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The Institute for Computer Applications in Science and Engineering computer science program is discussed in outline form. Information is given on such topics as problem decomposition, algorithm development, programming languages, and parallel architectures.
Over the past 15 years numerous new techniques have been developed for solving systems of equations and eigenvalue problems arising in finite element computations. A package called SPARSPAK has been developed by the author and his co-workers which exploits these new methods. The broad objective of this research project is to incorporate some of this software in the Computational Structural Mechanics (CSM) testbed, and to extend the techniques for use on multiprocessor architectures.
An efficient O(mN) algorithm for dynamic simulation of simple closed-chain robotic mechanisms is presented, where m is the number of chains, and N is the number of degrees of freedom for each chain. It is based on computation of the operational space inertia matrix (6 x 6) for each chain as seen by the body, load, or object. Also, computation of the chain dynamics, when opened at one end, is required, and the most efficient algorithm is used for this purpose. Parallel implementation of the dynamics for each chain results in an O(N) + O(log sub 2 m+1) algorithm.
A Choleski method is described and used to solve linear systems of equations that arise in large scale structural analysis. The method uses a novel variable-band storage scheme and is structured to exploit fast local memory caches while minimizing data access delays between main memory and vector registers. Several parallel implementations of this method are described for the CRAY-2 and CRAY Y-MP computers demonstrating the use of microtasking and autotasking directives. A portable parallel language, FORCE, is used for comparison with the microtasked and autotasked implementations. Results are presented comparing the matrix factorization times for three representative structural analysis problems from runs made in both dedicated and multi-user modes on both computers. CPU and wall clock timings are given for the parallel implementations and are compared to single processor timings of the same algorithm.
Algorithm-to-architecture mapping model (ATAMM) is strategy minimizing time needed to periodically execute graphically described, data-driven application algorithm on multiple data processors. Implemented as operating system managing flow of data and dynamically assigns nodes of graph to processors. Predicts throughput versus number of processors available to execute given application algorithm. Includes rules ensuring application algorithm represented by graph executed periodically without deadlock and in shortest possible repetition time. ATAMM proves useful in maximizing effectiveness of parallel computing systems.
The MAP algorithm is a trellis-based maximum a posteriori probability decoding algorithm. It is the heart of the turbo (or iterative) decoding which achieves an error performance near the Shannon limit. Unfortunately, the implementation of this algorithm requires large computation and storage. Furthermore, its forward and backward recursions result in long decoding delay. For practical applications, this decoding algorithm must be simplified and its decoding complexity and delay must be reduced. In this paper, the MAP algorithm and its variations, such as Log-MAP and Max-Log-MAP algorithms, are first applied to sectionalized trellises for linear block codes and carried out as two-stage decodings. Using the structural properties of properly sectionalized trellises, the decoding complexity and delay of the MAP algorithms can be reduced. Computation-wise optimum sectionalizations of a trellis for MAP algorithms are investigated. Also presented in this paper are bi-directional and parallel MAP decodings.
Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.
In this paper we present the results of a series of numerical experiments done on the propagation and initiation of a detonation wave. The calculations are performed in one-dimension, with considerable grid resolution. Of particular interest are the following questions: (1) the nature of periodic and chaotic instabilities generated by the wave; (2) the influence of the grid resolution on these instabilities; (3) the influence of the 'quality' of the numerical scheme; and (4) the influence of 'noise'. In the calculations, we use a second-order Total Variation Diminishing (TVD) scheme as the basic numerical method, with grid spacings as low as a fraction of a micron. Detonations waves are generated at the closed end of a tube, and allowed to propagate for approximately 20 cm. The required energy for successful initiation of the detonation will be measured for different cases of grid resolution and numerical schemes. A modified version of the TVD scheme has also been devised, which allows for much lower numerical diffusion of the radical species in the exponentially growing region behind the shock. The effect of this modification will be demonstrated. Oscillations in peak pressure and induction length are seen to develop in some cases: the oscillations can go through a sequence of modes, from a regular, high frequency mode to a low frequency mode with period doubling. A chaotic regime can also be obtained. General conclusions on the quality of algorithms will be presented. We will also discuss the performance of a version of the code developed on the IBM SP2 parallel computer.
Real-time simulation of flexible and articulating systems is difficult because of the computational burden of the time varying calculations. The mobile servicing system of the NASA Space Station Freedom will handle heavy payloads by local arm manipulations and by translating along the spline of the Station, it is crucial to have real-time simulation available. To enable such a simulation to be of high fidelity and to be able to be hosted on a modest computer, special care must be made in formulating the structural dynamics. Frontal solution algorithms save considerable time in performing these calculations. In addition, it is necessary to take advantage of parallel processing be compatible to take full advantage of both. An approach is offered which will result in high fidelity, real-time simulation for flexible, articulating systems such as the space Station remote servicing system.
In this work, the integrated design and dispatch of behind-the-meter or distributed resources (e.g. stationary battery storage and solar PV generation) is considered. A simulation-based framework is employed, generating high-fidelity results with closed-loop predictive control at a fine resolution, at the expense of high computational cost (several minutes to a few hours per design point). To address this challenge, parallel derivative-free design methods are considered. Four methods are compared, including state-of-the-art surrogate-based methods (Radial-Basis Functions and Gaussian processes) and sampling strategies, an evolutionary-based method, and a simple sequential grid refinement method. As a case study, two types of design problem with increasing complexity are considered, namely, the design of behind-the-meter resources (three design variables) and the inclusion of grid capacity (four design variables). The second yields a constrained design problem for which violations can only be determined after solving the computationally expensive simulation. For the three-dimensional case, all methods present a good performance, achieving a solution within 1% of the optimum after the first iteration, with the sequential grid refinement exhibiting the fastest convergence and achieving the best final objective value. This indicates that the parallel evaluation of multiple sampling points may be more important than the choice of method for small decision spaces. For the four-dimensional constrained case, the Genetic Algorithm presents the best tradeoff between performance and computational effort, while the rough objective function terrain generated by constraint violation penalties reduces the performance of surrogate-based methods. Contour plots with flat regions indicate flexibility in the optimal design and highlight the importance of characterizing the solution space.
