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NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 1: Formulation

The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.

Schuler, James J.↗

NASA NTRS1996

Correction of WindScat Scatterometric Measurements by Combining with AMSR Radiometric Data

The Seawinds scatterometer on the advanced Earth observing satellite-2 (ADEOS-2) will determine surface wind vectors by measuring the radar cross section. Multiple measurements will be made at different points in a wind-vector cell. When dense clouds and rain are present, the signal will be attenuated, thereby giving erroneous results for the wind. This report describes algorithms to use with the advanced mechanically scanned radiometer (AMSR) scanning radiometer on ADEOS-2 to correct for the attenuation. One can determine attenuation from a radiometer measurement based on the excess brightness temperature measured. This is the difference between the total measured brightness temperature and the contribution from surface emission. A major problem that the algorithm must address is determining the surface contribution. Two basic approaches were developed for this, one using the scattering coefficient measured along with the brightness temperature, and the other using the brightness temperature alone. For both methods, best results will occur if the wind from the preceding wind-vector cell can be used as an input to the algorithm. In the method based on the scattering coefficient, we need the wind direction from the preceding cell. In the method using brightness temperature alone, we need the wind speed from the preceding cell. If neither is available, the algorithm can work, but the corrections will be less accurate. Both correction methods require iterative solutions. Simulations show that the algorithms make significant improvements in the measured scattering coefficient and thus is the retrieved wind vector. For stratiform rains, the errors without correction can be quite large, so the correction makes a major improvement. For systems of separated convective cells, the initial error is smaller and the correction, although about the same percentage, has a smaller effect.

Song, S.↗

NASA NTRS1998

Analysis of Physical Properties of Dust Suspended in the Mars Atmosphere

Methods for iteratively determining the infrared optical constants for dust suspended in the Mars atmosphere are described. High quality spectra for wavenumbers from 200 to 2000 1/cm were obtained over a wide range of view angles by the Mariner 9 spacecraft, when it observed a global Martian dust storm in 1971-2. In this research, theoretical spectra of the emergent intensity from Martian dust clouds are generated using a 2-stream source-function radiative transfer code. The code computes the radiation field in a plane-parallel, vertically homogeneous, multiply scattering atmosphere. Calculated intensity spectra are compared with the actual spacecraft data to iteratively retrieve the optical properties and opacity of the dust, as well as the surface temperature of Mars at the time and location of each measurement. Many different particle size distributions a-re investigated to determine the best fit to the data. The particles are assumed spherical and the temperature profile was obtained from the CO2 band shape. Given a reasonable initial guess for the indices of refraction, the searches converge in a well-behaved fashion, producing a fit with error of less than 1.2 K (rms) to the observed brightness spectra. The particle size distribution corresponding to the best fit was a lognormal distribution with a mean particle radius, r(sub m) 0.66 pm, and variance, omega(sup 2) = 0.412 (r(sub eff) = 1.85 microns, v(sub eff) =.51), in close agreement with the size distribution found to be the best fit in the visible wavelengths in recent studies. The optical properties and the associated single scattering properties are shown to be a significant improvement over those used in existing models by demonstrating the effects of the new properties both on heating rates of the Mars atmosphere and in example spectral retrieval of surface characteristics from emission spectra.

Snook, Kelly↗

NASA NTRS1999

NPARC v3.1 User's Guide: A Companion to the NPARC v3.0 User's Guide

NPARC v3.1 is a modification to the NPARC v3.0 computer program which expands the capabilities for time-accurate computations through the use of a Newton iterative implicit method, time-varying boundary conditions, and planar dynamic grids. This document discusses some of the changes from the NPARC v3.0, specifically: changes to the directory structure and execution, changes to the input format. background on new methods, new boundary conditions. dynamic grids, new options for output, usage concepts, and some test cases to serve as tutorials. This document is intended to be used in conjunction with the NPARC v3.0 user's guide.

