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At least 1,045 records · Page 58
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

The Discontinuous Galerkin Finite Element Method

The purpose of this report is to present details of the Discontinuous Galerkin (DG) Finite Element Method (DG FEM). First the weighted-residual (WR) form is introduced and then the Galerkin Finite Element (FE) (GFE) and the Petrov-Galerkin FE (PG FE) methods are discussed. The details of the implementation of the DG FEM are presented along with two examples, 2nd order and 4th order differential equations, and the performance of the method is discussed.

Finite element↗
NASA NTRS1969

Root-cubing and general root-powering methods for finding the zeros of polynomials

Mathematical analysis technique generalizes a root squaring and root cubing method into a general root powering method. The introduction of partitioned polynomials into this general root powering method simplifies the coding of the polynomial transformations into input data suitable for processing by computer. The method includes analytic functions.

Bareiss, E. H.↗
NASA NTRS1970

Methods for measuring the loudness and noisiness of complex sounds

Physical and temporal aspects of sound which influence the rating of subjective noisiness are intensity, spectrum shape and bandwidth, spectral complexity, and duration. Objective rating methods include a graphic method, full octave and one-third octave methods, and methods that measure one value over all frequencies.

Kryter, K.↗
NASA NTRS1971

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Gatewood, B. E.↗
NASA NTRS1971

On the method of Ermakov and Zolotukhin for multiple integration

The method of Ermakov and Zolotukhin is discussed along with its later developments. By introducing the idea of pseudo-implementation a practical assessment of the method is made. The performance of the method is found to be unimpressive in comparison with a recent regression method.

Cranley, R.↗
NASA NTRS1971

The overlap methods

The different methods of reducing measurements on photographic plates by the overlap methods are compared. An attempt is made to distinguish the methods accepted by most astronomers from those not generally agreed upon and from those that are still being studied. Questions examined are: organization of future works, improvement of AGK2 and AGK3, and solutions for the astrographic catalog, as well as considerations of some empirical methods.

Lacroute, P.↗
NASA NTRS1971

Nonplanar Method for Predicting Incompressible Aerodynamic Coefficients of Rectangular Wings with Circular-Arc Camber

The development of a nonplanar lifting surface method having a continuous distribution of singularities and satisfying the tangent flow boundary condition on the mean camber surface is given. The method predicts some incompressible longitudinal aerodynamic coefficients of rectangular wings which have circular-arc camber. The solution method is of the integral-equation type and the resulting surface integrals are evaluated by either using numerical or analytical techniques, as are appropriate. Applications are made and the results compared with those from an exact two-dimensional circular-arc camber solution, a three-dimensional flat-wing solution which represents the camber by a projected slope onto the flat surface, and a flat-wing experiment. From these comparisons, the present method is found to predict well the flat-wing experiment and limiting values, in addition to the center of pressure variation at an angle of attack of zero for any camber. For wings having camber ratios larger than about 1.25% and moderate to high aspect ratios, the results deterioriate due to the inadequacy of lifting pressure modes employed.

Lamar, J. E.↗
NASA NTRS1972

A new method for in situ electron temperature determinations from plasma wave phenomena

A discrepancy has been reported between the values of the electron temperature t sub e deduced from satellite electrostatic probe measurements and ground based radar backscatter measurements. This discrepancy (radar backscatter temperature less than the probe temperature) is not present when the probe experiment is flown on a rocket to lower altitudes but reappears when the rocket probe attains higher altitudes. There is a need for an independent radio wave method for making in-situ t sub e measurements in order to help resolve this problem. A new method of determining t sub e from the satellite resonant phenomena is presented. It is based on the splitting (observed at high latitudes) of the diffuse resonance which occurs at the frequency f sub d1 between f sub h and 2 f sub h. The advantage of this method over the other methods involving ionospheric resonances is the simplicity of the required calculations. There is, however, the limitation of plasma conditions where the f sub d1 resonance can be observed and the limitation to mid-to-high latitudes where the splitting is observed.

Oya, H.↗
NASA NTRS1972

The methods of paired comparisons and magnitude estimation in judging the noisiness of aircraft

The point of subjective equality in regard to perceived noisiness for each of 14 pairs of aircraft noises was obtained using both magnitude estimation technique and the method of paired comparisons. Both methods gave approximately the same estimates of the points of subjective equality for the noise pairs, and both showed similar correspondence to predictive physical measures. Nevertheless, the two methods appear to have greater face validity to the listeners. However, the magnitude estimation technique appears to be more efficient; for a given level of reliability it requires approximately 50% of the testing time required by the paired comparison method. The functions relating physical intensity to the estimated magnitude of subjective noisiness had slopes ranging from about .61 to .29 for the aircraft noises employed in this study, indicating a required change of about 5 to 10 db for a doubling in subjective magnitude. Some physical units of noise measurement were found to be very predictive (standard errors of estimate as low as 1.9 db) of the subjective judgements of noisiness.