A theory is developed for a selection rule governing collisions in a particle simulation of rarefied gas-dynamic flows. The selection rule leads to an algorithmic form highly compatible with fine grain parallel decomposition, allowing for efficient utilization of supercomputers having vector or massively parallel single instruction multiple data architectures. A comparison of shock-wave profiles obtained using both the selection rule and Bird's direct simulation Monte Carlo (DSMC) method show excellent agreement. The equation on which the selection rule is based is shown to be directly related to the time-counter procedure in the DSMC method. The results of several example simulations of representative rarefied flows are presented, for which the number of particles used ranged from 10 to the 6th to 10 to the 7th demonstrating the greatly improved computational efficiency of the method.
A new set of benchmarks has been developed for the performance evaluation of highly parallel supercomputers in the framework of the NASA Ames Numerical Aerodynamic Simulation (NAS) Program. These consist of five 'parallel kernel' benchmarks and three 'simulated application' benchmarks. Together they mimic the computation and data movement characteristics of large-scale computational fluid dynamics applications. The principal distinguishing feature of these benchmarks is their 'pencil and paper' specification-all details of these benchmarks are specified only algorithmically. In this way many of the difficulties associated with conventional benchmarking approaches on highly parallel systems are avoided.
Objective: To develop a software application utilizing general purpose graphics processing units (GPUs) for the analysis of large sets of thermographic data. Background: Over the past few years, an increasing effort among scientists and engineers to utilize the GPU in a more general purpose fashion is allowing for supercomputer level results at individual workstations. As data sets grow, the methods to work them grow at an equal, and often great, pace. Certain common computations can take advantage of the massively parallel and optimized hardware constructs of the GPU to allow for throughput that was previously reserved for compute clusters. These common computations have high degrees of data parallelism, that is, they are the same computation applied to a large set of data where the result does not depend on other data elements. Signal (image) processing is one area were GPUs are being used to greatly increase the performance of certain algorithms and analysis techniques. Technical Methodology/Approach: Apply massively parallel algorithms and data structures to the specific analysis requirements presented when working with thermographic data sets.
This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].
Spaceborne sensors like NASA's Hyperion hyperspectral imager generate huge data volumes, and several near-term trends indicate that data volumes will only increase. Next-generation hyperspectral missions, such as NASA's Hyperspectral Infrared Imager (HyspIRI), will operate at higher duty cycles and higher data rates, and their users will expect products to be generated from the data in near real time [1]. Barring a sudden advance in satellite downlink capacity, these trends point to a need to process data and generate products onboard the spacecraft. Rather than downlink an entire hyperspectral image cube, onboard processing enables satellites to downlink partial or completed scientific data products, which are often one to two orders of magnitude smaller than the original image. In addition, a satellite with onboard data processing resources and direct broadcast transmission equipment could send data products directly to first responders, research scientists or other users on the ground. Next-generation space-capable data processors will have a combination of reconfigurable gate arrays, digital signal processors and general-purpose CPUs. Correctly programmed and configured, these resources are sufficient to run sophisticated data analysis programs, including hyperspectral image processing algorithms that commonly run on desktop computers [2]. This paper describes how we implemented one such program, the HSEG hierarchical image segmentation algorithm, software commonly used on desktop and parallel processors, on a hardware platform designed to mimic a next-generation space-capable data processor [3]. We also describe our approach to porting the algorithm to and optimizing it for the new platform, and determine the expected performance gains enabled by our design. This extended abstract will describe the HSEG algorithm and hardware platform in greater detail, provide an analysis of the key function within the algorithm that required hardware acceleration, and describe our implementation of that function in hardware.
This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].
Various tridiagonal solvers have been proposed in recent years for different parallel platforms. In this paper, the performance of three tridiagonal solvers, namely, the parallel partition LU algorithm, the parallel diagonal dominant algorithm, and the reduced diagonal dominant algorithm, is studied. These algorithms are designed for distributed-memory machines and are tested on an Intel Paragon and an IBM SP2 machines. Measured results are reported in terms of execution time and speedup. Analytical study are conducted for different communication topologies and for different tridiagonal systems. The measured results match the analytical results closely. In addition to address implementation issues, performance considerations such as problem sizes and models of speedup are also discussed.
Two parallel algorithms for standard cell placement using simulated annealing are developed to run on distributed-memory message-passing hypercube multiprocessors. The cells can be mapped in a two-dimensional area of a chip onto processors in an n-dimensional hypercube in two ways, such that both small and large cell exchange and displacement moves can be applied. The computation of the cost function in parallel among all the processors in the hypercube is described, along with a distributed data structure that needs to be stored in the hypercube to support the parallel cost evaluation. A novel tree broadcasting strategy is used extensively for updating cell locations in the parallel environment. A dynamic parallel annealing schedule estimates the errors due to interacting parallel moves and adapts the rate of synchronization automatically. Two novel approaches in controlling error in parallel algorithms are described: heuristic cell coloring and adaptive sequence control.