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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1994

The Dynamics of Some Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations is analyzed using the theory of dynamical systems. With the aid of parallel Connection Machines (CM-2 and CM-5), the associated bifurcation diagrams as a function of the time step, and the complex behavior of the associated 'numerical basins of attraction' of these iterative implicit schemes are revealed and compared. Studies showed that all of the four implicit LMMs exhibit a drastic distortion and segmentation but less shrinkage of the basin of attraction of the true solution than standard explicit methods. The numerical basins of attraction of a noniterative implicit procedure mimic more closely the basins of attraction of the differential equations than the iterative implicit procedures for the four implicit LMMs.

Yee, H. C.↗
NASA NTRS2003

An Iterative Decambering Approach for Post-Stall Prediction of Wing Characteristics using known Section Data

An iterative decambering approach for the post stall prediction of wings using known section data as inputs is presented. The method can currently be used for incompressible .ow and can be extended to compressible subsonic .ow using Mach number correction schemes. A detailed discussion of past work on this topic is presented first. Next, an overview of the decambering approach is presented and is illustrated by applying the approach to the prediction of the two-dimensional C(sub l) and C(sub m) curves for an airfoil. The implementation of the approach for iterative decambering of wing sections is then discussed. A novel feature of the current e.ort is the use of a multidimensional Newton iteration for taking into consideration the coupling between the di.erent sections of the wing. The approach lends itself to implementation in a variety of finite-wing analysis methods such as lifting-line theory, discrete-vortex Weissinger's method, and vortex lattice codes. Results are presented for a rectangular wing for a from 0 to 25 deg. The results are compared for both increasing and decreasing directions of a, and they show that a hysteresis loop can be predicted for post-stall angles of attack.

Mukherjee, Rinku↗
NASA NTRS2003

Iterative pass optimization of sequence data

The problem of determining the minimum-cost hypothetical ancestral sequences for a given cladogram is known to be NP-complete. This "tree alignment" problem has motivated the considerable effort placed in multiple sequence alignment procedures. Wheeler in 1996 proposed a heuristic method, direct optimization, to calculate cladogram costs without the intervention of multiple sequence alignment. This method, though more efficient in time and more effective in cladogram length than many alignment-based procedures, greedily optimizes nodes based on descendent information only. In their proposal of an exact multiple alignment solution, Sankoff et al. in 1976 described a heuristic procedure--the iterative improvement method--to create alignments at internal nodes by solving a series of median problems. The combination of a three-sequence direct optimization with iterative improvement and a branch-length-based cladogram cost procedure, provides an algorithm that frequently results in superior (i.e., lower) cladogram costs. This iterative pass optimization is both computation and memory intensive, but economies can be made to reduce this burden. An example in arthropod systematics is discussed. c2003 The Willi Hennig Society. Published by Elsevier Science (USA). All rights reserved.

NASA Discipline Evolutionary Biology↗
NASA NTRS2006

An Iterative Information-Reduced Quadriphase-Shift-Keyed Carrier Synchronization Scheme Using Decision Feedback for Low Signal-to-Noise Ratio Applications

In a previous publication [1], an iterative closed-loop carrier synchronization scheme for binary phase-shift keyed (BPSK) modulation was proposed that was based on feeding back data decisions to the input of the loop, the purpose being to remove the modulation prior to carrier synchronization as opposed to the more conventional decision-feedback schemes that incorporate such feedback inside the loop. The idea there was that, with sufficient independence between the received data and the decisions on it that are fed back (as would occur in an error-correction coding environment with sufficient decoding delay), a pure tone in the presence of noise would ultimately be produced (after sufficient iteration and low enough error probability) and thus could be tracked without any squaring loss. This article demonstrates that, with some modification, the same idea of iterative information reduction through decision feedback can be applied to quadrature phase-shift keyed (QPSK) modulation, something that was mentioned in the previous publication but never pursued.

