Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Arithmetic”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26

Free vibration and dynamic response analysis of spinning structures

The proposed effort involved development of numerical procedures for efficient solution of free vibration problems of spinning structures. An eigenproblem solution procedure, based on a Lanczos method employing complex arithmetic, was successfully developed. This task involved formulation of the numerical procedure, FORTRAN coding of the algorithm, checking and debugging of software, and implementation of the routine in the STARS program. A graphics package for the E/S PS 300 as well as for the Tektronix terminals was successfully generated and consists of the following special capabilities: (1) a dynamic response plot for the stresses and displacements as functions of time; and (2) a menu driven command module enabling input of data on an interactive basis. Finally, the STARS analysis capability was further improved by implementing the dynamic response analysis package that provides information on nodal deformations and element stresses as a function of time. A number of test cases were run utilizing the currently developed algorithm implemented in the STARS program and such results indicate that the newly generated solution technique is significantly more efficient than other existing similar procedures.

Source record↗

A generalized algorithm to design finite field normal basis multipliers

Finite field arithmetic logic is central in the implementation of some error-correcting coders and some cryptographic devices. There is a need for good multiplication algorithms which can be easily realized. Massey and Omura recently developed a new multiplication algorithm for finite fields based on a normal basis representation. Using the normal basis representation, the design of the finite field multiplier is simple and regular. The fundamental design of the Massey-Omura multiplier is based on a design of a product function. In this article, a generalized algorithm to locate a normal basis in a field is first presented. Using this normal basis, an algorithm to construct the product function is then developed. This design does not depend on particular characteristics of the generator polynomial of the field.

Wang, C. C.↗

The fault-tree compiler

The Fault Tree Compiler Program is a new reliability tool used to predict the top event probability for a fault tree. Five different gate types are allowed in the fault tree: AND, OR, EXCLUSIVE OR, INVERT, and M OF N gates. The high level input language is easy to understand and use when describing the system tree. In addition, the use of the hierarchical fault tree capability can simplify the tree description and decrease program execution time. The current solution technique provides an answer precise (within the limits of double precision floating point arithmetic) to the five digits in the answer. The user may vary one failure rate or failure probability over a range of values and plot the results for sensitivity analyses. The solution technique is implemented in FORTRAN; the remaining program code is implemented in Pascal. The program is written to run on a Digital Corporation VAX with the VMS operation system.

Martensen, Anna L.↗

Chemical network problems solved on NASA/Goddard's massively parallel processor computer

The single instruction stream, multiple data stream Massively Parallel Processor (MPP) unit consists of 16,384 bit serial arithmetic processors configured as a 128 x 128 array whose speed can exceed that of current supercomputers (Cyber 205). The applicability of the MPP for solving reaction network problems is presented and discussed, including the mapping of the calculation to the architecture, and CPU timing comparisons.

Cho, Seog Y.↗

Digital control system for space structure dampers

A digital controller was developed using an SKD-51 System Design Kit, which incorporates an 8031 microcontroller. The necessary interfaces were installed in the wire wrap area of the SKD-51 and a pulse width modulator was developed to drive the coil of the actuator. Also, control equations were developed, using floating-point arithmetic. The design of the digital control system is emphasized, and it is shown that, provided certain rules are followed, an adequate design can be achieved. It is recommended that the so-called w-plane design method be used, and that the time elapsed before output of the up-dated coil-force signal be kept as small as possible. However, the cycle time for the controller should be watched carefully, because very small values for this time can lead to digital noise.

Haviland, J. K.↗

Supercomputing on massively parallel bit-serial architectures

Research on the Goodyear Massively Parallel Processor (MPP) suggests that high-level parallel languages are practical and can be designed with powerful new semantics that allow algorithms to be efficiently mapped to the real machines. For the MPP these semantics include parallel/associative array selection for both dense and sparse matrices, variable precision arithmetic to trade accuracy for speed, micro-pipelined train broadcast, and conditional branching at the processing element (PE) control unit level. The preliminary design of a FORTRAN-like parallel language for the MPP has been completed and is being used to write programs to perform sparse matrix array selection, min/max search, matrix multiplication, Gaussian elimination on single bit arrays and other generic algorithms. A description is given of the MPP design. Features of the system and its operation are illustrated in the form of charts and diagrams.

