Connection Machine CM-2 Research Articles

A Data-Parallel FP Compiler

In data-parallel programming, operations are performed simultaneously on all elements of large data structures. Backus′s FP functional language promotes this view. FP provides a large set of data rearrangement primitives, and a useful set of functional combining forms that are applied to entire data structures. We describe an FP compiler that generates programs capable of exploiting data-parallelism. The FP compiler deduces the type and shape of objects through type inference, and generates efficient parallel implementations of combining forms. In addition, the compiler determines the effects of data rearrangement functions at compile-time, thereby avoiding creation of large intermediate data structures, and reducing interprocessor communication overhead. FP and its compiler are formally specified, reducing ambiguity concerning constructs of the language and results of the compiler. Performance and speed-ups achieved from our compilation and optimization techniques are demonstrated with timings from a prototype implementation on the Connection Machine CM-2.

Parallel adaptive finite element analysis of large scale structures

A scalable parallel feedback algorithm for adaptive finite element modeling of large scale structures is presented. This algorithm is implementable on MIMD parallel processors, and uses the p-extension of the finite element method. The problem domain is partitioned into a number of suitable subdomains by using an automatic domain decomposer, and each subdomain is thereupon assigned to a processor in the multiprocessor system. Connection Machine's CM-5 system is being used for the present implementation. Most of the previous efforts to parallelize finite element analysis were confined to parallel algorithms for direct or iterative equation solvers, and did not produce satisfactory performance because of the small granularity of parallel tasks. Also, these efforts were based on the h-extension of the finite element method, and hence could not exploit some of the inherent advantages available in the p-extension. As the current algorithm utilizes the domain decomposition technique and is based on the p-version of the finite element method, it is expected to produce good performance, particularly for large scale structures. The feedback algorithm is based on an iterative scheme derived from the domain decomposition technique for applications to problems of solid mechanics. It has been tested for two-dimensional problems showing good convergence characteristics. Current efforts are also directed towards generalizing the scheme, and include adaptive model refinement.

On the Leaving Coefficients of Real Many-Variable Polynomials

For a homogeneous polynomial P in N variables, x 1, ..., x N , of degree k, the leading terms are those which contain only one variable, raised to the power k. If 0 ≤ P ≤ 1 when all variables satisfy 0 ≤ x j ≤ 1, how large can the leading coefficients be? Estimates were given by R. Aron, B. Beauzamy, and P. Enflo ( J. Approx. Theory 74 (2) (1993), 181-198); we improve these estimates in general and solve the problem completely for k = 2 and 3. Symbolic computation (MAPLE on a Digital DecStation 5000) was heavily used at two levels: first in order to get a preliminary intuition on the concepts discussed here, and second, as symbolic manipulation on polynomials, in most proofs. Numerical analysis was made on a Connection Machine CM2, using the hypercube representation obtained by B. Beauzamy, J.-L. Frot, and C. Millour (Massively parallel computations on many-variable polynomials: When seconds count, preprint).

Data parallel computing for network-structured optimization problems

Data level parallelism is a type of parallelism whereby operations are performed on many data elements concurrently, by many processors. These operations are (more or less) identical, and are executed in a synchronous, orderly fashion. This type of parallelism is used by massively parallel SIMD (i.e., Single Instruction, Multiple Data) architectures, like the Connection Machine CM-2, the AMT DAP and Masspar, and MIMD (i.e., Multiple Instruction, Multiple Data) architectures, like the Connection Machine CM-5. Data parallelism can also be described by a theoretical model of computation: the Vector-Random Access Machine (V-RAM).

A comparative study of gauge fixing procedures on the connection machines CM2 and CM5

Gauge fixing is a frequent task encountered in practical lattice gauge theory calculations. We review the performance characterisics of some standard gauging procedures for non-Abelian gauge theories, implemented on the parallel machines CM2 and CM5.

