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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 NTRS1983

Preconditioned Minimal Residual Methods for Chebyshev Spectral Caluclations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗

NASA NTRS1985

Preconditioned minimal residual methods for Chebyshev spectral calculations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗

NASA NTRS1989

Adaptive feed array compensation system for reflector antenna surface distortion

The feasibility of a closed loop adaptive feed array system for compensating reflector surface deformations has been investigated. The performance characteristics (gain, sidelobe level, pointing, etc.) of large communication antenna systems degrade as the reflector surface distorts mainly due to thermal effects from a varying solar flux. The compensating systems described in this report can be used to maintain the design performance characteristics independent of thermal effects on the reflector surface. The proposed compensating system employs the concept of conjugate field matching to adjust the feed array complex excitation coefficients.

Acosta, Roberto J.↗

NASA NTRS1992

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

Jin, Jian-Ming↗

NASA NTRS1986

Multi-color incomplete Cholesky conjugate gradient methods for vector computers

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.

Poole, E. L.↗

NASA NTRS1993

Variational approaches to CFD: Applications to potential Euler and Navier-Stokes equations

Flow simulations based on variational techniques are discussed. Variational techniques are applied for the problem formulation, for the construction of discrete schemes, and for the solution procedures. Inviscid transonic flows, as well as viscous incompressible and compressible flows, are analyzed by several methods. Variational techniques to solve the discrete systems of equations are well known. The most popular one is the conjugate gradient method. Extensions to nonsymmetric and nonpositive definite systems were under investigation for the last two decades. Variational techniques were used for convergence acceleration of iterative procedures. Some of these ideas based on recent work are examined. The lectures are organized in three parts including numerical simulation of inviscid as well as viscous incompressible and compressible flows.

Hafez, M.↗

NASA NTRS1950

Fundamental flame velocities of pure hydrocarbons II : alkadienes

Data are presented for the fundamental flame velocities of 10 pure alkadienes that have isolated, conjugated, or cumulative double-bond systems. On the basis of this limited amount of data and the flame velocities previously reported, it is concluded that unsaturation changes the flame velocity in the order alkanes ? alkenes ? alkadienes with isolated double bonds ?= alkadienes with conjugated double bonds ? alkadienes with cumulative double bonds ?= alkynes. There were no significant differences in the flame velocities of cis and trans 1,3-pentadiene. The alkadienes 1,2-pentadiene and 2,3-pentadiene, with different positions of the cumulative double bond in the straight chain, have similar flame velocities. Methyl substitution in a hydrocarbon reduces the flame velocity; the extent of the reduction increases with the degree of unsaturation of the hydrocarbon.

Levine, Oscar↗

NASA NTRS1994

Thin membrane sensor with biochemical switch

A modular biosensor system for chemical or biological agent detection utilizes electrochemical measurement of an ion current across a gate membrane triggered by the reaction of the target agent with a recognition protein conjugated to a channel blocker. The sensor system includes a bioresponse simulator or biochemical switch module which contains the recognition protein-channel blocker conjugate, and in which the detection reactions occur, and a transducer module which contains a gate membrane and a measuring electrode, and in which the presence of agent is sensed electrically. In the poised state, ion channels in the gate membrane are blocked by the recognition protein-channel blocker conjugate. Detection reactions remove the recognition protein-channel blocker conjugate from the ion channels, thus eliciting an ion current surge in the gate membrane which subsequently triggers an output alarm. Sufficiently large currents are generated that simple direct current electronics are adequate for the measurements. The biosensor has applications for environmental, medical, and industrial use.

Case, George D.↗

NASA NTRS1990

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Freund, Roland W.↗

NASA NTRS1990

Adaptive optics and optical structures; Proceedings of the Meeting, European Congress on Optics, 3rd, The Hague, Netherlands, Mar. 12-14, 1990

The present conference on adaptive optics (AO) and optical structures addresses AO systems and controls, AO components, nonlinear optics applications to AO, astronomical applications of AO, large telescopes and optical alignment, as well as the wavefront control experiment for the use of AO in beam propagation. Specific references are made to applications of electromagnetic theory in optics, theoretical studies of system performance and design parameters, Hartmann-Shack wavefront sensing, the use of ray-based techniques in cophasing segmented mirrors, the use of a phase-conjugating mirror for real-time phase visualization, and the absolute instability of oppositely directed waves with respect to a high-reflectivity phase-conjugate mirror. Also addressed are automatic control systems, precision segmented reflectors, AO system creation, the VLT's 8.2-m primary mirrors, an optical 12-m telescope, alignment optimization via the Talbot effect, and a combination of interferometry and ray-tracing analysis.