Chung, Joongkee↗

NASA NTRS2000

Simulation of Aluminum Micro-mirrors for Space Applications at Cryogenic Temperatures

Closed form and finite element models are developed to predict the device response of aluminum electrostatic torsion micro-mirrors fabricated on silicon substrate for space applications at operating temperatures of 30K. Initially, closed form expressions for electrostatic pressure arid mechanical restoring torque are used to predict the pull-in and release voltages at room temperature. Subsequently, a detailed mechanical finite element model is developed to predict stresses and vertical beam deflection induced by the electrostatic and thermal loads. An incremental and iterative solution method is used in conjunction with the nonlinear finite element model and closed form electrostatic equations to solve. the coupled electro-thermo-mechanical problem. The simulation results are compared with experimental measurements at room temperature of fabricated micro-mirror devices.

Kuhn, J. L.↗

NASA NTRS2014

Automated Testcase Generation for Numerical Support Functions in Embedded Systems

We present a tool for the automatic generation of test stimuli for small numerical support functions, e.g., code for trigonometric functions, quaternions, filters, or table lookup. Our tool is based on KLEE to produce a set of test stimuli for full path coverage. We use a method of iterative deepening over abstractions to deal with floating-point values. During actual testing the stimuli exercise the code against a reference implementation. We illustrate our approach with results of experiments with low-level trigonometric functions, interpolation routines, and mathematical support functions from an open source UAS autopilot.

Metrics↗

NASA NTRS2013

The Force-Free Magnetosphere of a Rotating Black Hole

We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner "light surface" located inside the ergosphere and the outer "light surface" which is the generalization of the pulsar light cylinder.We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both "light surfaces."

Contopoulos, Ioannis↗

NASA NTRS2019

Modeling transmittance of MODIS solar diffuser stability monitor sun view screen

Earlier work by Sun et al. [2005] modeled the Sun view screen transmittance of the solar diffuser stability monitor (SDSM) on Moderate Resolution Imaging Spectroradiometer (MODIS) which explains the oscillatory pattern in the Terra/Aqua MODIS SDSM Sun view response collected during the post-launch yaw maneuvers. The SDSM screen consists of small size pinholes which limit the screen transmittance. The SDSM Sun view transmittance pattern is affected by the size and distribution of pinholes, screen thickness, and orientation between the aperture stop and the Sun view screen. Planning of post-launch yaw maneuver test often requires comprehensive angular coverage to resolve the angular variation of the screen transmittance. This paper developed a Gauss-Kronrod quadrature method-based model to simulate the SDSM Sun view transmittance. This method performs iterative integration of the interception area between pinhole and aperture stop which is critical in the screen transmittance calculation. Parametric dependences of the MODIS SDSM Sun view transmittance on various geometric factors such as the pinhole size or spacing and misalignment between the SDSM Sun view screen and aperture stop are studied. The implications for the post-launch yaw maneuver planning to resolve the angular variation of the SDSM Sun view transmittance due to the SDSM Sun view screen misalignment are discussed.

MODIS↗

NASA NTRS2021

Thermal Inspection of a Composite Fuselage Section Using theMethod of Proper Generalized Decomposition

Proper Generalized Decomposition (PGD) is a reduced order modeling technique for the simulation of physical systems whose governing equations depend on boundary conditions, initial conditions, material properties, and geometric parameters. It uses separated representations of system covariates combined with an iterative approximation method known as successive enrichment in order to compute an accurate parameter-dependent approximation to the full governing equations. PGD can also be used as an alternative to the Singular Value Decomposition (SVD) of a matrix and therefore as an alternative to PCA thermography. In this paper PGD was used to analyze data derived from the inspection of a composite fuselage forward section using flash thermography, and the results were compared against the standard PCA approach.

