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At least 1,081 records · Page 60

Algorithms and software for solving finite element equations on serial 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.

George, Alan↗

Efficient dynamic simulation for multiple chain robotic mechanisms

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.

Lilly, Kathryn W.↗

Efficient multitasking of Choleski matrix factorization on CRAY supercomputers

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.

Overman, Andrea L.↗

Graph-Based Dynamic Assignment Of Multiple Processors

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.

Hayes, Paul J.↗

Map Algorithms for Decoding Linear Block codes Based on Sectionalized Trellis Diagrams

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.

Lin, Shu↗

Parallel Preconditioning for CFD Problems on the CM-5

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.

Simon, Horst D.↗

Some Numerical Experiments on Detonation Wave Propagation

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.

Cambier, Jean-Luc↗

The power and efficiency of advanced software and parallel processing

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.

Singh, Ramen P.↗

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. Here we introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated an d human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors

Tensor based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making it an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTMc) in general sparse tensors, the Sparse Symmetric Tensor Times Same Matrix chain (S3TTMc) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. In this work, we present a novel compressed storage format CSS for sparse symmetric tensors, along with an efficient parallel algorithm for the S3TTMc operation. We theoretically establish that S3TTMc on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations. We demonstrate experimental findings that confirm these results and achieve up to 2.9× speedup on synthetic and real datasets.

Shivakumar, Shruti↗

Parallel derivative-free optimization for simulation-based design of behind-the-meter energy systems

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.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Neuromorphic Graph Algorithms: Extracting Longest Shortest Paths and Minimum Spanning Trees

Neuromorphic computing is poised to become a promising computing paradigm in the post Moore's law era due to its extremely low power usage and inherent parallelism. Traditionally speaking, a majority of the use cases for neuromorphic systems have been in the field of machine learning. In order to expand their usability, it is imperative that neuromorphic systems be used for non-machine learning tasks as well. The structural aspects of neuromorphic systems (i.e., neurons and synapses) are similar to those of graphs (i.e., nodes and edges), However, it is not obvious how graph algorithms would translate to their neuromorphic counterparts. In this work, we propose a preprocessing technique that introduces fractional offsets on the synaptic delays of neuromorphic graphs in order to break ties. This technique, in turn, enables two graph algorithms: longest shortest path extraction and minimum spanning trees.

Kay, Bill↗

A collision-selection rule for a particle simulation method suited to vector computers

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.

Baganoff, D.↗

The NAS parallel benchmarks

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.

Bailey, D. H.↗

The fusion code XGC: Enabling kinetic study of multi-scale edge turbulent transport in ITER [Book Chapter]

The XGC fusion gyrokinetic code combines state-of-the-art, portable computational and algorithmic technologies to enable complicated multiscale simulations of turbulence and transport dynamics in ITER edge plasma on the largest US open-science computer, the CRAY XK7 Titan, at its maximal heterogeneous capability, which have not been possible before due to a factor of over 10 shortage in the time-to-solution for less than 5 days of wall-clock time for one physics case. Frontier techniques such as nested OpenMP parallelism, adaptive parallel I/O, staging I/O and data reduction using dynamic and asynchronous applications interactions, dynamic repartitioning for balancing computational work in pushing particles and in grid related work, scalable and accurate discretization algorithms for non-linear Coulomb collisions, and communication-avoiding subcycling technology for pushing particles on both CPUs and GPUs are also utilized to dramatically improve the scalability and time-to-solution, hence enabling the difficult kinetic ITER edge simulation on a present-day leadership class computer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Graphics Processing Unit Assisted Thermographic Compositing

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.

Ragasa, Scott↗

Reconstructing householder vectors from Tall-Skinny QR

The Tall-Skinny QR (TSQR) algorithm is more communication efficient than the standard Householder algorithm for QR decomposition of matrices with many more rows than columns. However, TSQR produces a different representation of the orthogonal factor and therefore requires more software development to support the new representation. Further, implicitly applying the orthogonal factor to the trailing matrix in the context of factoring a square matrix is more complicated and costly than with the Householder representation. We show how to perform TSQR and then reconstruct the Householder vector representation with the same asymptotic communication efficiency and little extra computational cost. We demonstrate the high performance and numerical stability of this algorithm both theoretically and empirically. The new Householder reconstruction algorithm allows us to design more efficient parallel QR algorithms, with significantly lower latency cost compared to Householder QR and lower bandwidth and latency costs compared with Communication-Avoiding QR (CAQR) algorithm. Experiments on supercomputers demonstrate the benefits of the communication cost improvements: in particular, our experiments show substantial improvements over tuned library implementations for tall-and-skinny matrices. Furthermore, we also provide algorithmic improvements to the Householder QR and CAQR algorithms, and we investigate several alternatives to the Householder reconstruction algorithm that sacrifice guarantees on numerical stability in some cases in order to obtain higher performance.

97 MATHEMATICS AND COMPUTING↗

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