately 5 in. down to 1 in. Traditional metallic or polymer-matrix composites covered with tile or blanket thermal protection system (TPS) materials cannot be used as there is insufficient volume to fabricate such multi-component structures. Therefore, carbon-carbon (C-C) and carbodsilicon-carbide (C-SiC) composite HSCS structures are being developed in parallel by two teams supporting the X-37 prime contractor (The Boeing Company). The Science Applications International Coy. (SAIC) and Carbon-Carbon Advanced Technologies, Inc. (C-CAT) team is developing the C-C HSCS, while the General Electric Energy Power Systems Composites (GE-PSC) and Materials Research and Design (MRD) team is developing the C-SiC HSCS. These two teams were selected to reduce the high level of risk associated with developing advanced control surface components. They have continued HSCS development work as part of the X-37 critical technology development contract. The SAIC/C-CAT team is using Advanced Carbon-Carbon (ACC) because its fabrication is very similar to the process used for Space Shuttle Reinforced Carbon-Carbon fabrication, including the Sic-based pack cementation conversion coating systems using with both materials. ACC was selected over RCC because it has much higher tension and compressions strengths, and because T-300 fiber is readily available, whereas RCC rayon fiber is no longer manufactured. The GE-PSC/MRD team is using a T-300 fiber-reinforced Sic matrix composite material densified by chemical vapor infiltration. The C-Sic material has an Sic-based environmental barrier coating. Major accomplishments have been made over the past year by both HSCS teams. C-C and C- SiC flaperon subcomponents, which are truncated full-scale versions of flight hardware, have been fabricated and are undergoing testing at the NASA Dryden Flight Research Center, NASA Langley Research Center, and U.S. Air Force Research Laboratory. By the end of 2004, ruddervator subcomponents also will be delivered and tested. As NASA moves forward in realizing the Vision for Space Exploration, it will continue to invest in advanced research and development aimed at making new generations of spacecraft safer, more reliable, and more affordable. The X-37 HSCS effort ultimately will benefit the Agency's vision and mission.

Valentine, P. G.↗
NASA NTRS2004

Simulation of Aerosols and Chemistry with a Unified Global Model

This project is to continue the development of the global simulation capabilities of tropospheric and stratospheric chemistry and aerosols in a unified global model. This is a part of our overall investigation of aerosol-chemistry-climate interaction. In the past year, we have enabled the tropospheric chemistry simulations based on the GEOS-CHEM model, and added stratospheric chemical reactions into the GEOS-CHEM such that a globally unified troposphere-stratosphere chemistry and transport can be simulated consistently without any simplifications. The tropospheric chemical mechanism in the GEOS-CHEM includes 80 species and 150 reactions. 24 tracers are transported, including O3, NOx, total nitrogen (NOy), H2O2, CO, and several types of hydrocarbon. The chemical solver used in the GEOS-CHEM model is a highly accurate sparse-matrix vectorized Gear solver (SMVGEAR). The stratospheric chemical mechanism includes an additional approximately 100 reactions and photolysis processes. Because of the large number of total chemical reactions and photolysis processes and very different photochemical regimes involved in the unified simulation, the model demands significant computer resources that are currently not practical. Therefore, several improvements will be taken, such as massive parallelization, code optimization, or selecting a faster solver. We have also continued aerosol simulation (including sulfate, dust, black carbon, organic carbon, and sea-salt) in the global model to cover most of year 2002. These results have been made available to many groups worldwide and accessible from the website http://code916.gsfc.nasa.gov/People/Chin/aot.html.

