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Explicit and implicit solution of the Navier-Stokes equations on a massively parallel computer

The design, implementation, and performance of a two-dimensional time-accurate Navier-Stokes solver for the CM2 supercomputer are described. The program uses a single processor for each grid point. Two different time-stepping methods have so far been implemented: an explicit third-order Runge-Kutta method and an implicit approximation-factorization method. The CM2 results are checked against those of a mature well-vectorized Cray 2 program, both for correctness and performance. The code is found to be correct, and the performance in some cases is up to several times that of the Cray 2.

Levit, Creon

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.

Progressive Vector Quantization on a massively parallel SIMD machine with application to multispectral image data

A progressive vector quantization (VQ) compression approach is discussed which decomposes image data into a number of levels using full search VQ. The final level is losslessly compressed, enabling lossless reconstruction. The computational difficulties are addressed by implementation on a massively parallel SIMD machine. We demonstrate progressive VQ on multispectral imagery obtained from the Advanced Very High Resolution Radiometer instrument and other Earth observation image data, and investigate the trade-offs in selecting the number of decomposition levels and codebook training method.

Manohar, Mareboyana

Computational fluid dynamics on a massively parallel computer

A finite difference code was implemented for the compressible Navier-Stokes equations on the Connection Machine, a massively parallel computer. The code is based on the ARC2D/ARC3D program and uses the implicit factored algorithm of Beam and Warming. The codes uses odd-even elimination to solve linear systems. Timings and computation rates are given for the code, and a comparison is made with a Cray XMP.

Jespersen, Dennis C.

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.

A simple atmospheric model on the sphere with 100% parallelism

A simple shallow water equations model used to test numerical weather prediction schemes is presented. The spherical geometry is transformed into a formally doubly periodic configuration which can be implemented on a massively parallel computer at 100% parallelism. A nonstaggered grid with all variables defined at the grid points (circles) is used. The parallel structure was simulated by performing step 1 in a FORTRAN array, on an Amdahl serial machine, changing the signs of the winds on the dark side.

Kalnay, E.

Linear static structural and vibration analysis on high-performance computers

Parallel computers offer the oppurtunity to significantly reduce the computation time necessary to analyze large-scale aerospace structures. This paper presents algorithms developed for and implemented on massively-parallel computers hereafter referred to as Scalable High-Performance Computers (SHPC), for the most computationally intensive tasks involved in structural analysis, namely, generation and assembly of system matrices, solution of systems of equations and calculation of the eigenvalues and eigenvectors. Results on SHPC are presented for large-scale structural problems (i.e. models for High-Speed Civil Transport). The goal of this research is to develop a new, efficient technique which extends structural analysis to SHPC and makes large-scale structural analyses tractable.

Baddourah, M. A.

An implementation of a barotropic quasigeostrophic model of ocean circulation on the MPP

The implementation on the Massively Parallel Processor (MPP) of a barotropic quasigeostrophic model of ocean circulation is discussed. The mathematical model, including scalings and boundary conditions is discussed. The numerical scheme, which uses compact differencing is also discussed. The implementation of this model on the MPP is then presented. Finally, some performance results are given and compared to results obtained using the VPS-32 and one processor of a CRAY-2.

Grosch, C. E.