Parallel volume rendering using binary-swap compositing

We describe a parallel volume-rendering algorithm, which consists of two parts: parallel ray tracing and parallel compositing. In the most recent implementation on Connection Machine's CM-5 and networked workstations, the parallel volume renderer evenly distributes data to the computing resources available. Without the need to communicate with other processing units, each subvolume is ray traced locally and generates a partial image. The parallel compositing process then merges all resulting partial images in depth order to produce the complete image. The compositing algorithm is particularly effective for massively parallel processing, as it always uses all processing units by repeatedly subdividing the partial images and distributing them to the appropriate processing units. Test results on both the CM-5 and the workstations are promising. They do, however, expose different performance issues for each platform.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Macro state Markov chain model for computer simulation of grand canonical ensemble

The existing Monte Carlo simulation models for the grand canonical ensemble proposed by many researchers to date use sequential state-generating schemes which require large amounts of computational time. In this study, a new Monte Carlo simulation model based on the stochastic Markov process theory for computer simulation of the grand canonical ensemble is developed. Essentially, in this new model the states in the grand canonical ensemble are grouped into macro states of the canonical ensembles, and a macro state Markov chain is established by a Monte Carlo sampling technique. This macro state Markov chain is then solved for a stationary solution. A prominent advantage of this new macro state Markov chain model is that it is suitable for massively parallel implementation, and hence the computational time required for the computer experiments can be reduced greatly. A massively parallel scheme for gas adsorption in zeolite 5A based on this model has been implemented on the Connection Machine CM2. A preliminary study shows that results are in good agreement with the experimental data available in the literature, and the simulation time is dramatically reduced in comparison with conventional sequential schemes.

EMBEDDED GRADIENT ITERATIVE SOLUTION OF A CLASS OF NONLINEAR PDE’S ON THE CONNECTION MACHINE

This study concerns the solution of a class of nonlinear second order partial differential equations on the Connection Machine CM-2 massively parallel computer. To solve the nonlinear problem, an “outer” successive approximation technique is first applied in order to iteratively linearize the problem. This results in a sequence of systems of linear equations to be solved for successive nonlinear iterates. A preconditioned conjugate gradient (CG) method is used to solve each “inner” linear system. Either Jacobi preconditioning or a fast direct solver is employed as preconditioner for the conjugate gradient method. The implementation of these methods on the Connection Machine is discussed, and the results of numerical experiments with nested iteration are presented.

Experiences in the pricing of trivariate contingent claims with finite difference methods on a massively parallel computer

Finite difference schemes have proved to be very flexible numerical methods for the pricing of contingent claims with one and two underlying state variables. This flexibility and the steady stream of new complex financial instruments imply that finite difference schemes for the valuation of contingent claims with three underlying state variables can supposedly be very useful. In this paper, two such schemes are developed and tested. For practical purposes, numerical valuation of contingent claims with three underlying state variables by means of finite difference methods is probably too laborious computationally to be performed on a single processor computer. Many calculations can, however, be performed in parallel. Therefore, the methods are well suited to be executed on a massively parallel computer, like the Connection Machine CM-200, which is used in this paper. The accuracy of the schemes proposed in this paper suggests that valuation of multivariate contingent claims with the help of finite difference methods on a massively parallel computer can be a useful approach for academics as well as practitioners.

Large scale natural vision simulations

A computationally intensive approach to pattern recognition in images is developed and applied to face recognition. Similarly to previous work, we compute functional inner products of a two-dimensional input signal (image) with a set of two-dimensional Gabor functions which fit the receptive fields of simple cells in the primary visual cortex of mammals. The proposed model includes nonlinearities, such as thresholding, orientation competition and lateral inhibition. The output of the model is a set of cortical images each of which contains only edge lines of a particular orientation in a particular light-to-dark transition direction. In this way the information of the original image is split into different channels. The cortical images are used to compute a lower-dimension space representation for object recognition. The method was implemented on the Connection Machine CM-5 1 1 Most of the computation were carried out on the Connection Machine CM-5 of the University of Groningen, the investments in which were partly supported by the Netherlands Computer Science Research Foundation (SION) and the Netherlands Organization for Scientific Research (NWO). and achieved a recognition rate of 97% when applied to a large database of face images.

Implementation of a Portable Nested Data-Parallel Language

This paper gives an overview of the implementation of NESL, a portable nested data-parallel language. This language and its implementation are the first to fully support nested data structures as well as nested data-parallel function calls. These features allow the concise description of parallel algorithms on irregular data, such as sparse matrices and graphs. In addition, they maintain the advantages of data-parallel languages: a simple programming model and portability. The current NESL implementation is based on an intermediate language called VCODE and a library of vector routines called CVL. It runs on the Connection Machines CM-2 and CM-5, the Cray Y-MP C90, and serial workstations. We compare initial benchmark results of NESL, with those of machine-specific code on these machines for three algorithms: least-squares line-fitting, median finding, and a sparse-matrix vector product. These results show that NESL′s performance is competitive with that of machine-specific codes for regular dense data, and is often superior for irregular data.

