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NASA NTRS1993

Analysis of multigrid methods on massively parallel computers: Architectural implications

We study the potential performance of multigrid algorithms running on massively parallel computers with the intent of discovering whether presently envisioned machines will provide an efficient platform for such algorithms. We consider the domain parallel version of the standard V cycle algorithm on model problems, discretized using finite difference techniques in two and three dimensions on block structured grids of size 10(exp 6) and 10(exp 9), respectively. Our models of parallel computation were developed to reflect the computing characteristics of the current generation of massively parallel multicomputers. These models are based on an interconnection network of 256 to 16,384 message passing, 'workstation size' processors executing in an SPMD mode. The first model accomplishes interprocessor communications through a multistage permutation network. The communication cost is a logarithmic function which is similar to the costs in a variety of different topologies. The second model allows single stage communication costs only. Both models were designed with information provided by machine developers and utilize implementation derived parameters. With the medium grain parallelism of the current generation and the high fixed cost of an interprocessor communication, our analysis suggests an efficient implementation requires the machine to support the efficient transmission of long messages, (up to 1000 words) or the high initiation cost of a communication must be significantly reduced through an alternative optimization technique. Furthermore, with variable length message capability, our analysis suggests the low diameter multistage networks provide little or no advantage over a simple single stage communications network.

Matheson, Lesley R.↗

NASA NTRS1985

Algorithms and programming tools for image processing on the MPP, introduction

The programming tools and parallel algorithms created for the Massively Parallel Processor (MPP) located at the NASA Goddard Space Center are discussed. A user-friendly environment for high level language parallel algorithm development was developed. The issues involved in implementing certain algorithms on the MPP were researched. The expected results were compared with the actual results.

Source record↗

NASA NTRS1988

Scan line graphics generation on the massively parallel processor

Described here is how researchers implemented a scan line graphics generation algorithm on the Massively Parallel Processor (MPP). Pixels are computed in parallel and their results are applied to the Z buffer in large groups. To perform pixel value calculations, facilitate load balancing across the processors and apply the results to the Z buffer efficiently in parallel requires special virtual routing (sort computation) techniques developed by the author especially for use on single-instruction multiple-data (SIMD) architectures.

Dorband, John E.↗

DOE OSTI2022

Virtual Time III, Part 2: Combining Conservative and Optimistic Synchronization

This is Part 2 of a trio of works intended to provide a unifying framework in which conservative and optimistic synchronization for parallel discrete event simulations can be freely and transparently combined in the same logical process on an event-by-event basis. Here, in this article, we continue the outline of an approach called Unified Virtual Time (UVT) that was introduced in Part 1, showing in detail via two extended examples how conservative synchronization can be refactored and combined with optimistic synchronization in the UVT framework. We describe UVT versions of both a basic time windowing algorithm called Unified Simple Time Windows and a refactored version of the Chandy-Misra-Bryant Null Message algorithm called Unified CMB.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Image segmentation by iterative parallel region growing and splitting

The spatially constrained clustering (SCC) iterative parallel region-growing technique is applied to image analysis. The SCC algorithm is implemented on the massively parallel processor at NASA Goddard. Most previous region-growing approaches have the drawback that the segmentation produced depends on the order in which portions of the image are processed. The ideal solution to this problem (merging only the single most similar pair of spatially adjacent regions in the image in each iteration) becomes impractical except for very small images, even on a massively parallel computer. The SCC algorithm overcomes these problems by performing, in parallel, the best merge within each of a set of local, possibly overlapping, subimages. A region-splitting stage is also incorporated into the algorithm, but experiments show that region splitting generally does not improve segmentation results. The SCC algorithm has been tested on various imagery data, and test results for a Landsat TM image are summarized.

Tilton, James C.↗

NASA NTRS1987

An application of the MPP to the interactive manipulation of stereo images of digital terrain models

Massively Parallel Processor algorithms were developed for the interactive manipulation of flat shaded digital terrain models defined over grids. The emphasis is on real time manipulation of stereo images. Standard graphics transformations are applied to a 128 x 128 grid of elevations followed by shading and a perspective projection to produce the right eye image. The surface is then rendered using a simple painter's algorithm for hidden surface removal. The left eye image is produced by rotating the surface 6 degs about the viewer's y axis followed by a perspective projection and rendering of the image as described above. The left and right eye images are then presented on a graphics device using standard stereo technology. Performance evaluations and comparisons are presented.

Pol, Sanjay↗

NASA NTRS2009

Bio-Inspired Neural Model for Learning Dynamic Models

A neural-network mathematical model that, relative to prior such models, places greater emphasis on some of the temporal aspects of real neural physical processes, has been proposed as a basis for massively parallel, distributed algorithms that learn dynamic models of possibly complex external processes by means of learning rules that are local in space and time. The algorithms could be made to perform such functions as recognition and prediction of words in speech and of objects depicted in video images. The approach embodied in this model is said to be "hardware-friendly" in the following sense: The algorithms would be amenable to execution by special-purpose computers implemented as very-large-scale integrated (VLSI) circuits that would operate at relatively high speeds and low power demands.

Duong, Tuan↗

NASA NTRS1989

Ordered fast fourier transforms on a massively parallel hypercube multiprocessor

Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine.

