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NASA NTRS1991

Distributed memory compiler design for sparse problems

A compiler and runtime support mechanism is described and demonstrated. The methods presented are capable of solving a wide range of sparse and unstructured problems in scientific computing. The compiler takes as input a FORTRAN 77 program enhanced with specifications for distributing data, and the compiler outputs a message passing program that runs on a distributed memory computer. The runtime support for this compiler is a library of primitives designed to efficiently support irregular patterns of distributed array accesses and irregular distributed array partitions. A variety of Intel iPSC/860 performance results obtained through the use of this compiler are presented.

Wu, Janet↗
NASA NTRS1991

Complete exchange on the iPSC-860

The implementation of complete exchange on the circuit switched Intel iPSC-860 hypercube is described. This pattern, also known as all-to-all personalized communication, is the densest requirement that can be imposed on a network. On the iPSC-860, care needs to be taken to avoid edge contention, which can have a disastrous impact on communication time. There are basically two classes of algorithms that achieve contention-free complete exchange. The first contains the classical standard exchange algorithm that is generally useful for small message sizes. The second includes a number of optimal or near-optimal algorithms that are best for large messages. Measurement of communication overhead on the iPSC-860 are given and a notation for analyzing communication link usage is developed. It is shown that for the two classes of algorithms, there is substantial variation in performance with synchronization technique and choice of message protocol. Timings of six implementations are given; each of these is useful over a particular range of message size and cube dimension. Since the complete exchange is a superset of communication patterns, these timings represent upper bounds on the time required by an arbitrary communication requirement. These results indicate that the programmer needs to evaluate several possibilities before finalizing an implementation - a careful choice can lead to very significant savings in time.

Bokhari, Shahid H.↗
NASA NTRS1991

Multiphase complete exchange on a circuit switched hypercube

On a distributed memory parallel computer, the complete exchange (all-to-all personalized) communication pattern requires each of n processors to send a different block of data to each of the remaining n - 1 processors. This pattern is at the heart of many important algorithms, most notably the matrix transpose. For a circuit switched hypercube of dimension d(n = 2(sup d)), two algorithms for achieving complete exchange are known. These are (1) the Standard Exchange approach that employs d transmissions of size 2(sup d-1) blocks each and is useful for small block sizes, and (2) the Optimal Circuit Switched algorithm that employs 2(sup d) - 1 transmissions of 1 block each and is best for large block sizes. A unified multiphase algorithm is described that includes these two algorithms as special cases. The complete exchange on a hypercube of dimension d and block size m is achieved by carrying out k partial exchange on subcubes of dimension d(sub i) Sigma(sup k)(sub i=1) d(sub i) = d and effective block size m(sub i) = m2(sup d-di). When k = d and all d(sub i) = 1, this corresponds to algorithm (1) above. For the case of k = 1 and d(sub i) = d, this becomes the circuit switched algorithm (2). Changing the subcube dimensions d, varies the effective block size and permits a compromise between the data permutation and block transmission overhead of (1) and the startup overhead of (2). For a hypercube of dimension d, the number of possible combinations of subcubes is p(d), the number of partitions of the integer d. This is an exponential but very slowly growing function and it is feasible over these partitions to discover the best combination for a given message size. The approach was analyzed for, and implemented on, the Intel iPSC-860 circuit switched hypercube. Measurements show good agreement with predictions and demonstrate that the multiphase approach can substantially improve performance for block sizes in the 0 to 160 byte range. This range, which corresponds to 0 to 40 floating point numbers per processor, is commonly encountered in practical numeric applications. The multiphase technique is applicable to all circuit-switched hypercubes that use the common e-cube routing strategy.

Bokhari, Shahid H.↗
NASA NTRS1991

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Gropp, William D.↗
NASA NTRS1991

A Parallel Rendering Algorithm for MIMD Architectures

Applications such as animation and scientific visualization demand high performance rendering of complex three dimensional scenes. To deliver the necessary rendering rates, highly parallel hardware architectures are required. The challenge is then to design algorithms and software which effectively use the hardware parallelism. A rendering algorithm targeted to distributed memory MIMD architectures is described. For maximum performance, the algorithm exploits both object-level and pixel-level parallelism. The behavior of the algorithm is examined both analytically and experimentally. Its performance for large numbers of processors is found to be limited primarily by communication overheads. An experimental implementation for the Intel iPSC/860 shows increasing performance from 1 to 128 processors across a wide range of scene complexities. It is shown that minimal modifications to the algorithm will adapt it for use on shared memory architectures as well.

Crockett, Thomas W.↗
NASA NTRS1991

Mapping implicit spectral methods to distributed memory architectures

Spectral methods were proven invaluable in numerical simulation of PDEs (Partial Differential Equations), but the frequent global communication required raises a fundamental barrier to their use on highly parallel architectures. To explore this issue, a 3-D implicit spectral method was implemented on an Intel hypercube. Utilization of about 50 percent was achieved on a 32 node iPSC/860 hypercube, for a 64 x 64 x 64 Fourier-spectral grid; finer grids yield higher utilizations. Chebyshev-spectral grids are more problematic, since plane-relaxation based multigrid is required. However, by using a semicoarsening multigrid algorithm, and by relaxing all multigrid levels concurrently, relatively high utilizations were also achieved in this harder case.

