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At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Stability of matrix equations arising in electromagnetics

Many problems in electromagnetics can be formulated as a Fredholm equation of the first kind. In these problems it is desired to determine some function f(x) from its integral transform g(y). Except for special cases for which an explicit inverse operator is known, the equation is usually discretized by the method of moments into a matrix equation Af = g, which is then solved on a computer. A method of calculating the sensitivity of the solution of Af = g due to errors in either the vector g or the matrix A is developed. The usefulness of this method is demonstrated with problems from antenna theory, scattering theory, and remote sensing.

Klein, C.↗
NASA NTRS1982

A general algorithm for solving the algebraic Riccati equation

The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.

Walker, R. A.↗
NASA NTRS1987

On determining important aspects of mathematical models: Application to problems in physics and chemistry

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Rabitz, Herschel↗
NASA NTRS1993

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Fijany, Amir↗
NASA NTRS1976

On a numerical solution of the supersonic panel flutter eigenproblem

An automated digital computer procedure is presented in this paper which enables efficient solution of the eigenvalue problem associated with the supersonic panel flutter phenomena. The step-by-step incremental solution procedure is based on an inverse iteration technique which effectively utilizes solution results from the previous step in determining such results during the current solution step. Also, the computations are limited to the determination of a few specific roots only, which are expected to contain the flutter mode, and this is achieved at each step without having to compute any other root. The structural discretization achieved by the finite-element method yields highly banded stiffness, mass, and aerodynamic matrices; the aerodynamic matrix evaluated by the linearized piston theory is real but unsymmetric in nature. The solution algorithm presented in this paper fully exploits the banded form of the associated matrices, and the resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most efficient and economical when compared to existing procedures of such analysis. Numerical results are presented for a two-dimensional panel flutter problem.

Gupta, K. K.↗
NASA NTRS1985

Iterative methods for mixed finite element equations

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Nakazawa, S.↗
DOE OSTI2026

Possible paths for the production of 73 As

Inelastic scattering reactions including (n,2n) are particularly difficult to measure. Hardly any measurements on radioactive nuclei exist. The reason is that traditional methods require the detection of gammas or neutrons in a background of elastically scattered neutrons, which can interact with the detector or other materials. The 73 As(n,2n) and the 73 As(n,2n) reaction cross sections are the only neutron removal cross sections that can be measured with current methods. The corresponding cross sections for the short-lived isotopes 71,72,74 As can only be directly measured in inverse kinematics. Since 75 As is the only stable isotope of this element, the sample production is no problem at all. This report is therefore focused on the sample production for a possible 73 As(n,2n) campaign.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1972

Numerical method for the solution of large systems of differential equations of the boundary layer type

A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

Green, M. J.↗
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 NTRS1984

Another Look at the Optimum Frequencies for a Water Vapor Radiometer

A water vapor radiometer is used to estimate the columnar content of atmospheric water vapor or equivalently the line-of-sight path delay due to water vapor. Two measurement channels are used in order to separate the effects of the liquid and vapor phases of water. The efficiency of the path delay or columnar vapor estimate is dependent on the choice of on-line frequency channel. Previous analysis of this problem has suggested frequencies from 20.3 to 21 GHz. The frequency that yields the minimum error in the inversion algorithm is shown here to be both site and season dependent. Hence, the concept of an optimum frequency must represent an averaging process over the entire range of meteorological conditions that is expected. For a range of sites and condition representing a cross section of the continental United States the optimum on-line frequency seems to be 20.6 GHz.

Resch, G. M.↗
NASA NTRS1989

Development of direct-inverse 3-D methods for applied transonic aerodynamic wing design and analysis

Progress in the direct-inverse wing design method in curvilinear coordinates has been made. This includes the remedying of a spanwise oscillation problem and the assessment of grid skewness, viscous interaction, and the initial airfoil section on the final design. It was found that, in response to the spanwise oscillation problem that designing at every other spanwise station produced the best results for the cases presented, a smoothly varying grid is especially needed for the accurate design at the wing tip, the boundary layer displacement thicknesses must be included in a successful wing design, the design of high and medium aspect ratio wings is possible with this code, and the final airfoil section designed is fairly independent of the initial section.

Carlson, Leland A.↗
NASA NTRS1989

Shape control of high degree-of-freedom variable geometry trusses

Common static trusses are constrained to permit no relative motion between truss elements. A Variable Geometry Truss (VGT), however, is a truss which contains some number of variable length links. The extensible links allow the truss to change shape in a precise, controllable manner. These changes can also be used to control the vibrational response of a truss structure or to perform robotic tasks. Many geometric configurations, both planar and spatial, are possible candidates for VGT manipulators. Here, only two geometries are discussed; the three degree-of-freedom (DOF) spatial octahedral/octahedral truss and the three DOF planar tetrahedral truss. These truss geometries are used as the fundamental element in a repeating chain of trusses. This results in a highly dexterous manipulator with perhaps 30 to 60 degrees of freedom that retains the favorable stiffness properties of a conventional truss. From a fixed base, this type of manipulator could perform shape or vibration control while extending and snaking through complex passageways or moving around obstacles to perform robotic tasks. The approach taken here is to first concentrate on fully understanding the forward and inverse kinematics of the fundamental elements and then utilizing the insight thus gained to solve the more complex problem of the kinematic chains.