Simon, M.↗
NASA NTRS2007

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

Nark, Douglas M.↗
NASA NTRS2007

Representation-Independent Iteration of Sparse Data Arrays

An approach is defined that describes a method of iterating over massively large arrays containing sparse data using an approach that is implementation independent of how the contents of the sparse arrays are laid out in memory. What is unique and important here is the decoupling of the iteration over the sparse set of array elements from how they are internally represented in memory. This enables this approach to be backward compatible with existing schemes for representing sparse arrays as well as new approaches. What is novel here is a new approach for efficiently iterating over sparse arrays that is independent of the underlying memory layout representation of the array. A functional interface is defined for implementing sparse arrays in any modern programming language with a particular focus for the Chapel programming language. Examples are provided that show the translation of a loop that computes a matrix vector product into this representation for both the distributed and not-distributed cases. This work is directly applicable to NASA and its High Productivity Computing Systems (HPCS) program that JPL and our current program are engaged in. The goal of this program is to create powerful, scalable, and economically viable high-powered computer systems suitable for use in national security and industry by 2010. This is important to NASA for its computationally intensive requirements for analyzing and understanding the volumes of science data from our returned missions.

James, Mark↗
NASA NTRS2011

Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids.

Diskin, Boris↗
NASA NTRS2011

Application of Temperature Sensitivities During Iterative Strain-Gage Balance Calibration Analysis

A new method is discussed that may be used to correct wind tunnel strain-gage balance load predictions for the influence of residual temperature effects at the location of the strain-gages. The method was designed for the iterative analysis technique that is used in the aerospace testing community to predict balance loads from strain-gage outputs during a wind tunnel test. The new method implicitly applies temperature corrections to the gage outputs during the load iteration process. Therefore, it can use uncorrected gage outputs directly as input for the load calculations. The new method is applied in several steps. First, balance calibration data is analyzed in the usual manner assuming that the balance temperature was kept constant during the calibration. Then, the temperature difference relative to the calibration temperature is introduced as a new independent variable for each strain--gage output. Therefore, sensors must exist near the strain--gages so that the required temperature differences can be measured during the wind tunnel test. In addition, the format of the regression coefficient matrix needs to be extended so that it can support the new independent variables. In the next step, the extended regression coefficient matrix of the original calibration data is modified by using the manufacturer specified temperature sensitivity of each strain--gage as the regression coefficient of the corresponding temperature difference variable. Finally, the modified regression coefficient matrix is converted to a data reduction matrix that the iterative analysis technique needs for the calculation of balance loads. Original calibration data and modified check load data of NASA's MC60D balance are used to illustrate the new method.

Ulbrich, N.↗
NASA NTRS2012

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

Xu, Feng↗
NASA NTRS2013

The Iterative Design Process in Research and Development: A Work Experience Paper

The iterative design process is one of many strategies used in new product development. Top-down development strategies, like waterfall development, place a heavy emphasis on planning and simulation. The iterative process, on the other hand, is better suited to the management of small to medium scale projects. Over the past four months, I have worked with engineers at Johnson Space Center on a multitude of electronics projects. By describing the work I have done these last few months, analyzing the factors that have driven design decisions, and examining the testing and verification process, I will demonstrate that iterative design is the obvious choice for research and development projects.

Sullivan, George F. III↗
NASA NTRS2018

Implementation and Use of a Convergence Test for Iterative Wind Tunnel Balance Load Predictions

A modified and extended version of a convergence test for wind tunnel strain-gage balance load iterations was implemented. The test uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions if the Iterative Method is applied. Convergence is expected within the use envelope of the balance whenever this upper bound is less than the threshold of one. It is explained in great detail how the convergence test can be applied to the two load iteration equation types that are currently being used in the aerospace testing community. In addition, the application of the test to balances with bi-directional output characteristics is discussed. It is also shown how numerical differentiation can be used in order to obtain partial derivatives that are needed for the calculation of the Lipschitz constant. Finally, machine calibration data of NASA's MC60E six-component force balance is selected to demonstrate both implementation and use of the convergence test.