Overman, Andrea L.↗
NASA NTRS1990

Integrating performance data collection, analysis, and visualization

An integrated data collection, analysis, and data visualization environment is described for a specific parallel system - the Intel iPSC/2 hypercube. The data collection components of the environment encompass software event tracing at the operating system with a program level and a hardware-based performance monitoring system used to capture software events. A visualization system based on the X-window environment permits dynamic display and reduction of performance data. A performance data collection, analysis, and visualization environment makes it possible to access the effects of architectural and system software variations.

Malony, Allen D.↗
NASA NTRS1991

Particle simulation in a multiprocessor environment

A parallel implementation of a particle simulation method that is portable between a wide class of multiprocessor computers is presented. A fine grain spatial decomposition is utilized where several subdomains having a regular structure are computed at each processing node. This leads directly to an efficient and straightforward load balancing scheme if the number of subdomains at each processor is permitted to vary in an appropriate manner. Three dimensional simulations incorporating full thermochemical nonequilibrium are possible using the resulting code. Vectorizable algorithms are retained from earlier work allowing efficient use of deeply pipelined node processors where available. Performance results are presented from three different machine architectures demonstrating the portability of the code. On a 128-node Intel iPSC/860, performance is twice that of a single Cray-Y/MP CPU running a highly vectorized simulation code. Speedup is linear over the full range of number of processors on all target machines, indicating scalability of the method to higher degrees of parallelism.

Mcdonald, Jeffrey D.↗
NASA NTRS1991

Validation of chemistry models employed in a particle simulation method

The chemistry models employed in a statistical particle simulation method, as implemented in the Intel iPSC/860 multiprocessor computer, are validated and applied. Chemical relaxation of five-species air in these reservoirs involves 34 simultaneous dissociation, recombination, and atomic-exchange reactions. The reaction rates employed in the analytic solutions are obtained from Arrhenius experimental correlations as functions of temperature for adiabatic gas reservoirs in thermal equilibrium. Favorable agreement with the analytic solutions validates the simulation when applied to relaxation of O2 toward equilibrium in reservoirs dominated by dissociation and recombination, respectively, and when applied to relaxation of air in the temperature range 5000 to 30,000 K. A flow of O2 over a circular cylinder at high Mach number is simulated to demonstrate application of the method to multidimensional reactive flows.

Haas, Brian L.↗
NASA NTRS1992

Statistical discrete particle simulation studies

A particle simulation code was developed that is suited to Multiple Instruction Multiple Data multiprocessor computers. The resulting code is designed to be portable between a large class of multiprocessor computer architectures, including hypercubes (e.g., Intel iPSC/860), shared memory machines (e.g., Cray, SGI, DASH), and simple uniprocessors (e.g., SUN, VAX, IBM PC). This code provides a powerful general framework that can be adapted to specific applications, such as thermomechanical modeling, general 3-D geometry support, or visualization support via a codeveloped CPlot data reduction and visualization system. Chemistry models were implemented and validated with comparison to continuum solutions of thermochemically relaxing gas mixtures and with experimental results from the high speed flow about a circular cylinder. Furthermore, the exchange of energy between translational and internal modes was modeled. New models were developed, combining greater efficiency than earlier phenomenological models. They offer greater physical detail by addressing vibrational energy as a discretely distributed quantity.

Mcdonald, Jeffrey D.↗
NASA NTRS1991

Instrumentation, performance visualization, and debugging tools for multiprocessors

The need for computing power has forced a migration from serial computation on a single processor to parallel processing on multiprocessor architectures. However, without effective means to monitor (and visualize) program execution, debugging, and tuning parallel programs becomes intractably difficult as program complexity increases with the number of processors. Research on performance evaluation tools for multiprocessors is being carried out at ARC. Besides investigating new techniques for instrumenting, monitoring, and presenting the state of parallel program execution in a coherent and user-friendly manner, prototypes of software tools are being incorporated into the run-time environments of various hardware testbeds to evaluate their impact on user productivity. Our current tool set, the Ames Instrumentation Systems (AIMS), incorporates features from various software systems developed in academia and industry. The execution of FORTRAN programs on the Intel iPSC/860 can be automatically instrumented and monitored. Performance data collected in this manner can be displayed graphically on workstations supporting X-Windows. We have successfully compared various parallel algorithms for computational fluid dynamics (CFD) applications in collaboration with scientists from the Numerical Aerodynamic Simulation Systems Division. By performing these comparisons, we show that performance monitors and debuggers such as AIMS are practical and can illuminate the complex dynamics that occur within parallel programs.

