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Some of the parallel computational strategies are reviewed, and their adequacy assessed for a given architecture and a given problem. The performance of both extreme parallel hardware technologies on real-life structural problems is also reported.
The process of reforming supercritical quasi-parallel shocks is investigated using one-dimensional and two-dimensional hybrid (particle ion, massless fluid electron) simulations both of shocks and of simpler two-stream interactions. It is found that the supercritical quasi-parallel shock is not steady. Instread of a well-defined shock ramp between upstream and downstream states that remains at a fixed position in the flow, the ramp periodically steepens, broadens, and then reforms upstream of its former position. It is concluded that the wave generation process is localized at the shock ramp and that the reformation process proceeds in the absence of upstream perturbations intersecting the shock.
This paper continues the study of Thomas et al. (1990) in which hybrid simulations of quasi-parallel shocks were performed in one and two spatial dimensions. To identify the wave generation processes, the electromagnetic structure of the shock is examined by performing a number of one-dimensional hybrid simulations of quasi-parallel shocks for various upstream conditions. In addition, numerical experiments were carried out in which the backstreaming ions were removed from calculations to show their fundamental importance in reformation process. The calculations show that the waves are excited before ions can propagate far enough upstream to generate resonant modes. At some later times, the waves are regenerated at the leading edge of the interface, with properties like those of their initial interactions.
This paper examines the JPL/Caltech parallel processing system designed for rapid processing and transfer of large quantities of data from remote sensing instruments flown on NASA missions. Two remote sensing analysis applications that use this processing system are described: (1) an analysis system for retrieval of atmospheric parameters (such as species abundance, atmospheric temperature, and water vapor profiles) from data obtained by a Fourier transform IR spectrometer and (2) a prototype airborne SAR processing system. It is shown that a parallel processing system such as the JPL/Caltech system can offer supercomputer computational capability and high-volume data throughput and still be cost-effective.
Among the highly parallel computing architectures required for advanced scientific computation, those designated 'MIMD' and 'SIMD' have yielded the best results to date. The present development status evaluation of such architectures shown neither to have attained a decisive advantage in most near-homogeneous problems' treatment; in the cases of problems involving numerous dissimilar parts, however, such currently speculative architectures as 'neural networks' or 'data flow' machines may be entailed. Data flow computers are the most practical form of MIMD fine-grained parallel computers yet conceived; they automatically solve the problem of assigning virtual processors to the real processors in the machine.
A data parallel mesh-vertex upwind finite-volume scheme for solving the Euler equations on triangular unstructured meshes is described. A novel vertex-based partitioning of the problem is introduced which minimizes the computation and communication costs associated with distributing the computation to the processors of a massively parallel computer. Finally, the performance of this unstructured computation on 8K processors of the Connection Machine CM-2 is compared with one processor of a Cray-YMP. The experiments show that 8K processors of the CM-2 achieve approximately 70 percent of the performance of one processor of the Cray-YMP on the unstructured mesh computations described here.
Recently implemented parallel system address-tracing methods based on several metrics are surveyed. The issues specific to collection of traces for both shared and distributed memory parallel computers are highlighted. Five general categories of address-trace collection methods are examined: hardware-captured, interrupt-based, simulation-based, altered microcode-based, and instrumented program-based traces. The problems unique to shared memory and distributed memory multiprocessors are examined separately.
Model calculations are performed demonstrating the effect of weak parallel electric fields on the differential spectra of the low-energy electrons observed in the inverted-V electron precipitation events in the topside ionosphere. A comparison of the altitude dependence of the observed spectra with the model calculations shows that there can be, on average, no more than a 2-V potential drop between the altitudes of 400 and 900 km, corresponding to a distributed parallel dc electric field of less than 4 microV/m under the inverted-V electron precipitation regions. Statistical results are presented on the spectral dependence of secondary electrons on the inverted-V primary beam parameters.
A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are twofold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.