Chin, Mian↗
NASA NTRS1992

Spatial orientation of the vestibular system

1. A simplified three-dimensional state space model of visual vestibular interaction was formulated. Matrix and dynamical system operators representing coupling from the semicircular canals and the visual system to the velocity storage integrator were incorporated into the model. 2. It was postulated that the system matrix for a tilted position was a composition of two linear transformations of the system matrix for the upright position. One transformation modifies the eigenvalues of the system matrix while another rotates the pitch and roll eigenvectors with the head, while maintaining the yaw axis eigenvector approximately spatially invariant. Using this representation, the response characteristics of the pitch, roll, and yaw eye velocity were obtained in terms of the eigenvalues and associated eigenvectors. 3. Using OKAN data obtained from monkeys and comparing to the model predictions, the eigenvalues and eigenvectors of the system matrix were identified as a function of tilt to the side or of tilt to the prone positions, using a modification of the Marquardt algorithm. The yaw eigenvector for right-side-down tilt and for downward pitch cross-coupling was approximately 30 degrees from the spatial vertical. For the prone position, the eigenvector was computed to be approximately 20 degrees relative to the spatial vertical. For both side-down and prone positions, oblique OKN induced along eigenvector directions generated OKAN which decayed to zero along a straight line with approximately a single time constant. This was verified by a spectral analysis of the residual sequence about the straight line fit to the decaying data. The residual sequence was associated with a narrow autocorrelation function and a wide power spectrum. 4. Parameters found using the Marquardt algorithm were incorporated into the model. Diagonal matrices in a head coordinate frame were introduced to represent the direct pathway and the coupling of the visual system to the integrator. Model simulations predicted the behavior of yaw and pitch OKN and OKAN when the animal was upright, as well as the cross-coupling in the tilted position. The trajectories in velocity space were also accurately simulated. 5. There were similarities between the monkey eigenvectors and human perception of the spatial vertical. For side-down tilts and downward eye velocity cross-coupling, there was only an Aubert (A) effect. For upward eye velocity cross-coupling there were both Muller (E) and Aubert (A) effects. The mean of the eigenvectors for upward and downward eye velocities overlay human 1 x g perceptual data.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Neuroscience↗
NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗
NASA NTRS1975

Sparse matrix techniques applied to modal analysis of multi-section duct liners

A simplified procedure is presented for analysis of ducts with discretely nonuniform properties. The analysis uses basis functions as the generalized coordinates. The duct eigenfunctions are approximated by finite series of these functions. The emphasis is on solution of the resulting large sparse set of linear equations. Characteristics of sparse matrix algorithms are outlined and some criteria for application are established. Analogies with structural methods are used to illustrate variations which can increase efficiency in generating values for design optimization routines. The effects of basis function selection, number of eigenfunctions and identification and ordering of equations on the sparsity and solution stability are included.

Arnold, W. R.↗
NASA NTRS2002

Knowledge of Pest Resistance in SiC/BN/SiC Composites Improved

Ceramic-matrix composites (CMC's) consisting of a silicon carbide matrix reinforced with boron-nitride- (BN-) coated silicon carbide (SiC) fibers are strong contenders for commercial and aerospace applications (in particular, the hot sections of high-performance turbine engines in advanced aircraft and generators). They have very good mechanical properties below approximately 600 C and above approximately 1000 C. Between those temperatures, however, the BN coating oxidizes easily, and the oxidation of the SiC matrix is too sluggish to seal off the composite with a protective layer of silica. In that temperature interval, the preferential oxidation of the BN weakens and embrittles the composite. That phenomenon, referred to as "pest" degradation, is the focus of this work, which aims to identify the causes of and remedies for pesting. Previous work established that pesting in Hi-Nicalon (Nippon Carbon Co., Ltd., Japan)/SiC composites was caused by a layer of free carbon that undermined the oxidation resistance of the BN. New work suggests that composites containing a source of carbon are prone to severe pesting and that those that are free of elemental carbon are resistant pesting. Pest resistance was assessed by exposing machined samples for 100 to 150 hr in an atmospheric burner rig at 600 to 1100 C, followed by a tensile fracture test to measure residual mechanical properties and by characterization of the interphase microstructure. Whether the elemental carbon came from intrinsic or extrinsic sources, its presence induced the tensile strength to drop by over 50 percent in the burner rig, with an even more severe loss of fracture strain. A likely mechanism by which burnoff of the carbon layer exposes the BN to accelerated flank attack by ambient oxidants is shown. The BN is replaced with borosilicates that attack the fiber, and ultimately with silica that embrittles the composites by rigidly bonding components. Thus, the study has shown that pesting can be prevented in SiC/BN/SiC, or at least reduced, by simply excluding free carbon. These studies continue, and plans for future work include investigating the role that carbon may play elsewhere in the interphase region.

