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NASA NTRS1989

Multiplier-continuation algorthms for constrained optimization

Several path following algorithms based on the combination of three smooth penalty functions, the quadratic penalty for equality constraints and the quadratic loss and log barrier for inequality constraints, their modern counterparts, augmented Lagrangian or multiplier methods, sequential quadratic programming, and predictor-corrector continuation are described. In the first phase of this methodology, one minimizes the unconstrained or linearly constrained penalty function or augmented Lagrangian. A homotopy path generated from the functions is then followed to optimality using efficient predictor-corrector continuation methods. The continuation steps are asymptotic to those taken by sequential quadratic programming which can be used in the final steps. Numerical test results show the method to be efficient, robust, and a competitive alternative to sequential quadratic programming.

Lundberg, Bruce N.↗

NASA NTRS1990

A compressed marine data set for geomagnetic field modeling

Some 13 million scalar magnetic field data points that have been collected from the world's ocean areas reside in the collection of the National Geophysical Data Center. In order to derive a suitable data set for modeling the geomagnetic field of the earth, each ship track is divided into 220 km segments. The distribution of the reduced data in position, time and local time is discussed. The along-track filtering process described has proved to be an effective method of condensing large numbers of shipborne magnetic data into a manageable and meaningful data set for field modeling. This process also provides the benefits of smoothing short-wavelength crystal anomalies, discarding data recorded during magnetically noisy periods, and assigning reasonable error estimates to be utilized in the least squares modeling.

Langel, R. A.↗

NASA NTRS2011

Analysis of the Radiative Transfer Equation with Highly Asymmetric Phase Function

This paper considers a scalar radiative transfer problem with high scattering anisotropy, Two computational methods are presented based on decomposition of the diffuse light field into a regular and anisotropic part. The first algorithm (DOMAS) singles out the anisotropic radiance in the forward scattering peak using the Small-Angle Modification of RTE. The second algorithm (DOM2+) separates the single scattering radiance as an anisotropic part, which largely defines the fine detail of the total radiance in the backscattering directions. In both cases, the anisotropic part is represented analytically. With anisotropy subtraction, the regular part of the signal. which requires a numerical solution, is essentially smoothed as a function of angles. Further, the transport equation is obtained for the regular part that contains an additional source function from the anisotropic part of the signal. This equation is solved with the discrete ordinates method. A conducted numerical analysis of this work showed that algorithm DOMAS has a strong advantage as compared to the standard discrete ordinates method for simulation of the radiance transmission, and DOM2 + is the best of the three for the reflection computations. Both algorithms offer at least a factor of three acceleration of convergence of the azimuthal series for highly anisotropic phase functions.

Korkin, Sergey V.↗

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

Brandt, A.↗

NASA NTRS1996

Space-Related Applications of Intelligent Control: Which Algorithm to Choose? (Theoretical Analysis of the Problem)

For a space mission to be successful it is vitally important to have a good control strategy. For example, with the Space Shuttle it is necessary to guarantee the success and smoothness of docking, the smoothness and fuel efficiency of trajectory control, etc. For an automated planetary mission it is important to control the spacecraft's trajectory, and after that, to control the planetary rover so that it would be operable for the longest possible period of time. In many complicated control situations, traditional methods of control theory are difficult or even impossible to apply. In general, in uncertain situations, where no routine methods are directly applicable, we must rely on the creativity and skill of the human operators. In order to simulate these experts, an intelligent control methodology must be developed. The research objectives of this project were: to analyze existing control techniques; to find out which of these techniques is the best with respect to the basic optimality criteria (stability, smoothness, robustness); and, if for some problems, none of the existing techniques is satisfactory, to design new, better intelligent control techniques.

Kreinovich, Vladik↗

NASA NTRS1974

Sticking probabilities for the adsorption of hydrogen on clean Ni/111/, Ni/100/, Ni sheet and evaporated Ni films

Determination of the sticking probability for hydrogen adsorption on clean Ni(111), Ni(100), polycrystalline nickel sheet, and polycrystalline evaporated nickel films, using a modification of the reflection detector technique of Horgan and King (1970) for metal films. The initial sticking probability for hydrogen adsorption on a nickel film at 300 K by the proposed method is found to be 0.25 in comparison to 0.35 for hydrogen adsorption on a nickel film using the reflection detector technique. Also, the sticking probabilities on smooth single-crystal (111) and (100) planes and polycrystalline sheets are found to be lower than those on the rougher polycrystalline nickel films.