Elastic electron scattering cross sections from 5-30 eV are reported for the molecules C2H4, C2H6, C3H8, Si2H6, and GeH4, obtained using an implementation of the Schwinger multichannel method for distributed-memory parallel computer architectures. These results, obtained within the static-exchange approximation, are in generally good agreement with the available experimental data. These calculations demonstrate the potential of highly parallel computation in the study of collisions between low-energy electrons and polyatomic gases. The computational methodology discussed is also directly applicable to the calculation of elastic cross sections at higher levels of approximation (target polarization) and of electronic excitation cross sections.
Recent work on the problem of mapping pipelined or parallel computations onto linear array, shared memory, and host-satellite systems is extended. It is shown how these problems can be solved even more efficiently when computation module execution times are bounded from below, intermodule communication times are bounded from above, and the processors satisfy certain homogeneity constraints. The improved algorithms have significantly lower time and space complexities than the more general algorithms: in one case, an O(nm3) time algorithm for mapping m modules onto n processors is replaced with an O(nm log m) time algorithm, and the space requirements are reduced from O(nm2) to O(m). Run-time complexity is reduced further with parallel mapping algorithms based on these improvements, which run on the architectures for which they create mappings.
The present evaluation of alternative, massively parallel hypercube processor-applicable designs for ordered radix-2 decimation-in-frequency FFT algorithms gives attention to the reduction of computation time-dominating communication. A combination of the order and computational phases of the FFT is accordingly employed, in conjunction with sequence-to-processor maps which reduce communication. Two orderings, 'standard' and 'cyclic', in which the order of the transform is the same as that of the input sequence, can be implemented with ease on the Connection Machine (where orderings are determined by geometries and priorities. A parallel method for trigonometric coefficient computation is presented which does not employ trigonometric functions or interprocessor communication.
Run-time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run-time, wavefronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing, and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run-time reordering of loop indexes can have a significant impact on performance.
The direction of propagation of low frequency magnetic fluctuations generated by cometary ion pick-up is examined by means of 1D electromagnetic hybrid simulations. The newborn ions are injected at a constant rate, and the helicity and direction of propagation of magnetic fluctuations are explored for cometary ion injection angles of 0 and 90 deg relative to the solar wind magnetic field. The parameter eta represents the relative contribution of wave energy propagating in the direction away from the comet, parallel to the beam. For small (quasi-parallel) injection angles eta was found to be of order unity, while for larger (quasi-perpendicular) angles eta was found to be of order 0.5.
The steepening mechanism of parallel propagating low-frequency MHD-like waves observed upstream of the earth's quasi-parallel bow shock has been investigated by means of electromagnetic hybrid simulations. It is shown that an ion beam through the resonant electromagnetic ion/ion instability excites large-amplitude waves, which consequently pitch angle scatter, decelerate, and eventually magnetically trap beam ions in regions where the wave amplitudes are largest. As a result, the beam ions become bunched in both space and gyrophase. As these higher-density, nongyrotropic beam segments are formed, the hydromagnetic waves rapidly steepen, resulting in magnetic pulsations, with properties generally in agreement with observations. This steepening process operates on the scale of the linear growth time of the resonant ion/ion instability. Many of the pulsations generated by this mechanism are left-hand polarized in the spacecraft frame.
Recent observations at comets Giacobini-Zinner and Halley suggest that simple nonreacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that mass-loading is an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. The paper considers parallel magnetized shocks subjected to mass-loading, describes some properties which distinguish them from classical MHD parallel shocks, and establishes the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the comet-solar wind interaction.
Hypercluster computer system includes multiple digital processors, operation of which coordinated through specialized software. Configurable according to various parallel-computing architectures of shared-memory or distributed-memory class, including scalar computer, vector computer, reduced-instruction-set computer, and complex-instruction-set computer. Designed as flexible, relatively inexpensive system that provides single programming and operating environment within which one can investigate effects of various parallel-computing architectures and combinations on performance in solution of complicated problems like those of three-dimensional flows in turbomachines. Hypercluster software and architectural concepts are in public domain.
An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.