Nondestructive Evaluation↗

NASA NTRS2022

Statistical Distribution of Gear Surface Fatigue Lives at High Reliability

The reliability of gears is important for a wide variety of applications, and the gearing community has a desire for better prediction of fatigue life at very high reliability. To improve predictions, a set of 950 NASA-conducted gear surface fatigue test results were gathered, pooled together using the general standardized Weibull variate, and then fit to a Weibull three-parameter distribution. An iterative fitting method was developed and then applied to the gear fatigue data to determine the values of the distribution parameters. Additional analyses were done using bearing and gear data that demonstrate a trend of increasing minimum life coefficient as correlated to the timeframe of the fatigue testing, and material cleanliness is proposed as a primary explanation for such correlation. It is noted that this observed trend supports published findings from analytical modeling and experimental studies that improvements to material cleanliness improves minimum fatigue life. Further use and study of the three-parameter Weibull distribution is recommended as a tool to quantify fatigue life most accurately in the high reliability regime.

gear↗

NASA NTRS1986

Simultaneous iterations algorithm for general eigenvalue problems on parallel processors

The method of simultaneous iteration with shift is extended to extraction of m-eigenpairs of a general eigenvalue problem of large order n in a parallel processing environment. The algorithm combines the power method and the Jacobi technique, and reduces to performing four basic operations. Parallel implementation of the algorithm is discussed in detail. The analysis accounts for computation and communication costs, and utilizes a parallel processing architecture of the ensemble type. Expressions for the computational efficiency and speedup are defined as a function of the problem and hardware parameters. Selected representative problems exhibit efficiencies ranging from 60 to 98 percent.

Utku, S.↗

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 NTRS1987

Development of generalized block correction procedures for the solution of discretized Navier-Stokes equations

Effort is directed towards developing a solution method which combines advantages of both the iterative and the direct methods. It involves iterative solution on the fine grid, convergence of which is enhanced by a direct solution for correction quantities on a coarse grid. The proposed block correction procedure was applied to compute recirculating flow in a driven cavity.

Kelkar, Kanchan M.↗

NASA NTRS1998

Progressive content-based retrieval of image and video with adaptive and iterative refinement

A method and apparatus for minimizing the time required to obtain results for a content based query in a data base. More specifically, with this invention, the data base is partitioned into a plurality of groups. Then, a schedule or sequence of groups is assigned to each of the operations of the query, where the schedule represents the order in which an operation of the query will be applied to the groups in the schedule. Each schedule is arranged so that each application of the operation operates on the group which will yield intermediate results that are closest to final results.

Li, Chung-Sheng↗

NASA NTRS1997

Computational Issues in Damping Identification for Large Scale Problems

Two damping identification methods are tested for efficiency in large-scale applications. One is an iterative routine, and the other a least squares method. Numerical simulations have been performed on multiple degree-of-freedom models to test the effectiveness of the algorithm and the usefulness of parallel computation for the problems. High Performance Fortran is used to parallelize the algorithm. Tests were performed using the IBM-SP2 at NASA Ames Research Center. The least squares method tested incurs high communication costs, which reduces the benefit of high performance computing. This method's memory requirement grows at a very rapid rate meaning that larger problems can quickly exceed available computer memory. The iterative method's memory requirement grows at a much slower pace and is able to handle problems with 500+ degrees of freedom on a single processor. This method benefits from parallelization, and significant speedup can he seen for problems of 100+ degrees-of-freedom.

Pilkey, Deborah L.↗

NASA NTRS1978

Finite elements and finite differences for transonic flow calculations

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Hafez, M. M.↗

NASA NTRS1993

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Taylor, Arthur C., III↗

NASA NTRS2021

Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

The unstructured, mixed-element, cell-centered, finite-volume flow solver USM3D is enhanced with new capabilities such as line generation for general unstructured grids and optimization of the iterative solver. The efficiency of the new developments is assessed in a massively parallel environment. The assessments are conducted using a baseline method and the recent hierarchical adaptive nonlinear iteration method framework. Three benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere cylinder configuration, a transonic flow around the ONERA M6 wing, and a supersonic flow through a square duct are considered.

Mohagna J Pandya↗