calibration analysis↗
NASA NTRS2019

Fundamental Improvement of a Convergence Test for Iterative Strain-Gage Balance Load Predictions

A fundamental improvement of a convergence test for wind tunnel strain-gage balance load iterations was developed. The improvement became necessary because incorrect test results were obtained whenever the original test was applied to multi-component balances with large load capacity differences. The original test was first published in NASA TN D-6860. It uses an upper bound of the Lipschitz constant to assess convergence characteristics of balance load predictions whenever the Iterative Method is applied. The Lipschitz constant is a function of the partial derivatives of each balance load component with respect to all other load components. Unfortunately, the original definition of the convergence test overlooked the fact that the Lipschitz constant is a dimensionless quantity and that the partial derivative of one load component with respect to another load component is not always dimensionless. Therefore, an improvement of the original test was successfully developed that uses load capacities to make all inputs for the calculation of the Lipschitz constant dimensionless before use. Results from the calibration data analysis of a six-component force balance and a five-component semi-span balance are used to illustrate the application of the improved load iteration convergence test.

Strain-Gage Balance↗
NASA NTRS2020

Development of a Non-Iterative Balance Load Prediction Algorithm for the NASA Ames Unitary Plan Wind Tunnel

A non-iterative load prediction algorithm for strain-gage balances was developed for the NASA Ames Unitary Plan Wind Tunnels that computes balance loads from the electrical outputs of the balance bridges and a set of state variables. A state variable could be, for example, a balance temperature difference or the bellows pressure of a flow-through balance. The algorithm directly uses regression models of the balance loads for the load prediction that were obtained by applying global regression analysis to balance calibration data. This choice greatly simplifies both implementation and use of the load prediction process for complex balance configurations as no load iteration needs to be performed. The regression model of a balance load is constructed by using terms from a total of nine term groups. Four term groups are derived from a Taylor Series expansion of the relationship between the load, gage outputs, and state variables. The remaining five term groups are defined by using absolute values of the gage outputs and state variables. Terms from these groups should only be included in the regression model if calibration data from a balance with known bi-directional outputs is analyzed. It is illustrated in detail how global regression analysis may be applied to obtain the coefficients of the chosen regression model of a load component assuming that no linear or massive near-linear dependencies between the regression model terms exist. Data from the machine calibration of a six-component force balance is used to illustrate both application and accuracy of the non-iterative load prediction process.

Ulbrich, Norbert M.↗
NASA NTRS2012

Rest-wavelength Fiducials for the ITER Core Imaging X-ray Spectrometer

Absolute wavelength references are needed to derive the plasma velocities from the Doppler shift of a given line emitted by a moving plasma. We show that such reference standards exist for the strongest x-ray line in neonlike W64+, which has become the line of choice for the ITER (Latin the way) core imaging x-ray spectrometer. Close-by standards are the Hf L3 line and the Ir L2 line, which bracket the W64+ line by 30 eV; other standards are given by the Ir L1 and L2 lines and the Hf L1 and L2 lines, which bracket the W64+ line by 40 and 160 eV, respectively. The reference standards can be produced by an x-ray tube built into the ITER spectrometer. We present spectra of the reference lines obtained with an x-ray microcalorimeter and compare them to spectra of the W64+ line obtained both with an x-ray microcalorimeter and a crystal spectrometer

Rest-wavelength↗
NASA NTRS1965

Computer modification reduces time of performing iterative division

Time reduction in performing iterative division results from using a serial-by-parallel divider employing a look-ahead feature that predetermines the sign relationships of several iterations before the computer cycle begins. This method can be employed in any data handling system performing high-speed division.

Source record↗
NASA NTRS1975

A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics

A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.

Martin, E. D.↗
NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