Massively Parallel Monte Carlo Simulations On Cm2 for Gas Adsorption in Zeolite Molecular Sieves

A massively parallel scheme for gas adsorption in zeo lite molecular sieves based on the Macro State Markov Chain Model (Chen, 1993; Chen and Hirtzel, 1993a) has been developed and implemented on the Connection Machine CM2. Implementation details that are impor tant in achieving high efficiency of the parallel algo rithm are described. The results show that the parallel implementation is very efficient, and that simulation time is dramatically reduced in comparison with con ventional sequential schemes.

An efficient communications strategy for finite element methods on the Connection Machine CM-5 system

The objective of this paper is to propose communication procedures suitable for unstructured finite element solvers implemented on distributed-memory parallel computers such as the Connection Machine CM-5 system. First, a data-parallel implementation of the recursive spectral bisection (RSB) algorithm proposed by Pothen et al. is presented. The RSB algorithm is associated with a node renumbering scheme which improves data locality of reference. Two-step gather and scatter operations taking advantage of this data locality are then designed. These communication primitives make use of the indirect addressing capability of the CM-5 vector units to achieve high gather and scatter bandwidths. The performance of the proposed communication strategy is illustrated on large-scale three-dimensional fluid dynamics problems.

Low-energy neutral atom emission from the Earth's magnetosphere

Imaging of the terrestrial magnetosphere is possible through the detection of low-energy neutral atoms (LENA5) produced by charge exchange between magnetospheric plasma ions and neutral atoms of the Earth's geocorona. We present calculations of both hydrogen and oxygen line-of-sight LENA fluxes expected on orbit for various plasma regimes as predicted by the Rice University Magnetospheric Specification Model. To decrease the required computation time, we are in the process of adapting our code for massively parallel computers. The speed gains achieved from parallel algorithms are substantial, and we present results from computational runs on the Connection Machine CM-2 data parallel supercomputer. We also estimate expected image count rates and image quality based on realistic instrument geometric factors, energy passbands, neutral atom scattering in the instrument, and image accumulation intervals. The results indicate that LENA imaging instruments will need a geometric factor ( G ) on the order of 0.1 cm 2 sr eV/eV to be capable of imaging storm time ring currents, and a G of 1.0 cm 2 sr eV/eV in order to image the quiet time ring current fluxes, ion injections from the tail, and subsequent ion drifts toward the dayside magnetopause.

A REAL-TIME NETWORK TRAFFIC SIMULATION MODEL FOR ATMS APPLICATIONS: PART II—MASSIVELY PARALLEL MODEL

Abstract This paper presents three traffic network simulation models implemented on massively parallel computer, the Connection Machine CM-2. The proposed simulation models have been parallelized to take advantage of the parallel computers since they can offer the required computational power at an economical cost/performance ratio. The paper presents detailed discussion of parallel data structure and parallel logic for each simulation model. Several simulation experiments have been carried out to compare the execution speed of each methodology. The preliminary research results indicate that parallel computing architecture offers a very promising alternative for the implementation of real-time traffic simulation.