Tyson, Robert K.↗

NASA NTRS2002

Intelligent Text Retrieval and Knowledge Acquisition from Texts for NASA Applications: Preprocessing Issues

A system that retrieves problem reports from a NASA database is described. The database is queried with natural language questions. Part-of-speech tags are first assigned to each word in the question using a rule based tagger. A partial parse of the question is then produced with independent sets of deterministic finite state a utomata. Using partial parse information, a look up strategy searches the database for problem reports relevant to the question. A bigram stemmer and irregular verb conjugates have been incorporated into the system to improve accuracy. The system is evaluated by a set of fifty five questions posed by NASA engineers. A discussion of future research is also presented.

Source record↗

NASA NTRS1974

Control system design using frequency domain models and parameter optimization, with application to supersonic inlet controls

A technique is described for designing feedback control systems using frequency domain models, a quadratic cost function, and a parameter optimization computer program. FORTRAN listings for the computer program are included. The approach is applied to the design of shock position controllers for a supersonic inlet. Deterministic or random system disturbances, and the presence of random measurement noise are considered. The cost function minimization is formulated in the time domain, but the problem solution is obtained using a frequency domain system description. A scaled and constrained conjugate gradient algorithm is used for the minimization. The approach to a supersonic inlet included the calculations of the optimal proportional-plus integral (PI) and proportional-plus-integral-plus-derivative controllers. A single-loop PI controller was the most desirable of the designs considered.

Seidel, R. C.↗

NASA NTRS1992

Electromagnetic characterization of conformal antennas

The ultimate objective of this project is to develop a new technique which permits an accurate simulation of microstrip patch antennas or arrays with various feed, superstrate and/or substrate configurations residing in a recessed cavity whose aperture is planar, cylindrical or otherwise conformed to the substructure. The technique combines the finite element and boundary integral methods to formulate a system suitable for solution via the conjugate gradient method in conjunction with the fast Fourier transform. The final code is intended to compute both scattering and radiation patterns of the structure with an affordable memory demand. With upgraded capabilities, the four included papers examined the radar cross section (RCS), input impedance, gain, and resonant frequency of several rectangular configurations using different loading and substrate/superstrate configurations.

Volakis, John L.↗

NASA NTRS1996

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗

NASA NTRS1989

A fast, preconditioned conjugate gradient Toeplitz solver

A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

Pan, Victor↗

NASA NTRS1991

A look-ahead variant of the Lanczos algorithm and its application to the quasi-minimal residual method for non-Hermitian linear systems

The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.

Nachtigal, Noel M.↗

NASA NTRS1982

Iterative algorithms for large sparse linear systems on parallel computers

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Adams, L. M.↗

NASA NTRS2007

Bench-Top Antigen Detection Technique that Utilizes Nanofiltration and Fluorescent Dyes which Emit and Absorb Light in the Near Infrared

This article discusses the development of a bench-top technique to detect antigens in fluids. The technique involves the use of near infrared NIR fluorescent dyes conjugated to antibodies, centrifugation, nanofilters, and spectrometry. The system used to detect the antigens utilizes a spectrometer, fiber optic cables, NIR laser, and laptop computer thus making it portable and ideally suited for desk top analysis. Using IgM as an antigen and the secondary antibody, anti-IgM conjugated to the near infrared dye, IRDye (trademark) 800, for detection, we show that nanofiltration can efficiently and specifically separate antibody-antigen complexes in solution and that the complexes can be detected by a spectrometer and software using NIR laser excitation at 778 nm and NIR dye offset emission at 804 nm. The peak power detected at 778 nm for the excitation emission and at 804 nm for the offset emission is 879 pW (-60.06 dBm) and 35.7 pW (-74.5 dBm), respectively.

Varaljay-Spence, Vanessa A.↗