Iobst, Ken↗

Counterface effects on the tribological properties of polyimide composites

Graphite fiber reinforced polyimide composite pins were slid against seven different counterfaces to determine the effect of material type on the tribological properties of polymer composites. In addition, the effect of sliding a new pin on a pre-established transfer film was investigated. The results indicated that almost a five order of magnitude difference in composite wear rate can occur just by varying the counterface material. An attempt to make all surfaces as smooth as possible was made, but due to differences in material composition this was not possible and a range of surface roughnesses were obtained. The results indicate that the smoother the surface, the lower the composite wear rate; but that small protrusions (not discernible with arithmetic surface roughness measurements) can markedly increase wear rates. A pre-established transfer film improved both run in and steady state wear rates.

Fusaro, Robert L.↗

Rarefied aerodynamics and upper atmospheric flight results from the Orbiter High Resolution Accelerometer Package experiment

Data from the High Resolution Accelerometer Package (HiRAP) experiment on the Space Shuttle Orbiter have been analyzed for 10 flights to produce lift-drag (L/D) ratios in the free molecule, transition, and continuum flow flight regimes. Freestream density is also obtained in the altitude range from 60 km to 160 km using an aerodynamic model based upon earlier flight analysis of accelerometer data. The results of the L/D analysis of the latest four flights have been compared with the aerodynamic model developed from the first six HiRAP missions. The new data agree with the established flight-derived model, thereby validating earlier analysis. However, the arithmetic mean of the 10 flight-derived L/D values in the free molecular flow regime is 0.053 (+ or - 0.1) as compared to the initial value of 0.10 (+ or - 0.3), determined from STS-6. Updates to the Orbiter aerodynamic model values and calibration factors have been incorporated into the density calculations for all 10 flights to provide realistic absolute density. The derived density altitude profiles, which have been normalized to the U.S. Standard Atmosphere 1976, are characterized by a large amplitude wave pattern relative to the standard as seen in the initial flight analysis.

Blanchard, R. C.↗

Robust eigensystem assignment for flexible structures

An improved method is developed for eigenvalues and eigenvectors placement of a closed-loop control system using either state or output feedback. The method basically consists of three steps. First, the singular value of QR decomposition is used to generate an orthonormal basis that spans admissible eigenvector space corresponding to each assigned eigenvalue. Secondly, given a unitary matrix, the eigenvector set which best approximates the given matrix in the least-square sense and still satisfy eigenvalue cosntraints is determined. Thirdly, a unitary matrix is sought to minimize the error between the unitary matrix and the assignable eigenvector matrix. For use as the desired eigenvector set, two matrices, namely, the open-loop eigenvector matrix and its closest unitary matrix are proposed. The latter matrix generally encourages both minimum conditioning and control gains. In addition, the algorithm is formulated in real arithmetic for efficient implementation. To illustrate the basic concepts, numerical examples are included.

Juang, Jer-Nan↗

The BLAZE language - A parallel language for scientific programming

A Pascal-like scientific programming language, BLAZE, is described. BLAZE contains array arithmetic, forall loops, and APL-style accumulation operators, which allow natural expression of fine grained parallelism. It also employs an applicative or functional procedure invocation mechanism, which makes it easy for compilers to extract coarse grained parallelism using machine specific program restructuring. Thus BLAZE should allow one to achieve highly parallel execution on multiprocessor architectures, while still providing the user with conceptually sequential control flow. A central goal in the design of BLAZE is portability across a broad range of parallel architectures. The multiple levels of parallelism present in BLAZE code, in principle, allow a compiler to extract the types of parallelism appropriate for the given architecture while neglecting the remainder. The features of BLAZE are described and it is shown how this language would be used in typical scientific programming.