Solving very large, sparse linear systems on mesh-connected parallel computers

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

Opsahl, Torstein

Automated matching of pairs of SIR-B images for elevation mapping

During the SIR-B mission in October 1984, a significant number of overlapping synthetic aperture radar (SAR) images of various ground areas was collected. This has offered the first opportunity to perform stereo analyses on images from space that cover large ground areas to determine elevation information. This paper presents the preliminary results of an investigation to obtain elevation data from stereo pairs of SIR-B images. First, the accuracy with which elevation information can be derived from SIR-B image pairs is evaluated theoretically. It is shown that elevation accuracy is a function of the slant range resolution, the incidence angles with which the stereo pair is obtained, the accuracies in spacecraft state estimation, and determination of corresponding pixels in the stereo pair. Next, a hierarchical method is developed to match the corresponding pixels. This method involves iterative removal of local distortions and correlations of pairs of local neighborhoods in the two images. Since it is necessary to perform the matching at every pixel in the image, it is very computationally intensive. Therefore, it has been implemented on the Massively Parallel Processor (MPP) at the Goddard Space Flight Center (GSFC). The MPP's speed permits two iterations of this technique to operate on a pair of 512 x 512 images within 7 s. Results of applying this algorithm of SIR-B images of Mount Shasta, CA, are shown. The matching algorithm performs well in regions of the image with significant features. An approximate elevation image derived from the matching process corresponds to published topographic map data, except for certain obvious discontinuities.

Ramapriyan, H. K.

Image analysis by integration of disparate information

Image analysis often starts with some preliminary segmentation which provides a representation of the scene needed for further interpretation. Segmentation can be performed in several ways, which are categorized as pixel based, edge-based, and region-based. Each of these approaches are affected differently by various factors, and the final result may be improved by integrating several or all of these methods, thus taking advantage of their complementary nature. In this paper, we propose an approach that integrates pixel-based and edge-based results by utilizing an iterative relaxation technique. This approach has been implemented on a massively parallel computer and tested on some remotely sensed imagery from the Landsat-Thematic Mapper (TM) sensor.

Lemoigne, Jacqueline

Constraint-Based Scheduling System

Report describes continuing development of software for constraint-based scheduling system implemented eventually on massively parallel computer. Based on machine learning as means of improving scheduling. Designed to learn when to change search strategy by analyzing search progress and learning general conditions under which resource bottleneck occurs.

Zweben, Monte

Computation and parallel implementation for early vision

The problem of early vision is to transform one or more retinal illuminance images-pixel arrays-to image representations built out of such primitive visual features such as edges, regions, disparities, and clusters. These transformed representations form the input to later vision stages that perform higher level vision tasks including matching and recognition. Researchers developed algorithms for: (1) edge finding in the scale space formulation; (2) correlation methods for computing matches between pairs of images; and (3) clustering of data by neural networks. These algorithms are formulated for parallel implementation of SIMD machines, such as the Massively Parallel Processor, a 128 x 128 array processor with 1024 bits of local memory per processor. For some cases, researchers can show speedups of three orders of magnitude over serial implementations.

Gualtieri, J. Anthony

Parallel Implicit Algorithms for CFD

The main goal of this project was efficient distributed parallel and workstation cluster implementations of Newton-Krylov-Schwarz (NKS) solvers for implicit Computational Fluid Dynamics (CFD.) "Newton" refers to a quadratically convergent nonlinear iteration using gradient information based on the true residual, "Krylov" to an inner linear iteration that accesses the Jacobian matrix only through highly parallelizable sparse matrix-vector products, and "Schwarz" to a domain decomposition form of preconditioning the inner Krylov iterations with primarily neighbor-only exchange of data between the processors. Prior experience has established that Newton-Krylov methods are competitive solvers in the CFD context and that Krylov-Schwarz methods port well to distributed memory computers. The combination of the techniques into Newton-Krylov-Schwarz was implemented on 2D and 3D unstructured Euler codes on the parallel testbeds that used to be at LaRC and on several other parallel computers operated by other agencies or made available by the vendors. Early implementations were made directly in Massively Parallel Integration (MPI) with parallel solvers we adapted from legacy NASA codes and enhanced for full NKS functionality. Later implementations were made in the framework of the PETSC library from Argonne National Laboratory, which now includes pseudo-transient continuation Newton-Krylov-Schwarz solver capability (as a result of demands we made upon PETSC during our early porting experiences). A secondary project pursued with funding from this contract was parallel implicit solvers in acoustics, specifically in the Helmholtz formulation. A 2D acoustic inverse problem has been solved in parallel within the PETSC framework.