Horgan, A. M.↗

NASA NTRS1984

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Roberts, G. O.↗

NASA NTRS1984

Applications of a conservative zonal scheme to transient and geometrically complex problems

A conservative zoning technique, wherein the flow field for a finite-difference calculation is divided into several regions to simplify grid generation, is discussed and is applied in the solution of a two-dimensional problem of complex topology. Calculations are performed on two zonal, or patched, grid systems for the supersonic flow over a double-airfoil configuration. The solution is smooth and continuous across the zonal interfaces, and shock waves pass through the boundaries without distortion. In addition, the time-accuracy of the zonal-boundary method is verified by a two-zone cyclinder calculation with a stationary inner and a rotating outer mesh.The feasibility of the zonal approach for use in the solution of geometrically complex and unsteady problems is thus demonstrated.

Hessenius, K. A.↗

NASA NTRS1985

Numerical simulation of a turbulent flame stabilized behind a rearward-facing step

Flow of combustible mixtures in a plane channel past a smooth contraction followed by an abrupt expansion, in a typical dump combustor configuration, is modeled by a two-dimensional numerical technique based on the random vortex method. Both the inert and the reacting case are considered. In the latter, the flame is treated as an interface, self-advancing at a prescribed normal burning speed, while the dynamic effects of expansion due to the exothermicity of combustion are expressed by volumetric source lines delineated by its front. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and the reattachment length. The stochastic turbulent velocity components manifest interesting differences, especially near the walls where three-dimensional effects of turbulence are expected to be of importance.

Hsiao, C. C.↗

NASA NTRS2006

Terrestrial Water Mass Load Changes from Gravity Recovery and Climate Experiment (GRACE)

Recent studies show that data from the Gravity Recovery and Climate Experiment (GRACE) is promising for basin- to global-scale water cycle research. This study provides varied assessments of errors associated with GRACE water storage estimates. Thirteen monthly GRACE gravity solutions from August 2002 to December 2004 are examined, along with synthesized GRACE gravity fields for the same period that incorporate simulated errors. The synthetic GRACE fields are calculated using numerical climate models and GRACE internal error estimates. We consider the influence of measurement noise, spatial leakage error, and atmospheric and ocean dealiasing (AOD) model error as the major contributors to the error budget. Leakage error arises from the limited range of GRACE spherical harmonics not corrupted by noise. AOD model error is due to imperfect correction for atmosphere and ocean mass redistribution applied during GRACE processing. Four methods of forming water storage estimates from GRACE spherical harmonics (four different basin filters) are applied to both GRACE and synthetic data. Two basin filters use Gaussian smoothing, and the other two are dynamic basin filters which use knowledge of geographical locations where water storage variations are expected. Global maps of measurement noise, leakage error, and AOD model errors are estimated for each basin filter. Dynamic basin filters yield the smallest errors and highest signal-to-noise ratio. Within 12 selected basins, GRACE and synthetic data show similar amplitudes of water storage change. Using 53 river basins, covering most of Earth's land surface excluding Antarctica and Greenland, we document how error changes with basin size, latitude, and shape. Leakage error is most affected by basin size and latitude, and AOD model error is most dependent on basin latitude.

Seo, K.-W.↗

NASA NTRS2014

Smooth Pursuit of Flicker-Defined Motion

We examined the pursuit response to stimuli defined by space-variant flicker of a dense random dot carrier pattern. On each frame, every element of the pattern could change polarity, with a probability given by a two-dimensional Gaussian distribution. A normal distribution produces a circular region of twinkle, while inverting the distribution results in a spot of static texture in a twinkling surround. In this latter case, the carrier texture could be stationary, or could move with the twinkle modulator,thereby producing first-order motion in the region of the spot. While the twinkle-defined spot produces a strong sensation of motion, the complementary stimulus defined by the absence of twinkle does not;when viewed peripherally, it appears to move in steps even when the generating distribution moves smoothly. We examined pursuit responses to these stimuli using two techniques: 1) the eye movement correlogram, obtained by cross-correlating eye velocity with the velocity of a randomly-moving stimulus; and 2) delayed visual feedback, where transient stabilization of a target can produce spontaneous oscillations of the eye, with a period empirically observed to vary linearly with the applied delay. Both techniques provide an estimate of the internal processing time, which can be as short as100 milliseconds for a first-order target. Assessed by the correlogram method, the response to flicker defined motion is delayed by more than 100 milliseconds, and significantly weaker (especially in the vertical dimension). When initially presented in the delayed feedback condition, purely saccadic oscillation is observed. One subject eventually developed smooth oscillations (albeit with significant saccadic intrusions), showing a period-versus-delay slope similar to that observed for first-order targets. This result is somewhat surprising, given that we interpret the slope of the period-versus-delayfunction as reflecting the balance between position- and velocity-sensitive inputs to pursuit.

smooth pursuit↗

NASA NTRS1975

Surface fitting three-dimensional bodies

The geometry of general three-dimensional bodies was generated from coordinates of points in several cross sections. Since these points may not be on smooth curves, they are divided into groups forming segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction through longitudinal curves. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines or specifying slopes at selected points. This method was used to surface fit a 70 deg slab delta wing and the HL-10 Lifting Body. The results for the delta wing were very close to the exact geometry. Although there is no exact solution for the lifting body, the surface fit generated a smooth surface with cross-sectional planes very close to prescribed coordinate points.

