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NASA NTRS1997

A Portable MPI Implementation of the SPAI Preconditioner in ISIS++

A parallel MPI implementation of the Sparse Approximate Inverse (SPAI) preconditioner is described. SPAI has proven to be a highly effective preconditioner, and is inherently parallel because it computes columns (or rows) of the preconditioning matrix independently. However, there are several problems that must be addressed for an efficient MPI implementation: load balance, latency hiding, and the need for one-sided communication. The effectiveness, efficiency, and scaling behavior of our implementation will be shown for different platforms.

Barnard, Stephen T.↗

NASA NTRS1984

Inverse design technique for cascades

A numerical technique to generate cascades is presented. The basic prescribed parameters are: inlet angle, exit pressure, and distribution of blade thickness and lift along a blade. Other sets of parameters are also discussed. The technique is based on the lambda scheme. The problem of stability of the computation as a function of the prescribed set of parameters and the treatment of boundary conditions is discussed. A one dimensional analysis to indicate a possible way for assuring stability for any two dimensional calculation is provided.

Zannetti, L.↗

NASA NTRS1982

Alternative ways for formulation of hybrid stress elements

An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.

Pian, T. H. H.↗

NASA NTRS1992

High-resolution gravity model of Venus

The anomalous gravity field of Venus shows high correlation with surface features revealed by radar. We extract gravity models from the Doppler tracking data from the Pioneer Venus Orbiter by means of a two-step process. In the first step, we solve the nonlinear spacecraft state estimation problem using a Kalman filter-smoother. The Kalman filter has been evaluated through simulations. This evaluation and some unusual features of the filter are discussed. In the second step, we perform a geophysical inversion using a linear Bayesian estimator. To allow an unbiased comparison between gravity and topography, we use a simulation technique to smooth and distort the radar topographic data so as to yield maps having the same characteristics as our gravity maps. The maps presented cover 2/3 of the surface of Venus and display the strong topography-gravity correlation previously reported. The topography-gravity scatter plots show two distinct trends.

Reasenberg, R. D.↗

NASA NTRS2015

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Gnoffo, Peter A.↗

NASA NTRS1976

Remote probing of atmospheric particulates from radiation extinction experiments: A review of methods

The existing methodology for reconstructing the particle size distribution and inferring the refractive index of absorbing and scattering atmospheric particulates is critically reviewed. Emphasis is placed on method capabilities and shortcomings and, wherever possible, on achievable accuracy. The nature of the associated remote probing problem is analyzed with regard to the effects of the particulates on EM wave propagation in the atmosphere. The parameterization of size distribution is studied within the unifying framework of Pearson's distribution curves. The inversions of extinction measurements and their ratios are considered separately, and the potentialities of each type of measurement are identified. Work lacking in each of the methods reviewed is indicated. A method of determining both the effective complex refractive index and size distribution model parameters from the same data is also presented. Lastly, determination from extinction ratio data of the complex refractive index independent of size distribution is discussed and error analyzed.

Fymat, A. L.↗

NASA NTRS1977

Fission induced plasmas

The possibility of creating a plasma from fission fragments was investigated, as well as the probability of utilizing the energy of these particles to create population inversion leading to laser action. Eventually, it is hoped that the same medium could be used for both fissioning and lasing, thus avoiding inefficiences in converting one form of energy to the other. A central problem in understanding a fission induced plasma is to obtain an accurate model of the electron behavior; some calculations are presented to this end. The calculations are simple, providing a compendium of processes for reference.