Thomas-Ogbuji, Linus U.↗
NASA NTRS1975

Stochastic process approximation for recursive estimation with guaranteed bound on the error covariance

An approach, is proposed for the design of approximate, fixed order, discrete time realizations of stochastic processes from the output covariance over a finite time interval, was proposed. No restrictive assumptions are imposed on the process; it can be nonstationary and lead to a high dimension realization. Classes of fixed order models are defined, having the joint covariance matrix of the combined vector of the outputs in the interval of definition greater or equal than the process covariance; (the difference matrix is nonnegative definite). The design is achieved by minimizing, in one of those classes, a measure of the approximation between the model and the process evaluated by the trace of the difference of the respective covariance matrices. Models belonging to these classes have the notable property that, under the same measurement system and estimator structure, the output estimation error covariance matrix computed on the model is an upper bound of the corresponding covariance on the real process. An application of the approach is illustrated by the modeling of random meteorological wind profiles from the statistical analysis of historical data.

Menga, G.↗
NASA NTRS1977

A distorted-wave methodology for electron-ion impact excitation - Calculation for two-electron ions

A distorted-wave program is being developed for calculating the excitation of few-electron ions by electron impact. It uses the exchange approximation to represent the exact initial-state wavefunction in the T-matrix expression for the excitation amplitude. The program has been implemented for excitation of the 2/1,3/(S,P) states of two-electron ions. Some of the astrophysical applications of these cross sections as well as the motivation and requirements of the calculational methodology are discussed.

Bhatia, A. K.↗
NASA NTRS1982

Structural tailoring of engine blades (STAEBL)

A mathematical optimization procedure was developed for the structural tailoring of engine blades and was used to structurally tailor two engine fan blades constructed of composite materials without midspan shrouds. The first was a solid blade made from superhybrid composites, and the second was a hollow blade with metal matrix composite inlays. Three major computerized functions were needed to complete the procedure: approximate analysis with the established input variables, optimization of an objective function, and refined analysis for design verification.

Platt, C. E.↗
NASA NTRS1984

Composite interlaminar fracture - Effect of matrix fracture energy

A major result of the use of the double cantilever beam test to provide a measure of the interlaminar fracture energy in composites subjected to simple Mode I-type loading is the observation that increasing the toughness of the matrix resin by as much as a factor of 20 produced a major (approximately four-fold) increase in interlaminar fracture energy. The data presently analyzed show that, with brittle polymers, resin toughness is fully transferred to the composite, while in the case of tougher polymers the resin toughness is only partially transferred due to the fibers' restriction of the crack tip deformation zone in the polymer, together with their changing of local stress field details. Factors which tend to increase interlaminar toughness are fiber nesting and bridging, as well as fiber breakage and pull-out during crack growth.

Hunston, D. L.↗
NASA NTRS1985

Superconducting magnet

Extensive computer based engineering design effort resulted in optimization of a superconducting magnet design with an average bulk current density of approximately 12KA/cm(2). Twisted, stranded 0.0045 inch diameter NbTi superconductor in a copper matrix was selected. Winding the coil from this bundle facilitated uniform winding of the small diameter wire. Test coils were wound using a first lot of the wire. The actual packing density was measured from these. Interwinding voltage break down tests on the test coils indicated the need for adjustment of the wire insulation on the lot of wire subsequently ordered for construction of the delivered superconducting magnet. Using the actual packing densities from the test coils, a final magnet design, with the required enhancement and field profile, was generated. All mechanical and thermal design parameters were then also fixed. The superconducting magnet was then fabricated and tested. The first test was made with the magnet immersed in liquid helium at 4.2K. The second test was conducted at 2K in vacuum. In the latter test, the magnet was conduction cooled from the mounting flange end.