Dejarnette, F. R.↗

NASA NTRS2014

Smooth Pursuit of Flicker-Defined Motion

We examined the pursuit response to stimuli defined by space-variant flicker of a dense random dot carrier pattern. On each frame, every element of the pattern could change polarity, with a probability given by a two-dimensional Gaussian distribution. A normal distribution produces a circular region of twinkle, while inverting the distribution results in a spot of static texture in a twinkling surround. In this latter case, the carrier texture could be stationary, or could move with the twinkle modulator, thereby producing first-order motion in the region of the spot. While the twinkle-defined spot produces a strong sensation of motion, the complementary stimulus defined by the absence of twinkle does not, when viewed peripherally, it appears to move in steps even when the generating distribution moves smoothly. We examined pursuit responses to these stimuli using two techniques: 1) the eye movement correlogram, obtained by cross-correlating eye velocity with the velocity of a randomly-moving stimulus; and 2) delayed visual feedback, where transient stabilization of a target can produce spontaneous oscillations of the eye, with a period empirically observed to vary linearly with the applied delay. Both techniques provide an estimate of the internal processing time, which can be as short as 100 milliseconds for a first-order target. Assessed by the correlogram method, the response to flicker-defined motion is delayed by more than 100 milliseconds, and significantly weaker (especially in the vertical dimension). When initially presented in the delayed feedback condition, purely saccadic oscillation is observed. One subject eventually developed smooth oscillations (albeit with significant saccadic intrusions), showing a period-versus-delay slope similar to that observed for first-order targets. This result is somewhat surprising, given that we interpret the slope of the period-versus-delay-function as reflecting the balance between position- and velocity-sensitive inputs to pursuit.

eye movements↗

NASA NTRS1978

Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions

A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations.

Rubin, S. G.↗

NASA NTRS1980

Geometric methods in computational fluid dynamics

General methods for the construction of geometric computational fluid dynamic algorithms are presented which simulate a variety of flow fields in various nontrivial regions. Included are: basic developments with tensors; various forms for the equations of motion; generalized numerical methods and boundary conditions; and methods for mesh generation to meet the strong geometric constraints of turbomachines. Coordinate generation is shown generally to yield mesh descriptions from one or more transformations that are smoothly joined together to form a composite mesh.

Eiseman, P. R.↗

NASA NTRS1981

Optimum structural design with plate bending elements - A survey

A survey is presented of recently published papers in the field of optimum structural design of plates, largely with respect to the minimum-weight design of plates subject to such constraints as fundamental frequency maximization. It is shown that, due to the availability of powerful computers, the trend in optimum plate design is away from methods tailored to specific geometry and loads and toward methods that can be easily programmed for any kind of plate, such as finite element methods. A corresponding shift is seen in optimization from variational techniques to numerical optimization algorithms. Among the topics covered are fully stressed design and optimality criteria, mathematical programming, smooth and ribbed designs, design against plastic collapse, buckling constraints, and vibration constraints.

Haftka, R. T.↗

NASA NTRS1982

High spatial resolution Mg/Al maps of the western Crisium and Sulpicius Gallus regions

High spatial resolution Mg/Al ratio maps of the western Crisium and Sulpicius Gallus regions of the moon are presented. The data is from the X-ray fluorescence experiment and the image enhancement technique in the Laplacian subtraction method using a special least-squares version of the Laplacian to reduce noise amplification. In the highlands region west of Mare Crisium several relatively small patches of smooth material have high local Mg/Al ratio similar to values found in mare sites, suggesting volcanism in the highlands. In the same highland region there were other smooth areas with no high Mg/Al local values and they are probably Cayley Formation material produced by impact mass wasting. The Sulpicius Gallus region has variable Mg/Al ratios. In this region there are several high Mg/Al ratio spots, two of which occur at the highland-mare interface. Another high Mg/Al ratio area corresponds to the Sulpicius Gallus Rima I region. The high Mg/Al ratio material in the Sulpicius Gallus region is probably pyroclastic.

Schonfeld, E.↗