Keyes, David E.

Hierarchical Image Segmentation of Remotely Sensed Data using Massively Parallel GNU-LINUX Software

A hierarchical set of image segmentations is a set of several image segmentations of the same image at different levels of detail in which the segmentations at coarser levels of detail can be produced from simple merges of regions at finer levels of detail. In [1], Tilton, et a1 describes an approach for producing hierarchical segmentations (called HSEG) and gave a progress report on exploiting these hierarchical segmentations for image information mining. The HSEG algorithm is a hybrid of region growing and constrained spectral clustering that produces a hierarchical set of image segmentations based on detected convergence points. In the main, HSEG employs the hierarchical stepwise optimization (HSWO) approach to region growing, which was described as early as 1989 by Beaulieu and Goldberg. The HSWO approach seeks to produce segmentations that are more optimized than those produced by more classic approaches to region growing (e.g. Horowitz and T. Pavlidis, [3]). In addition, HSEG optionally interjects between HSWO region growing iterations, merges between spatially non-adjacent regions (i.e., spectrally based merging or clustering) constrained by a threshold derived from the previous HSWO region growing iteration. While the addition of constrained spectral clustering improves the utility of the segmentation results, especially for larger images, it also significantly increases HSEG s computational requirements. To counteract this, a computationally efficient recursive, divide-and-conquer, implementation of HSEG (RHSEG) was devised, which includes special code to avoid processing artifacts caused by RHSEG s recursive subdivision of the image data. The recursive nature of RHSEG makes for a straightforward parallel implementation. This paper describes the HSEG algorithm, its recursive formulation (referred to as RHSEG), and the implementation of RHSEG using massively parallel GNU-LINUX software. Results with Landsat TM data are included comparing RHSEG with classic region growing.

Tilton, James C.

Block iterative restoration of astronomical images with the massively parallel processor

A method is described for algebraic image restoration capable of treating astronomical images. For a typical 500 x 500 image, direct algebraic restoration would require the solution of a 250,000 x 250,000 linear system. The block iterative approach is used to reduce the problem to solving 4900 121 x 121 linear systems. The algorithm was implemented on the Goddard Massively Parallel Processor, which can solve a 121 x 121 system in approximately 0.06 seconds. Examples are shown of the results for various astronomical images.

Heap, Sara R.

Implementation of Helioseismic Data Reduction and Diagnostic Techniques on Massively Parallel Architectures

Under the direction of Dr. Rhodes, and the technical supervision of Dr. Korzennik, the data assimilation of high spatial resolution solar dopplergrams has been carried out throughout the program on the Intel Delta Touchstone supercomputer. With the help of a research assistant, partially supported by this grant, and under the supervision of Dr. Korzennik, code development was carried out at SAO, using various available resources. To ensure cross-platform portability, PVM was selected as the message passing library. A parallel implementation of power spectra computation for helioseismology data reduction, using PVM was successfully completed. It was successfully ported to SMP architectures (i.e. SUN), and to some MPP architectures (i.e. the CM5). Due to limitation of the implementation of PVM on the Cray T3D, the port to that architecture was not completed at the time.

Korzennik, Sylvain

Climate Data Assimilation on a Massively Parallel Supercomputer

We have designed and implemented a set of highly efficient and highly scalable algorithms for an unstructured computational package, the PSAS data assimilation package, as demonstrated by detailed performance analysis of systematic runs on up to 512-nodes of an Intel Paragon. The preconditioned Conjugate Gradient solver achieves a sustained 18 Gflops performance. Consequently, we achieve an unprecedented 100-fold reduction in time to solution on the Intel Paragon over a single head of a Cray C90. This not only exceeds the daily performance requirement of the Data Assimilation Office at NASA's Goddard Space Flight Center, but also makes it possible to explore much larger and challenging data assimilation problems which are unthinkable on a traditional computer platform such as the Cray C90.

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