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At least 433 records · Page 24

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NASA NTRS1983

Accelerating an iterative process by explicit annihilation

A slowly convergent stationary iterative process can be accelerated by explicitly annihilating (i.e., eliminating) the dominant eigenvector component of the error. The dominant eigenvalue or complex pair of eigenvalues can be estimated from the solution during the iteration. The corresponding eigenvector or complex pair of eigenvectors can then be annihilated by applying an explicit Richardson process over the basic iterative method. This can be done entirely in real arithmetic by analytically combining the complex conjugate annihilation steps. The technique is applied to an implicit algorithm for the calculation of two dimensional steady transonic flow over a circular cylinder using the equations of compressible inviscid gas dynamics. This demonstrates the use of explicit annihilation on a nonlinear problem.

Jespersen, D. C.↗

NASA NTRS1983

Massively parallel processor computer

An apparatus for processing multidimensional data with strong spatial characteristics, such as raw image data, characterized by a large number of parallel data streams in an ordered array is described. It comprises a large number (e.g., 16,384 in a 128 x 128 array) of parallel processing elements operating simultaneously and independently on single bit slices of a corresponding array of incoming data streams under control of a single set of instructions. Each of the processing elements comprises a bidirectional data bus in communication with a register for storing single bit slices together with a random access memory unit and associated circuitry, including a binary counter/shift register device, for performing logical and arithmetical computations on the bit slices, and an I/O unit for interfacing the bidirectional data bus with the data stream source. The massively parallel processor architecture enables very high speed processing of large amounts of ordered parallel data, including spatial translation by shifting or sliding of bits vertically or horizontally to neighboring processing elements.

Fung, L. W.↗

NASA NTRS1983

An efficient algorithm for generating random number pairs drawn from a bivariate normal distribution

An efficient algorithm for generating random number pairs from a bivariate normal distribution was developed. Any desired value of the two means, two standard deviations, and correlation coefficient can be selected. Theoretically the technique is exact and in practice its accuracy is limited only by the quality of the uniform distribution random number generator, inaccuracies in computer function evaluation, and arithmetic. A FORTRAN routine was written to check the algorithm and good accuracy was obtained. Some small errors in the correlation coefficient were observed to vary in a surprisingly regular manner. A simple model was developed which explained the qualities aspects of the errors.

Campbell, C. W.↗

NASA NTRS1983

JT150 1/2-scale nozzle jet noise experiment and comparison with prediction

As part of a program to study flight effects on the exhaust noise of a full scale JT15D engine, static half scale model jet noise experiments were conducted. Acoustic data were recorded for microphone angles of 45 deg to 155 deg with jet conditions for the model scale nozzle corresponding closely to those at 55, 73 and 97 percent of corrected rated speed for the full scale engine. These data are useful for determining the relative importance of jet and core noise in the static full scale engine test data and will in turn allow for a proper evaluation of flight effects on the exhaust noise results. The model scale data are also compared with the coaxial jet noise prediction. Above 1000 Hz, the prediction is nominally 0 to 3 dB higher than the data. The arithmetic mean of the differences between the experimental OASPL and the predicted OASPL for all angles for each run ranged from 0 to -3.2 dB. The standard deviation of all the OASPL differences is 2.2 dB. The discrepancies are greatest at low primary jet velocities and appear to be due to inadequacy in the variable jet density exponent incorporated in the prediction procedure.

Groesbeck, D. E.↗

NASA NTRS1983

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.↗

NASA NTRS1983

Effects of aircraft noise on human activities

The effects of aircrft noise on human activities was investigated by developing a battery of tasks (1) representative of a range of human activities and (2) sensitive to the disruptive effects of noise. The noise used were recordings of jet aircraft and helicopter sounds at three lvels of loudness--60, 70, and 80 dB(A). Experiment 1 investigated 12 different cognitive tasks, along with two intelligibility tasks included to validate that the noises were being effective. Interference with intelligibility was essentially the same as found in the research literature, but only inconsistent effects were found on either accuracy or latency of performance on the cognitive tasks. When the tasks were grouped into four categories (Intelligibility, Matching, Verbal, and Arithmetic), reliable differences in rated annoyingness of the noises were related to the task category and to the type of noise (jet or helicopter).

Arnoult, M. D.↗

NASA NTRS1982

Evaluation of the sensitivity and intrusion of workload estimation techniques in piloting tasks emphasizing mediational activity

In this experiment, pilots flew an instrumented moving-base simulator. Mediational loading was elicited by having them solve a variety of navigational problems. The problems were sorted into low, medium, and high load conditions based on the number and complexity of arithmetic and geometric operations required to solve them. Workload estimation techniques based on opinion, spare mental capacity, primary task performance, and physiological measures were obtained and compared. This paper describes: (1) the ability of the techniques to discriminate statistically between the three levels of loading conditions, and (2) changes in primary task performance caused by introduction of the workload technique procedures and equipment.

Rahimi, M.↗

NASA NTRS1983

A nonstationary relaxation method for the Cauchy-Riemann and 1-D Euler equations

The Cauchy-Riemann equations and the 1-D Euler equations are expressed in generalized coordinates and then cast in finite difference form by using central differencing throughout. The resulting matrix representation has an eigensystem that permits the development of an annihilation process using complex arithmetic in a block tridiagonal solver. Initial numerical experiments show that the process has potential for use as a relaxation procedure for the Euler equations.

Liu, Y.↗

NASA NTRS1985

Digital Ratiometer

Small, low-cost comparator with 24-bit-precision yields ratio signal from pair of analog or digital input signals. Arithmetic logic chips (bit-slice) sample two 24-bit analog-to-digital converters approximately once every millisecond and accumulate them in two 24-bit registers. Approach readily modified to arbitrary precision.