Mehrotra, Piyush↗

A parallel Householder tridiagonalization stratagem using scattered square decomposition

The parallel stratagem in this paper uses scattered square decomposition, introduced by Fox (1985), for its data assignment and then exploits parallelism in the solution steps of the sequential Householder tridiagonalization algorithm. One may condense a real symmetric full matrix A of order n into a tridiagonal form by the stratagem in concurrent machines where N(=D-squared) processors are used. Expressions for efficiency and speedup are given for the evaluation of the stratagem. An alternative stratagem which requires less data transmission but more computations is also discussed. The results shown that the Householder method of tridiagonalization may be implemented on a concurrent machine efficiently by scattered square decomposition provided that the number of matrix elements contained in each processor is much larger than the number of processors of the concurrent machine, and the ratio of the time to transmit one data item from one processor to any other processor to the time to perform a floating-point arithmetic operation is small enough.

Chang, H. Y.↗

An algorithm for a generalization of the Richardson extrapolation process

The paper presents a recursive method, designated the W exp (m)-algorithm, for implementing a generalization of the Richardson extrapolation process. Compared to the direct solution of the linear sytems of equations defining the extrapolation procedure, this method requires a small number of arithmetic operations and very little storage. The technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying a d-transformation to power series. In the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced, for solving the same problem. A FORTRAN program for the W exp (m)-algorithm is also appended.

Ford, William F.↗

Directed band ratioing for the retention of perceptually-independent topographic expression in chromaticity-enhanced imagery

A band ratioing method is developed which directs the retention of topographic expression and albedo information so that they remain depicted as prominent variations in image intensity. Band data are adjusted so that ratio values for each surface material coherently increase with increasing pixel bispectral radiance for all three ratios of the color composite. The retained topographic expression and albedo information do not significantly distort the ratio-enhanced band-variant reflectance information, and the resultant images are similar to chromaticity-enhanced band composite images, but require only simple arithmetic processing steps.

Crippen, Robert E.↗

Eight-Bit-Slice GaAs General Processor Circuit

Novel GaAs 8-bit slice enables quick and efficient implementation of variety of fast GaAs digital systems ranging from central processing units of computers to special-purpose processors for communications and signal-processing applications. With GaAs 8-bit slice, designers quickly configure and test hearts of many digital systems that demand fast complex arithmetic, fast and sufficient register storage, efficient multiplexing and routing of data words, and ease of control.

Weissman, John↗

Optical Firmware

Data-processing system exploits high speeds inherent in optical elements. Instruction sets for different computer operations reside on different external memory chips. Laser diodes activated for each operation generate light, reflected by holographic optical element to designated receptors in arithmetic and logic unit. Pattern of light beams embodies instruction set at given instant. With potential ability to reprogram in real time, conceptual system applicable to task-driven programming or artificial intelligence.

Bergman, Larry A.↗

The CSM testbed matrix processors internal logic and dataflow descriptions

This report constitutes the final report for subtask 1 of Task 5 of NASA Contract NAS1-18444, Computational Structural Mechanics (CSM) Research. This report contains a detailed description of the coded workings of selected CSM Testbed matrix processors (i.e., TOPO, K, INV, SSOL) and of the arithmetic utility processor AUS. These processors and the current sparse matrix data structures are studied and documented. Items examined include: details of the data structures, interdependence of data structures, data-blocking logic in the data structures, processor data flow and architecture, and processor algorithmic logic flow.

Regelbrugge, Marc E.↗

Formally verifying Ada programs which use real number types

Formal verification is applied to programs which use real number arithmetic operations (mathematical programs). Formal verification of a program P consists of creating a mathematical model of F, stating the desired properties of P in a formal logical language, and proving that the mathematical model has the desired properties using a formal proof calculus. The development and verification of the mathematical model are discussed.

Sutherland, David↗