Harries, W. L.↗

NASA NTRS1993

Evaluating the design of an Earth Radiation Budget Instrument with systen simulations. Part 1: Instantaneous estimates

A set of system simulations has been performed to evaluate candidate scanner designs for an Earth Radiation Budget Instrument (ERBI) for the Earth Observing System (EOS) of the late 1990s. Five different instruments are considered: (1) the Active Cavity Array (ACA), (2) the Clouds and Earth's Radiant Energy System-Instrument (CERES-I), (3) the Conically Scanning Radiometer (CSR), (4) the Earth Radiation Budget Experiment Cross-Track Scanner (ERBE), and (5) the Nimbus-7 Biaxial Scanner (N7). Errors in instantaneous, top-of-the-atmosphere (TOA) satellite flux estimates are assumed to arise from two measurement problems: the sampling of space over a given geographic domain, and sampling in angle about a given spatial location. When angular sampling errors vanish due to the application of correct angular dependence models (ADMs) during inversion, the accuracy of each scanner design is determined by the instrument's ability to map the TOA radiance field in a uniform manner. In this regard, the instruments containing a cross-track scanning component (CERES-I and ERBE) do best. As errors in ADMs are encountered, cross-track instruments incur angular sampling errors more rapidly than biaxial instruments (N7, ACA, and CSR) and eventually overtake the biaxial designs in their total error amounts. A latitude bias (north-south error gradient) in the ADM error of cross-track instruments also exists. This would be objectionable when ADM errors are systematic over large areas of the globe. For instantaneous errors, however, cross-track scanners outperform biaxial or conical scanners for 2.5 deg latitude x 2.5 deg longitude target areas, providing that the ADM error is less than or equal to 30%. A key issue is the amount of systematic ADM error (departures from the mean models) that is present at the 2.5 deg resolution of the ERBE target areas. If this error is less than 30%, then the CERES-I, ERBE, and CSR, in order of increasing error, provide the most accurate instantaneous flux estimates, within 2-3 W/sq m of each other in reflected shortwave flux. The magnitude of this error is near the 10 W/sq m accuracy requirement of the user community. Longwave flux errors have been found to have the same space and time characteristics as errors in shortwave radiation, but only about 25% as large.

Stowe, Larry↗

NASA NTRS2011

What's on the Surface? Physics and Chemistry of Delta-Doped Surfaces

Outline of presentation: 1. Detector surfaces and the problem of stability 2. Delta-doped detectors 3. Physics of Delta-doped Silicon 4. Chemistry of the Si-SiO2 Interface 5. Physics and Chemistry of Delta-doped Surfaces a. Compensation b. Inversion c. Quantum exclusion. Conclusions: 1. Quantum confinement of electrons and holes dominates the behavior of delta-doped surfaces. 2. Stability of delta-doped detectors: Delta-layer creates an approx 1 eV tunnel barrier between bulk and surface. 3. At high surface charge densities, Tamm-Shockley states form at the surface. 4. Surface passivation by quantum exclusion: Near-surface delta-layer suppresses T-S trapping of minority carriers. 5. The Si-SiO2 interface compensates the surface 6. For delta-layers at intermediate depth, surface inversion layer forms 7. Density of Si-SiO2 interface charge can be extremely high (>10(exp 14)/sq cm)