Source record↗
NASA NTRS1985

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Winget, J. M.↗
NASA NTRS1992

Prediction of thermal cycling induced matrix cracking

Thermal fatigue has been observed to cause matrix cracking in laminated composite materials. A method is presented to predict transverse matrix cracks in composite laminates subjected to cyclic thermal load. Shear lag stress approximations and a simple energy-based fracture criteria are used to predict crack densities as a function of temperature. Prediction of crack densities as a function of thermal cycling is accomplished by assuming that fatigue degrades the material's inherent resistance to cracking. The method is implemented as a computer program. A simple experiment provides data on progressive cracking of a laminate with decreasing temperature. Existing data on thermal fatigue is also used. Correlations of the analytical predictions to the data are very good. A parametric study using the analytical method is presented which provides insight into material behavior under cyclical thermal loads.

Mcmanus, Hugh L.↗
NASA NTRS1996

Algebraic Multigrid by Smoothed Aggregation for Second and Fourth Order Elliptic Problems

Multigrid methods are very efficient iterative solvers for system of algebraic equations arising from finite element and finite difference discretization of elliptic boundary value problems. The main principle of multigrid methods is to complement the local exchange of information in point-wise iterative methods by a global one utilizing several related systems, called coarse levels, with a smaller number of variables. The coarse levels are often obtained as a hierarchy of discretizations with different characteristic meshsizes, but this requires that the discretization is controlled by the iterative method. To solve linear systems produced by existing finite element software, one needs to create an artificial hierarchy of coarse problems. The principal issue is then to obtain computational complexity and approximation properties similar to those for nested meshes, using only information in the matrix of the system and as little extra information as possible. Such algebraic multigrid method that uses the system matrix only was developed by Ruge. The prolongations were based on the matrix of the system by partial solution from given values at selected coarse points. The coarse grid points were selected so that each point would be interpolated to via so-called strong connections. Our approach is based on smoothed aggregation introduced recently by Vanek. First the set of nodes is decomposed into small mutually disjoint subsets. A tentative piecewise constant interpolation (in the discrete sense) is then defined on those subsets as piecewise constant for second order problems, and piecewise linear for fourth order problems. The prolongation operator is then obtained by smoothing the output of the tentative prolongation and coarse level operators are defined variationally.

Vanek, Petr↗
NASA NTRS2019

Principal Component Analysis of Up-The-Ramp Sampled Infrared Array Data

We describe the results of principal component analysis (PCA) of up-the-ramp sampled infrared (IR) array data from the Hubble Space Telescope wide field camera 3 (WFC3 IR), James Webb Space Telescope NIRSpec, and prototype Wide Field Infrared Survey Telescope’s wide field instrument detectors. These systems use, respectively, Teledyne H1R, H2RG, and H4RG-10 near-IR detector arrays with a variety of IR array controllers. The PCA shows that the Legendre polynomials approximate the principal components of these systems (i.e., they roughly diagonalize the covariance matrix). In contrast to the monomial basis that is widely used for polynomial fitting and linearization today, the Legendre polynomials are an orthonormal basis. They provide a quantifiable, compact, and (nearly) linearly uncorrelated representation of the information content of the data. By fitting a few Legendre polynomials, nearly all of the meaningful information in representative WFC3 astronomical datacubes can be condensed from 15 up-the-ramp samples down to 6 compressible Legendre coefficients per pixel. The higher order coefficients contain time domain information that is lost when one projects up-the-ramp sampled datacubes onto two-dimensional images by fitting a straight line, even if the data are linearized before fitting the line. Going forward, we believe that this time domain information is potentially important for disentangling the various nonlinearities that can affect IR array observations, i.e., inherent pixel nonlinearity, persistence, burn in, brighter-fatter effect, (potentially) nonlinear interpixel capacitance, and perhaps others.

Rauscher, Bernard J.↗