Yan, Jerry C.↗
NASA NTRS1992

Mapping unstructured grid computations to massively parallel computers

Investigated here is this mapping problem: assign the tasks of a parallel program to the processors of a parallel computer such that the execution time is minimized. First, a taxonomy of objective functions and heuristics used to solve the mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange (CPE), and discuss its place in the taxonomy. CPE uses local pairwise exchanges of processor assignments to iteratively improve an initial mapping. A variety of initial mapping schemes are tested and recursive spectral bipartitioning (RSB) followed by CPE is shown to result in the best mappings. For the test cases studied here, problems arising in computational fluid dynamics and structural mechanics on unstructured triangular and tetrahedral meshes, RSB and CPE outperform methods based on simulated annealing. Much less time is required to do the mapping and the results obtained are better. Compared with random and naive mappings, RSB and CPE reduce the communication time two fold for the test problems used. Finally, we use CPE in two applications on a CM-2. The first application is a data parallel mesh-vertex upwind finite volume scheme for solving the Euler equations on 2-D triangular unstructured meshes. CPE is used to map grid points to processors. The performance of this code is compared with a similar code on a Cray-YMP and an Intel iPSC/860. The second application is parallel sparse matrix-vector multiplication used in the iterative solution of large sparse linear systems of equations. We map rows of the matrix to processors and use an inner-product based matrix-vector multiplication. We demonstrate that this method is an order of magnitude faster than methods based on scan operations for our test cases.

Hammond, Steven Warren↗
NASA NTRS1992

PARTI primitives for unstructured and block structured problems

Described here is a set of primitives (PARTI) developed to efficiently execute unstructured and block structured problems on distributed memory parallel machines. We present experimental data from a 3-D unstructured Euler solver run on the Intel Touchstone Delta to demonstrate the usefulness of our methods.

Sussman, Alan↗
NASA NTRS1992

A sweep algorithm for massively parallel simulation of circuit-switched networks

A new massively parallel algorithm is presented for simulating large asymmetric circuit-switched networks, controlled by a randomized-routing policy that includes trunk-reservation. A single instruction multiple data (SIMD) implementation is described, and corresponding experiments on a 16384 processor MasPar parallel computer are reported. A multiple instruction multiple data (MIMD) implementation is also described, and corresponding experiments on an Intel IPSC/860 parallel computer, using 16 processors, are reported. By exploiting parallelism, our algorithm increases the possible execution rate of such complex simulations by as much as an order of magnitude.

Gaujal, Bruno↗
NASA NTRS1992

Fault isolation detection expert (FIDEX). Part 1: Expert system diagnostics for a 30/20 Gigahertz satellite transponder

LeRC has recently completed the design of a Ka-band satellite transponder system, as part of the Advanced Communication Technology Satellite (ACTS) System. To enhance the reliability of this satellite, NASA funded the University of Akron to explore the application of an expert system to provide the transponder with an autonomous diagnosis capability. The results of this research was the development of a prototype diagnosis expert system called FIDEX (fault-isolation and diagnosis expert). FIDEX is a frame-based expert system that was developed in the NEXPERT Object development environment by Neuron Data, Inc. It is a MicroSoft Windows version 3.0 application, and was designed to operate on an Intel i80386 based personal computer system.

Durkin, John↗
NASA NTRS1991

Compiling global name-space parallel loops for distributed execution

Distributed memory machines do not provide hardware support for a global address space. Thus programmers are forced to partition the data across the memories of the architecture and use explicit message passing to communicate data between processors. The compiler support required to allow programmers to express their algorithms using a global name-space is examined. A general method is presented for analysis of a high level source program and its translation into a set of independently executing tasks communicating via messages. If the compiler has enough information, this translation can be carried out at compile time. Otherwise, run-time code is generated to implement the required data movement. The analysis required in both situations is described and the performance of the generated code on the Intel iPSC/2 is presented.

Koelbel, Charles↗
NASA NTRS1992

Domain decomposition methods in computational fluid dynamics

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

Gropp, William D.↗
NASA NTRS1992

A real-time robot arm collision avoidance system

A data structure and update algorithm are presented for a prototype real-time collision avoidance safety system simulating a multirobot workspace. The data structure is a variant of the octree, which serves as a spatial index. An octree recursively decomposes 3D space into eight equal cubic octants until each octant meets some decomposition criteria. The N-objects octree, which indexes a collection of 3D primitive solids is used. These primitives make up the two (seven-degrees-of-freedom) robot arms and workspace modeled by the system. As robot arms move, the octree is updated to reflect their changed positions. During most update cycles, any given primitive does not change which octree nodes it is in. Thus, modification to the octree is rarely required. Cycle time for interpreting current arm joint angles, updating the octree to reflect new positions, and detecting/reporting imminent collisions averages 30 ms on an Intel 80386 processor running at 20 MHz.

Shaffer, Clifford A.↗