Tong, Charles↗

NASA NTRS1991

Computations on the massively parallel processor at the Goddard Space Flight Center

Described are four significant algorithms implemented on the massively parallel processor (MPP) at the Goddard Space Flight Center. Two are in the area of image analysis. Of the other two, one is a mathematical simulation experiment and the other deals with the efficient transfer of data between distantly separated processors in the MPP array. The first algorithm presented is the automatic determination of elevations from stereo pairs. The second algorithm solves mathematical logistic equations capable of producing both ordered and chaotic (or random) solutions. This work can potentially lead to the simulation of artificial life processes. The third algorithm is the automatic segmentation of images into reasonable regions based on some similarity criterion, while the fourth is an implementation of a bitonic sort of data which significantly overcomes the nearest neighbor interconnection constraints on the MPP for transferring data between distant processors.

Strong, James P.↗

NASA NTRS1987

A fast MPP algorithm for Ising spin exchange simulations

A very efficient massively parallel processor (MPP) algorithm is described for performing one important class of Ising spin simulations. Results and physical significance of MPP calculations using the method described is discussed elsewhere. A few comments, however, are made on the problem under study and results so far are reported. Ted Einstein provided guidance in interpreting the initial results and in suggesting calculations to perform.

Sullivan, Francis↗

NASA NTRS1997

Massively Parallel and Scalable Implicit Time Integration Algorithms for Structural Dynamics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because of the following additional facts: (a) explicit schemes are easier to parallelize than implicit ones, and (b) explicit schemes induce short range interprocessor communications that are relatively inexpensive, while the factorization methods used in most implicit schemes induce long range interprocessor communications that often ruin the sought-after speed-up. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet be offset by the speed of the currently available parallel hardware. Therefore, it is essential to develop efficient alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating the low-frequency dynamics of aerospace structures.

Farhat, Charbel↗

NASA NTRS1990

Highly parallel sparse Cholesky factorization

Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.

Gilbert, John R.↗

NASA NTRS1988

The 2nd Symposium on the Frontiers of Massively Parallel Computations

Programming languages, computer graphics, neural networks, massively parallel computers, SIMD architecture, algorithms, digital terrain models, sort computation, simulation of charged particle transport on the massively parallel processor and image processing are among the topics discussed.

Mills, Ronnie↗

NASA NTRS1991

Parallel Methods on Large-Scale Structural Analysis and Physics Applications; Symposium, Hampton, VA, Feb. 5, 6, 1991, Selected Papers

Recent advances in parallel methods and algorithms integrated into large-scale codes are presented. Consideration is given to problem decomposition (substructuring), efficient matrix solution algorithms for shared memory architectures, dynamic and transient analysis algorithms for shared memory architectures, and algorithms for distributed and massively parallel architectures. Particular attention is given to partitioning of unstructured problems for parallel processing, parallel-vector computation for linear-structural analysis and nonlinear unconstraint optimization problems, a parallel-vector equation solver for unsymmetric matrices on supercomputers, parallel nonlinear finite element dynamic response, multigrid algorithms for solving structural mechanics problems on supercomputers, structural analysis on massively parallel computers, explicit finite element methods with contact-impact on SIMD computers, and the impact of mapping and sparsity on parallelized finite element method modules.

Storaasli, Olaf O.↗

NASA NTRS1987

Report from the MPP Working Group to the NASA Associate Administrator for Space Science and Applications

NASA's Office of Space Science and Applications (OSSA) gave a select group of scientists the opportunity to test and implement their computational algorithms on the Massively Parallel Processor (MPP) located at Goddard Space Flight Center, beginning in late 1985. One year later, the Working Group presented its report, which addressed the following: algorithms, programming languages, architecture, programming environments, the way theory relates, and performance measured. The findings point to a number of demonstrated computational techniques for which the MPP architecture is ideally suited. For example, besides executing much faster on the MPP than on conventional computers, systolic VLSI simulation (where distances are short), lattice simulation, neural network simulation, and image problems were found to be easier to program on the MPP's architecture than on a CYBER 205 or even a VAX. The report also makes technical recommendations covering all aspects of MPP use, and recommendations concerning the future of the MPP and machines based on similar architectures, expansion of the Working Group, and study of the role of future parallel processors for space station, EOS, and the Great Observatories era.

Fischer, James R.↗

NASA NTRS1980

Inventory estimation on the massively parallel processor

This paper describes algorithms for efficiently computing inventory estimates from satellite based images. The algorithms incorporate a one dimensional feature extraction which optimizes the pairwise sum of Fisher distances. Biases are eliminated with a premultiplication by the inverse of the analytically derived error matrix. The technique is demonstrated with a numerical example using statistics obtained from an actual Landsat scene. Attention was given to implementation of the Massively Parallel processor (MPP). A timing analysis demonstrates that the inventory estimation can be performed an order of magnitude faster on the MPP than on a conventional serial machine.

Argentiero, P. D.↗

NASA NTRS1987

Parallel image compression

A parallel compression algorithm for the 16,384 processor MPP machine was developed. The serial version of the algorithm can be viewed as a combination of on-line dynamic lossless test compression techniques (which employ simple learning strategies) and vector quantization. These concepts are described. How these concepts are combined to form a new strategy for performing dynamic on-line lossy compression is discussed. Finally, the implementation of this algorithm in a massively parallel fashion on the MPP is discussed.

Reif, John H.↗

NASA NTRS1984

Function algorithms for MPP scientific subroutines, volume 1

Design documentation and user documentation for function algorithms for the Massively Parallel Processor (MPP) are presented. The contract specifies development of MPP assembler instructions to perform the following functions: natural logarithm; exponential (e to the x power); square root; sine; cosine; and arctangent. To fulfill the requirements of the contract, parallel array and solar implementations for these functions were developed on the PDP11/34 Program Development and Management Unit (PDMU) that is resident at the MPP testbed installation located at the NASA Goddard facility.

Gouch, J. G.↗