Beer, R.↗

NASA NTRS1983

VLSI architectures for computing multiplications and inverses in GF(2-m)

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation.

Wang, C. C.↗

NASA NTRS1984

Data reduction programs for a laser radar system

The listing and description of software routines which were used to analyze the analog data obtained from LIDAR - system are given. All routines are written in FORTRAN - IV on a HP - 1000/F minicomputer which serves as the heart of the data acquisition system for the LIDAR program. This particular system has 128 kilobytes of highspeed memory and is equipped with a Vector Instruction Set (VIS) firmware package, which is used in all the routines, to handle quick execution of different long loops. The system handles floating point arithmetic in hardware in order to enhance the speed of execution. This computer is a 2177 C/F series version of HP - 1000 RTE-IVB data acquisition computer system which is designed for real time data capture/analysis and disk/tape mass storage environment.

Badavi, F. F.↗

NASA NTRS1984

Mathematical algorithms to maximize performance in numerical weather prediction

Numerical weather prediction models, which involve the solution of non-linear partial differential equations at points on an extensive three dimensional grid, are ideally suited for processing on vector machines. It was logical therefore that the new global forecast model to be implemented at the Meteorological Office should be written in vector code for the CYBER 205. In order to achieve full efficiency and to reduce storage requirements the model used 32-bit arithmetic which was found to provide high enough precision. Unfortunately, however, the trigonometrical and logarithmic functions provided by CDC could only handle 64-bit vectors and, although written in efficient scalar code, did not take advantage of the special facilities of a vector processor. It was therefore necessary to rewrite the functions in vector code to handle both 32 and 64-bit vectors. There was also no half-precision compiler available for the Cyber 205 at that time and so the functions, like the model, had to make extensive use of the special call syntax. This made the code more difficult to write but it allowed much greater flexibility in that it became possible to access the exponent of a floating-point number independently of its coefficient. A description is given of the technique and the results which were achieved are summarized.

Foreman, A.↗

NASA NTRS1984

A highly optimized vectorized code for Monte Carlo simulations of SU(3) lattice gauge theories

New methods are introduced for improving the performance of the vectorized Monte Carlo SU(3) lattice gauge theory algorithm using the CDC CYBER 205. Structure, algorithm and programming considerations are discussed. The performance achieved for a 16(4) lattice on a 2-pipe system may be phrased in terms of the link update time or overall MFLOPS rates. For 32-bit arithmetic, it is 36.3 microsecond/link for 8 hits per iteration (40.9 microsecond for 10 hits) or 101.5 MFLOPS.

Barkai, D.↗

NASA NTRS1984

Navier-Stokes Simulation of Homogeneous Turbulence on the CYBER 205

A computer code which solves the Navier-Stokes equations for three dimensional, time-dependent, homogenous turbulence has been written for the CYBER 205. The code has options for both 64-bit and 32-bit arithmetic. With 32-bit computation, mesh sizes up to 64 (3) are contained within core of a 2 million 64-bit word memory. Computer speed timing runs were made for various vector lengths up to 6144. With this code, speeds a little over 100 Mflops have been achieved on a 2-pipe CYBER 205. Several problems encountered in the coding are discussed.

Wu, C. T.↗

NASA NTRS1984

Implementation of the Sun Position Calculation in the PDC-1 Control Microprocessor

The several computational approaches to providing the local azimuth and elevation angles of the Sun as a function of local time and then the utilization of the most appropriate method in the PDC-1 microprocessor are presented. The full algorithm, the FORTRAN form, is felt to be very useful in any kind or size of computer. It was used in the PDC-1 unit to generate efficient code for the microprocessor with its floating point arithmetic chip. The balance of the presentation consists of a brief discussion of the tracking requirements for PPDC-1, the planetary motion equations from the first to the final version, and the local azimuth-elevation geometry.

Stallkamp, J. A.↗

NASA NTRS1984

An efficient approximate factorization implicit scheme for the equations of gasdynamics

An efficient implicit finite-difference algorithm for the gas dynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved while maintaining the same favorable stability characteristics and generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows about a NACA 0012 airfoil. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations. It is shown that the method offers advantages over the conventional Beam and Warming scheme and can retrofit existing Beam and Warming codes with minimal effort.

Barth, T. J.↗

NASA NTRS1983

Infrared astronomical imaging using a microcomputer data system

A small, portable data-acquisition and display system with a unique coprocessor was designed and built to collect data from infrared array detectors for astronomical and laboratory use. The system consists of a microcomputer board, two 12-bit analog-to-digital data-acquisition boards, a color-graphics driver board, and two coprocessor boards. The coprocessors are arithmetic logic units designed to achieve the high computation rates necessary for real-time infrared background cancellation. The system can collect data from infrared detectors of 1 to 256 pixel elements with a computation rate of 768 kHz. The software for the system was designed to collect data in the system's background, while performing other tasks in the system's foreground. The data for the detector arrays is stored in block fashion to facilitate variable image size.

Stafford, P. S.↗

NASA NTRS1984

An implicit form for the Osher upwind scheme

Conservative upwind schemes for the Euler equations, such as the Osher scheme, accurately resolve flow discontinuities and correctly model the physics of the problem. However, these schemes require many more arithmetic operations per integration step than simple central-difference schemes and hence result in large computing times. An implicit version of the first-order- and second-order-accurate Osher schemes in two spatial dimensions and generalized coordinates is developed in this study. Because implicit schemes permit the use of large integration steps, in many cases they require fewer integration steps to reach steady-state (especially in calculations on grids with widely varying mesh-cell sizes). The implicit scheme developed in this study accelerated convergence speeds by almost an order of magnitude in the problems considered. Test cases include quasi-one-dimensional nozzle flow and supersonic flow past a cylinder.

Rai, M. M.↗