Clarke, F. R.↗
NASA NTRS1972

Experimental methods for geological remote sensing

During the past year a two channel IR technique for discrimination among silicate rocks was tested for a second time, a three channel IR method was tested for the first time, and a new visible-reflective IR ratio method was hypothesized and qualitatively tested for iron oxide recognition. Both the two channel and three channel IR ratios methods were capable of discriminating felsic from mafic rock types. The three-channel ratio values measured by the scanner were found to agree, within reasonable limits, with the values of R calculated from laboratory data. The capability of the three channel method to obtain absolute ratios is accompanied by a costly processing routine. The two channel technique is superior for low thermal contrast scenes about which some ground truth is available because of its speed and economy.

Vincent, R. K.↗
NASA NTRS1972

Comparison of genetic algorithms with conjugate gradient methods

Genetic algorithms for mathematical function optimization are modeled on search strategies employed in natural adaptation. Comparisons of genetic algorithms with conjugate gradient methods, which were made on an IBM 1800 digital computer, show that genetic algorithms display superior performance over gradient methods for functions which are poorly behaved mathematically, for multimodal functions, and for functions obscured by additive random noise. Genetic methods offer performance comparable to gradient methods for many of the standard functions.

Bosworth, J. L.↗
NASA NTRS1972

An engineering optimization method with application to STOL-aircraft approach and landing trajectories

An optimization method has been developed that computes the optimal open loop inputs for a dynamical system by observing only its output. The method reduces to static optimization by expressing the inputs as series of functions with parameters to be optimized. Since the method is not concerned with the details of the dynamical system to be optimized, it works for both linear and nonlinear systems. The method and the application to optimizing longitudinal landing paths for a STOL aircraft with an augmented wing are discussed. Noise, fuel, time, and path deviation minimizations are considered with and without angle of attack, acceleration excursion, flight path, endpoint, and other constraints.

Jacob, H. G.↗
NASA NTRS1972

Some efficient methods for obtaining infinite series solutions of n-th order linear ordinary differential equations

The use of the theta-operator method and generalized hypergeometric functions in obtaining solutions to nth-order linear ordinary differential equations is explained. For completeness, the analysis of the differential equation to determine whether the point of expansion is an ordinary point or a regular singular point is included. The superiority of the two methods shown over the standard method is demonstrated by using all three of the methods to work out several examples. Also included is a compendium of formulae and properties of the theta operator and generalized hypergeometric functions which is complete enough to make the report self-contained.

Allen, G.↗
NASA NTRS1972

Two new landmark navigation methods.

Two new methods for navigation on the land are reported. Both methods make use of landmarks which are in sight but whose positions are not known. Only angle measurements are needed. Although the methods were intended for guiding a Lunar Roving Vehicle as it travels on the lunar surface, they may also find applications on other planets as well as on earth. Besides the mathematical details, two examples are also included to demonstrate the correctness of the method.

Hung, J. C.↗
NASA NTRS1972

A method for calculating laminar viscous, compressible flows with small pressure gradients

A method is presented for calculating laminar viscous, compressible flows in which pressure gradients are assumed to be neglibible in energy conservation and in developing property relations, but not in momentum conservation. The equations are developed from Navier-Stokes equations in a noninertial reference frame. The method is an extension of an approximate method developed for calculating combined forced and contained natural convection in a rotating tank. The restriction to small density and temperature variations in the previous method is removed. For illustration, a two-dimensional simulation of the rotating tank problem is formulated, and the numerical computation procedure to be used is indicated.

Martin, E. D.↗
NASA NTRS1972

Statistical versus nonstatistical temperature inversion methods

Vertical temperature profiles are derived from radiation measurements by inverting the integral equation of radiative transfer. Because of the nonuniqueness of the solution, the particular temperature profile obtained depends on the numerical inversion technique used and the type of auxiliary information incorporated in the solution. The choice of an inversion algorithm depends on many factors; including the speed and size of computer, the availability of representative statistics, and the accuracy of initial data. Results are presented for a numerical study comparing two contrasting inversion methods: the statistical-matrix inversion method and the nonstatistical-iterative method. These were found to be the most applicable to the problem of determining atmospheric temperature profiles. Tradeoffs between the two methods are discussed.

Smith, W. L.↗
NASA NTRS1972

Davidon-Broyden rank-one minimization methods in Hilbert space with application to optimal control problems

The Davidon-Broyden class of rank one, quasi-Newton minimization methods is extended from Euclidean spaces to infinite-dimensional, real Hilbert spaces. For several techniques of choosing the step size, conditions are found which assure convergence of the associated iterates to the location of the minimum of a positive definite quadratic functional. For those techniques, convergence is achieved without the problem of the computation of a one-dimensional minimum at each iteration. The application of this class of minimization methods for the direct computation of the solution of an optimal control problem is outlined. The performance of various members of the class are compared by solving a sample optimal control problem. Finally, the sample problem is solved by other known gradient methods, and the results are compared with those obtained with the rank one quasi-Newton methods.

Straeter, T. A.↗