Salerno, R. J.↗
NASA NTRS1989

Color and population gradients in globular cluster cores

New observational results on color and population gradients in the cores of several highly concentrated globular clusters are reported. The gradients are in the sense of blueing toward the cluster center, and appear to be caused mostly or entirely by population gradients in the number of blue horizontal branch and red giant branch stars. Taken at face value, such gradients would imply an inverse mass segregation, but this interpretation is not fully secure. In any case, their dynamical understanding remains a problem.

Djorgovski, S.↗
NASA NTRS1990

Optimal impulsive time-fixed orbital rendezvous and interception with path constraints

Minimum-fuel, impulsive, time-fixed solutions are obtained for the problem of orbital rendezvous and interception with interior path constraints. Transfers between coplanar circular orbits in an inverse-square gravitational field are considered, subject to a circular path constraint representing a minimum or maximum permissible orbital radius. Primer vector theory is extended to incorporate path constraints. The optimal number of impulses, their times and positions, and the presence of initial or final coasting arcs are determined. The existence of constraint boundary arcs and boundary points is investigated as well as the optimality of a class of singular arc solutions. To illustrate the complexities introduced by path constraints, an analysis is made of optimal rendezvous in field-free space subject to a minimum radius constraint.

Taur, D.-R.↗
NASA NTRS2011

Improving the Automatic Inversion of Digital ISIS-2 Ionogram Reflection Traces into Topside Vertical Electron-Density Profiles

The topside-sounders on the four satellites of the International Satellites for Ionospheric Studies (ISIS) program were designed as analog systems. The resulting ionograms were displayed on 35-mm film for analysis by visual inspection. Each of these satellites, launched between 1962 and 1971, produced data for 10 to 20 years. A number of the original telemetry tapes from this large data set have been converted directly into digital records. Software, known as the TOPside Ionogram Scalar with True-height (TOPIST) algorithm has been produced that enables the automatic inversion of ISIS-2 ionogram reflection traces into topside vertical electron-density profiles Ne(h). More than million digital Alouette/ISIS topside ionograms have been produced and over 300,000 are from ISIS 2. Many of these ISIS-2 ionograms correspond to a passive mode of operation for the detection of natural radio emissions and thus do not contain ionospheric reflection traces. TOPIST, however, is not able to produce Ne(h) profiles from all of the ISIS-2 ionograms with reflection traces because some of them did not contain frequency information. This information was missing due to difficulties encountered during the analog-to-digital conversion process in the detection of the ionogram frame-sync pulse and/or the frequency markers. Of the many digital topside ionograms that TOPIST was able to process, over 200 were found where direct comparisons could be made with Ne(h) profiles that were produced by manual scaling in the early days of the ISIS program. While many of these comparisons indicated excellent agreement (<10% average difference over the entire profile) there were also many cases with large differences (more than a factor of two). Here we will report on two approaches to improve the automatic inversion process: (1) improve the quality of the digital ionogram database by remedying the missing frequency-information problem when possible, and (2) using the above-mentioned comparisons as teaching examples of how to improve the original TOPIST software.

Benson, R. F.↗
NASA NTRS2004

A Meshless Method Using Radial Basis Functions for Beam Bending Problems

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions (RBFs) as trial functions in the study of Euler-Bernoulli beam problems is presented. RBFs, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as they are in the conventional MLPG method. Compactly and noncompactly supported RBFs are considered. Noncompactly supported cubic RBFs are found to be preferable. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. Results obtained from the radial basis MLPG method are either of comparable or better accuracy than those obtained when using the conventional MLPG method.

Raju, I. S.↗
NASA NTRS1974

Development of inverse inviscid transonic solution methods

A numerical method suitable for the analysis and/or design of supercritical transonic airfoils is reported. In order to achieve accuracy, the method utilizes the full inviscid potential flow equations; and in order to remain simple it solves the problem in a stretched Cartesian grid system. The resulting computer program has several advantages over others of its type -- its use in either the direct analysis mode in which the airfoil shape is prescribed and the flow field and surface pressures are determined, or in the inverse mode in which the surface pressures are given and the airfoil shape and flow field are computed. Other advantages of the program include its use in a design program, the rotated finite difference scheme and its determination of the airfoil shape simultaneously with the flow field relaxation solution.

Carlson, L. A.↗
NASA NTRSDate not supplied

Validation of Machine Learning Algorithms for Hyperspectral Inversion of Common Water Quality Indicators

The upcoming transition to a diverse suite hyperspectral airborne and orbiting optical sensors will provide an unprecedented opportunity to measure inland water quality characteristics at a fidelity not previously achievable. This presentation will assess prototype deep learning models trained on synthetic hyperspectral data and validated with collocated in-situ measurements. Synthesized data is becoming increasingly popular for use in data-driven approaches to complex problems, and can compliment real data to increase performance on complex and unusual phenomenon, reduce or test bias, and experiment to demonstrate explainability. We will present insights from hyperspectral inversions of Chlorophyl-a, Phycocyanin, and concentration of non-algal particles using selected orbiting and airborne sensors over diverse, optically complex aquatic scenarios. We analyze how various optical water types affect fidelity of results and where improvements can be made as we prototype for globally operational water quality algorithms which can be leveraged by upcoming hyperspectral missions such as the Surface Biology and Geology (SBG) mission.

Surface Biology and Geology (SBG)↗