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NASA NTRS1985

Exploiting parallel computing with limited program changes using a network of microcomputers

Network computing and multiprocessor computers are two discernible trends in parallel processing. The computational behavior of an iterative distributed process in which some subtasks are completed later than others because of an imbalance in computational requirements is of significant interest. The effects of asynchronus processing was studied. A small existing program was converted to perform finite element analysis by distributing substructure analysis over a network of four Apple IIe microcomputers connected to a shared disk, simulating a parallel computer. The substructure analysis uses an iterative, fully stressed, structural resizing procedure. A framework of beams divided into three substructures is used as the finite element model. The effects of asynchronous processing on the convergence of the design variables are determined by not resizing particular substructures on various iterations.

Rogers, J. L., Jr.↗

NASA NTRS1985

Reordering computations for parallel execution

The computations are reordered in the SOR algorithm to maintain the same asymptotic rate of convergence as the rowwise ordering to obtain parallelism at different levels. A parallel program is written to illustrate these ideas and actual machines for implementation of this program are discussed.

Adams, L.↗

NASA NTRS1984

On the impact of communication complexity on the design of parallel numerical algorithms

This paper describes two models of the cost of data movement in parallel numerical alorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In this second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm-independent upper bounds on system performance are derived for several problems that are important to scientific computation.

Gannon, D. B.↗

NASA NTRS1985

Trapping of ion conics by downward parallel electric fields

Energetic particle data from electrostatic analyzers aboard the S3-3 satellite indicative of a downward parallel electric field at low altitudes are presented to argue for a causal connection between downward parallel electric fields and ion heating. The data include observations of upward field-aligned electron beams in regions where precipitating electron fluxes are suppressed. Evidence of downward acceleration of ions and locally mirroring ion conics is also presented. It is argued that the presence of a downward electric field may have important consequences for ion conic heating and might in fact be required for the observed heating of ions to several hundred electron volts.

Gorney, D. J.↗

NASA NTRS1986

Parallel-End-Point Drafting Compass

Parallelogram linkage ensures greater accuracy in drafting and scribing. Two members of arm of compass remain parallel for all angles pair makes with hub axis. They maintain opposing end members in parallelism. Parallelogram-linkage principle used on dividers as well as on compasses.

Cronander, J.↗

NASA NTRS1985

On cloud street development in three dimensional parallel and Rayleigh instabilities

Expected orientation angles and horizontal wavelengths of boundary layer rolls or cloud streets are determined from an analysis of a truncated spectral model of three dimensional shallow moist Boussinesq convection in a shearing environment. The nonlinear secondary circulations are organized into two dimensional forms by the height dependent wind field, and these rolls may develop from the combined effects of thermal stratification and mean wind shear. The associated thermal and parallel instability mechanisms are shown to be special cases of a single one. Only one mode is found when the stratification is unstable or neutral, but a second one is possible when the stratification is weakly stable. The first corresponds to relatively broadly spaced rolls having orientations for which the Fourier component of the roll perpendicular shear is nearly zero, but the second corresponds to relatively narrowly spaced rolls having orientations for which the Fourier coefficients of both the perpendicular and the parallel components of the shear are nearly equal.

Shirer, H. N.↗

NASA NTRS1985

Variation in efficiency of parallel algorithms

The present study has the objective to investigate some iterative parallel-processor linear equation solving algorithms with respect to efficiency for analyses of typical linear engineering systems. Attention is given to a set of n linear equations, Ku = p, where K = an n x n positive definite, sparsely populated, symmetric matrix, u = an n x 1 vector of unknown responses, and p = an n x 1 vector of prescribed constants. This study is concerned with a hybrid method in which iteration is used to solve the problem, while a direct method is used on the local processor level. Variations in the efficiency of parallel algorithms are explored. Measures of the efficiency are based on computer experiments regarding the algorithms. For all the algorithms, the wall clock time is found to decrease as the number of processors increases.

Hayashi, A.↗

NASA NTRS1986

On cloud street development in three dimensions - Parallel and Rayleigh instabilities

Shirer, H. N.↗

NASA NTRS1986

Two-stage earth-to-orbit vehicles with series and parallel burn

Recent studies have indicated that a fully reusable earth-to-orbit vehicle system will be needed near the beginning of the next century. One likely concept is a two-stage, vertical takeoff system with liquid rocket propulsion. Such vehicles have been examined with series burn and parallel burn of the engines of each stage. The results indicate that the preferred concept will have parallel burn with crossfeed, the booster will have hydrocarbon engines, the Orbiter will have both hydrocarbon and hydrogen engines, and the staging velocity will be low enough to allow the booster to glide back to the launch site.

Martin, J. A.↗

NASA NTRS1987

A parallel solution for the symmetric Eigenproblem

A completely parallel algorithm for the symmetric eigenproblem AX = Lambda BX is outlined. The algorithm is parallel in the sense that the numerical operations do not occur in a fixed sequence. Therefore, a large number of operations can be programmed to be performed concurrently on a computer with multiple central processing units. The standard symmetric eigenvalue problem AX = Lambda X has the property that the n eigenvalues of the principal submatrix of A of order n are separated by the (n-1) eignvalues of the principal submatrix of order (n-1). The separation property delineated n intervals containing one eigenvalue. Each eigenvalue and corresponding eigenvector can be computed independently. The n eigenproblem calculations can be divided among multiple processing units.