detectors↗

NASA NTRS1997

Retrieval of Soil Moisture and Roughness from the Polarimetric Radar Response

The main objective of this investigation was the characterization of soil moisture using imaging radars. In order to accomplish this task, a number of intermediate steps had to be undertaken. In this proposal, the theoretical, numerical, and experimental aspects of electromagnetic scattering from natural surfaces was considered with emphasis on remote sensing of soil moisture. In the general case, the microwave backscatter from natural surfaces is mainly influenced by three major factors: (1) the roughness statistics of the soil surface, (2) soil moisture content, and (3) soil surface cover. First the scattering problem from bare-soil surfaces was considered and a hybrid model that relates the radar backscattering coefficient to soil moisture and surface roughness was developed. This model is based on extensive experimental measurements of the radar polarimetric backscatter response of bare soil surfaces at microwave frequencies over a wide range of moisture conditions and roughness scales in conjunction with existing theoretical surface scattering models in limiting cases (small perturbation, physical optics, and geometrical optics models). Also a simple inversion algorithm capable of providing accurate estimates of soil moisture content and surface rms height from single-frequency multi-polarization radar observations was developed. The accuracy of the model and its inversion algorithm is demonstrated using independent data sets. Next the hybrid model for bare-soil surfaces is made fully polarimetric by incorporating the parameters of the co- and cross-polarized phase difference into the model. Experimental data in conjunction with numerical simulations are used to relate the soil moisture content and surface roughness to the phase difference statistics. For this purpose, a novel numerical scattering simulation for inhomogeneous dielectric random surfaces was developed. Finally the scattering problem of short vegetation cover above a rough soil surface was considered. A general scattering model for grass-blades of arbitrary cross section was developed and incorporated in a first order random media model. The vegetation model and the bare-soil model are combined and the accuracy of the combined model is evaluated against experimental observations from a wheat field over the entire growing season. A complete set of ground-truth data and polarimetric backscatter data were collected. Also an inversion algorithm for estimating soil moisture and surface roughness from multi-polarized multi-frequency observations of vegetation-covered ground is developed.

Sarabandi, Kamal↗

NASA NTRS1994

Using parallel banded linear system solvers in generalized eigenvalue problems

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speedup is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

DISTRIBUTED MEMORY MULTIPROCES↗

NASA NTRS1992

LAI inversion from optical reflectance using a neural network trained with a multiple scattering model

The inversion of the leaf area index (LAI) canopy parameter from optical spectral reflectance measurements is obtained using a backpropagation artificial neural network trained using input-output pairs generated by a multiple scattering reflectance model. The problem of LAI estimation over sparse canopies (LAI < 1.0) with varying soil reflectance backgrounds is particularly difficult. Standard multiple regression methods applied to canopies within a single homogeneous soil type yield good results but perform unacceptably when applied across soil boundaries, resulting in absolute percentage errors of >1000 percent for low LAI. Minimization methods applied to merit functions constructed from differences between measured reflectances and predicted reflectances using multiple-scattering models are unacceptably sensitive to a good initial guess for the desired parameter. In contrast, the neural network reported generally yields absolute percentage errors of <30 percent when weighting coefficients trained on one soil type were applied to predicted canopy reflectance at a different soil background.

Smith, James A.↗

NASA NTRS1993

Cancellation control law for lateral-directional dynamics of a supermaneuverable aircraft

Cancellation control laws are designed which reduce the high levels of lateral acceleration encountered during aggressive rolling maneuvers executed at high angle of attack. Two independent problem are examined. One is to reduce lateral acceleration at the mass center, while the other focuses on lateral acceleration at the pilot's station, located 7.0 m forward of the mass center. Both of these problems are challenging and somewhat different in their limitations. In each case the design is based on a linearization of the lateral-directional dynamics about a high angle of attack condition. The controllers incorporate dynamic inversion inner loops to provide control of stability-axis roll- and yaw-rates and then employ cancellation filters in both feed-forward and feed-back signal paths. The relative simplicity of the control laws should allow nonlinear generalizations to be devised. Although it is shown that lateral acceleration can be reduced substantially by such control laws, this is at the cost of slowed roll response, poor dutch-roll damping or a combination of the two.

Snell, Antony↗

NASA NTRS1980

Thermal structure of Jupiter's atmosphere obtained by inversion of Voyager 1 infrared measurements

Data from the Voyager 1 infrared spectroscopy investigation have been used to retrieve temperature profiles in the atmosphere of Jupiter. An analysis of information content indicates good vertical resolution with low measurement noise propagation in the Jovian troposphere and reduced resolution in the stratosphere. Among the problems found in common with the sounding of the terrestrial atmosphere are limited tropopause definition and dependence on upper boundary constraints. Preliminary results obtained by using a constrained linear algorithm and a filtered Chahine approach are presented.