Generic parallel adaptive-grid Navier-Stokes algorithm

A parallel adaptive-grid Navier-Stokes algorithm based on generic primitives has been developed. The parallel primitives are general for the class of explicit finite-volume Navier-Stokes numerical schemes. Furthermore, they allowed relatively simple implementation of the algorithm on two different parallel systems; an eight-processor Cray Y-MP and the Connection Machine CM-2. A novel data structure for the adaptive grid allowed efficient parallel refinement/coarsening of the mesh. Substantial speeds compared to the corresponding sequential algorithm were realized on both systems. I. Introduction C OMPUTATIONAL fluid dynamics (CFD) has advanced rapidly over the last two decades, and it is recognized as a valuable tool for engineering design. However, numerical simulation of viscous flowfields remains very expensive even with use of current vector computers. Advances in numerical algorithms are not expected to reduce the cost of those computations to the extent that they can routinely be applied for design. Vector computers accelerated computations by one or two orders of magnitude compared to scalar machines, which is not sufficient for efficient large-scale flow simulations. Another approach to computer architectures has been employment of a number of processors that work in parallel executing the same job. Parallel computing appears to be a promising approach for future design applications of CFD. Development of CFD applications on state-of-the-art parallel machines currently requires considerable effort on the part of the user to understand the intricacies of the underlying architecture and fine tune the application to match them. Most of the effort has to be duplicated when the same application has to be ported to another machine. All of this inefficiency can be eliminated to a large extent by allowing the user to design the application in a machine-independent fashion using general primitives. Several parallel algorithms have been developed in the past. The architectures that have been employed include the Cray Y-MP/8,1'2 as well as the Connection Machine CM-2.35 Many of the applications to date have dealt with structured meshes, in which data is stored in a regular manner. Unstructured grid solvers have also been developed.4'6'7 A large number of the parallel CFD codes have been developed for a specific architecture, and portability of the algorithms has not been considered. Adaptive algorithms have become quite popular in CFD. They provide flexibility to adjust the grid during the solution procedure without intervention by the user.810 Those adaptive grid algorithms have been developed for sequential execution and have reached a level of maturity. However, the area of parallel adaptive algorithms is relatively unexplored.1 The present work develops a parallel adaptive algorithm that employs generic primitives. Those parallel primitives are

MIMD VERSUS SIMD COMPUTATION: EXPERIENCE WITH NON-NUMERIC PARALLEL ALGORITHMS∗ †

We focus on differences inherent in the design and implementation of non-numeric parallel algorithms on MIMD and SIMD architectures. We take as our prototypical examples time-space optimal merging and sorting routines. Our representative MIMD and SIMD machines are the Sequent Symmetry S81 and the Connection Machine CM-2, respectively. In addition to the contrast provided by their differing execution philosophies, this choice of machines allows us to compare results from both shared-memory and distributed-memory models. Unlike many numerical parallel algorithms, non-numeric parallel programs are rarely well structured with respect to inter-processor cooperation, memory access and communication patterns. This is particularly apparent when one must deal with delicate issues such as process synchronization in the MIMD model and coding variations in the SIMD model. Our experiences are highlighted with examples obtained during the process of MIMD to SIMD program transformation Unexpected events can occur when a...

Similarity searching in files of three-dimensional chemical structures. Implementation of atom mapping on the distributed array processor DAP-610, the MasPar MP-1104, and the connection machine CM-200

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Microscopic traffic modeling on parallel high performance computers

A simple, rule-based approach to traffic flow can yield astonishingly realistic results and is therefore a candidate for very fast large scale microscopic traffic simulations. In the present article, we evaluate two conceptually different codings of the same dynamics on parallel supercomputers. We use a Parsytec GCel-3 (1024 nodes), an Intel iPSC/860 (32 nodes), and a Connection Machine CM-5 (32 nodes). For comparison purposes, we use as well a NEC-SX3/11 traditional single node vector computer, and a net of coupled workstations. Compared to published computing speeds of microscopic traffic models, our model proves to be up to about 1000 times faster. We find our highest computing speed by employing a single-bit coding scheme used in, e.g., Ising-model programming. As traffic flow is a one-dimensional problem, a complication is that geometric parallelization has to be done in the same direction as single-bit coding. Nevertheless, we reach efficiencies near 100 percent for large systems. We use these computational resources in order to obtain high quality data of the model's average behavior (fundamental diagrams). In addition, we present results from modeling a road network, whose composition out of basic objects leads in a natural way to some temporal ‘slackness’ which helps balancing load asymmetries.

THE STATIC QUARK-ANTIQUARK-POTENTIAL: A 'CLASSICAL' EXPERIMENT ON THE CONNECTION MACHINE CM-2

This meeting produces another evidence that present parallel computers are (a) real instruments of computational physics, (b) largely in the hands of still-pioneers, (c) efficiently promoted by basic research groups with large-scale computational needs. Progress in parallel computing is carried by two types of such groups, that either follow the build-it-yourself or the early-use strategies. In this contribution, we describe, as an example to the second approach, the Wuppertal university pilot project in applied parallel computing. We report in particular about one of our key applications in theoretical particle physics on the Connection Machine CM-2: a high statistics computer experiment to determine the static quark-antiquark potential from quenched quantum chromodynamics.