Thurston, Gaylen A.↗

NASA NTRS1987

Static and dynamic characteristics of parallel-grooved seals

Presented is an analytical method to determine static and dynamic characteristics of annular parallel-grooved seals. The governing equations were derived by using the turbulent lubrication theory based on the law of fluid friction. Linear zero- and first-order perturbation equations of the governing equations were developed, and these equations were analytically investigated to obtain the reaction force of the seals. An analysis is presented that calculates the leakage flow rate, the torque loss, and the rotordynamic coefficients for parallel-grooved seals. To demonstrate this analysis, we show the effect of changing number of stages, land and groove width, and inlet swirl on stability of the boiler feed water pump seals. Generally, as the number of stages increased or the grooves became wider, the leakage flow rate and rotor-dynamic coefficients decreased and the torque loss increased.

Iwatsubo, Takuzo↗

NASA NTRS1987

Rotordynamic coefficients and leakage flow of parallel grooved seals and smooth seals

Based on Childs finite length solution for annular plain seals an extension of the bulk flow theory is derived to calculate the rotordynamic coefficients and the leakage flow of seals with parallel grooves in the stator. Hirs turbulent lubricant equations are modified to account for the different friction factors in circumferential and axial direction. Furthermore an average groove depth is introduced to consider the additional circumferential flow in the grooves. Theoretical and experimental results are compared for the smooth constant clearance seal and the corresponding seal with parallel grooves. Compared to the smooth seal the direct and cross-coupled stiffness coefficients as well as the direct damping coefficients are lower in the grooved seal configuration. Leakage is reduced by the grooving pattern.

Nordmann, R.↗

NASA NTRS1987

Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.

Keyes, David E.↗

NASA NTRS1987

Particle simulation of plasmas on the massively parallel processor

Particle simulations, in which collective phenomena in plasmas are studied by following the self consistent motions of many discrete particles, involve several highly repetitive sets of calculations that are readily adaptable to SIMD parallel processing. A fully electromagnetic, relativistic plasma simulation for the massively parallel processor is described. The particle motions are followed in 2 1/2 dimensions on a 128 x 128 grid, with periodic boundary conditions. The two dimensional simulation space is mapped directly onto the processor network; a Fast Fourier Transform is used to solve the field equations. Particle data are stored according to an Eulerian scheme, i.e., the information associated with each particle is moved from one local memory to another as the particle moves across the spatial grid. The method is applied to the study of the nonlinear development of the whistler instability in a magnetospheric plasma model, with an anisotropic electron temperature. The wave distribution function is included as a new diagnostic to allow simulation results to be compared with satellite observations.

Gledhill, I. M. A.↗

NASA NTRS1987

The architecture of tomorrow's massively parallel computer

Goodyear Aerospace delivered the Massively Parallel Processor (MPP) to NASA/Goddard in May 1983, over three years ago. Ever since then, Goodyear has tried to look in a forward direction. There is always some debate as to which way is forward when it comes to supercomputer architecture. Improvements to the MPP's massively parallel architecture are discussed in the areas of data I/O, memory capacity, connectivity, and indirect (or local) addressing. In I/O, transfer rates up to 640 megabytes per second can be achieved. There are devices that can supply the data and accept it at this rate. The memory capacity can be increased up to 128 megabytes in the ARU and over a gigabyte in the staging memory. For connectivity, there are several different kinds of multistage networks that should be considered.

Batcher, Ken↗

NASA NTRS1987

Plasma simulation using the massively parallel processor

Two dimensional electrostatic simulation codes using the particle-in-cell model are developed on the Massively Parallel Processor (MPP). The conventional plasma simulation procedure that computes electric fields at particle positions by means of a gridded system is found inefficient on the MPP. The MPP simulation code is thus based on the gridless system in which particles are assigned to processing elements and electric fields are computed directly via Discrete Fourier Transform. Currently, the gridless model on the MPP in two dimensions is about nine times slower that the gridded system on the CRAY X-MP without considering I/O time. However, the gridless system on the MPP can be improved by incorporating a faster I/O between the staging memory and Array Unit and a more efficient procedure for taking floating point sums over processing elements. The initial results suggest that the parallel processors have the potential for performing large scale plasma simulations.

Lin, C. S.↗

NASA NTRS1987

Experience in highly parallel processing using DAP

Distributed Array Processors (DAP) have been in day to day use for ten years and a large amount of user experience has been gained. The profile of user applications is similar to that of the Massively Parallel Processor (MPP) working group. Experience has shown that contrary to expectations, highly parallel systems provide excellent performance on so-called dirty problems such as the physics part of meteorological codes. The reasons for this observation are discussed. The arguments against replacing bit processors with floating point processors are also discussed.

Parkinson, D.↗

NASA NTRS1987

Animated computer graphics models of space and earth sciences data generated via the massively parallel processor

The capability was developed of rapidly producing visual representations of large, complex, multi-dimensional space and earth sciences data sets via the implementation of computer graphics modeling techniques on the Massively Parallel Processor (MPP) by employing techniques recently developed for typically non-scientific applications. Such capabilities can provide a new and valuable tool for the understanding of complex scientific data, and a new application of parallel computing via the MPP. A prototype system with such capabilities was developed and integrated into the National Space Science Data Center's (NSSDC) Pilot Climate Data System (PCDS) data-independent environment for computer graphics data display to provide easy access to users. While developing these capabilities, several problems had to be solved independently of the actual use of the MPP, all of which are outlined.

Treinish, Lloyd A.↗