Conrath, B. J.↗

NASA NTRS1980

Numerical study of baroclinic instability

The effect of a power law gravity field on baroclinic instability is examined with emphasis on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by electrostatic means. Growth rates of unstable normal modes were obtained as a function of parameters of the problem by solving a second order differential equation numerically. Results are compared with those from an earlier study where gravity was a constant. The conclusion is that, over the range of parameter space explored here, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as a parameter.

Geisler, J. E.↗

NASA NTRS1987

Improvements in the perturbation simulations of the global reference atmospheric model

The Global Reference Atmospheric Model (GRAM) program includes the capability for simulating pseudo-random perturbations in density, temperature, pressure, or wind components along a simulated reentry trajectory or other path through the atmosphere. Some concerns were expressed by GRAM users, however, that the mean-square perturbation gradients may be too large for small values of the vertical separation Delta z. The present GRAM perturbation simulations, based on a one-step autoregressive model, yield a power spectrum versus wavenumber k which is proportional to k sup -2 at high wavenumbers. This feature also produces mean-square perturbation differences which are directly proportional to Delta z, and mean-square perturbation gradients which are inversely proportional to Delta z. Thus, root-mean-square gradients, (Delta f/Delta z) sub rms, increase with decreasing Delta a as Delta z sup -1/2. A simple modification to GRAM is suggested which overcomes this problem, i.e., which produce root-mean-square gradient that remain bound as Delta z approaches zero. Possible applications of more sophisticated simulation approaches, e.g., second order autoregressive models, or fractal model techniques, were also explored briefly but found to yield improvements which appear too small to justify their considerable added complexity for use in the GRAM programs.

Justus, C. G.↗

NASA NTRS1956

On the Contribution of Turbulent Boundary Layers to the Noise Inside a Fuselage

The following report deals in preliminary fashion with the transmission through a fuselage of random noise generated on the fuselage skin by a turbulent boundary layer. The concept of attenuation is abandoned and instead the problem is formulated as a sequence of two linear couplings: the turbulent boundary layer fluctuations excite the fuselage skin in lateral vibrations and the skin vibrations induce sound inside the fuselage. The techniques used are those required to determine the response of linear systems to random forcing functions of several variables. A certain degree of idealization has been resorted to. Thus the boundary layer is assumed locally homogeneous, the fuselage skin is assumed flat, unlined and free from axial loads and the 'cabin' air is bounded only by the vibrating plate so that only outgoing waves are considered. Some of the details of the statistical description have been simplified in order to reveal the basic features of the problem. The results, strictly applicable only to the limiting case of thin boundary layers, show that the sound pressure intensity is proportional to the square of the free stream density, the square of cabin air density and inversely proportional to the first power of the damping constant and to the second power of the plate density. The dependence on free stream velocity and boundary layer thickness cannot be given in general without a detailed knowledge of the characteristics of the pressure fluctuations in the boundary layer (in particular the frequency spectrum). For a flat spectrum the noise intensity depends on the fifth power of the velocity and the first power of the boundary layer thickness. This suggests that boundary layer removal is probably not an economical means for decreasing cabin noise. In general, the analysis presented here only reduces the determination of cabin noise intensity to the measurement of the effect of any one of our variables (free stream velocity, boundary layer thickness, plate thickness or the characteristic velocity of propagation in the plate). The plate generates noise by vibrating in resonance over a wide range of frequencies and increasing the damping constant is consequently an effective method of decreasing noise generation. One of the main features of the results is that the relevant quantities upon which noise intensity depends are non-dimensional numbers in which boundary layer and plate properties enter as ratios. This is taken as an indication that in testing models of structures for boundary layer noise it is not sufficient to duplicate in the model the structural characteristics of the fuselage. One must match properly the characteristics of the exicitng pressure fluctuations to that of the structure.

Corcos, G. M.↗

NASA NTRS1980

Theoretical regime diagrams for thermally driven flows in a beta-plane channel in the presence of variable gravity

The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.

Geisler, J. E.↗