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At least 667 records · Page 37

An adaptive discontinuous Petrov-Galerkin method for the Grad-Shafranov equation

In this work, we propose and develop an arbitrary-order adaptive discontinuous Petrov--Galerkin (DPG) method for the nonlinear Grad--Shafranov equation. An ultraweak formulation of the DPG scheme for the equation is given based on a minimal residual method. The DPG scheme has the advantage of providing more accurate gradients compared to conventional finite element methods, which is desired for numerical solutions to the Grad--Shafranov equation. The numerical scheme is augmented with an adaptive mesh refinement approach, and a criterion based on the residual norm in the minimal residual method is developed to achieve dynamic refinement. Nonlinear solvers for the resulting system are explored and a Picard iteration with Anderson acceleration is found to be efficient to solve the system. Finally, the proposed algorithm is implemented in parallel on MFEM using a domain-decomposition approach, and our implementation is general, supporting arbitrary order of accuracy and general meshes. Furthermore, numerical results are presented to demonstrate the efficiency and accuracy of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

An improved simulated annealing algorithm for standard cell placement

Simulated annealing is a general purpose Monte Carlo optimization technique that was applied to the problem of placing standard logic cells in a VLSI ship so that the total interconnection wire length is minimized. An improved standard cell placement algorithm that takes advantage of the performance enhancements that appear to come from parallelizing the uniprocessor simulated annealing algorithm is presented. An outline of this algorithm is given.

Jones, Mark↗

An Investigation of Parallel Programming Techniques Applied to Monte Carlo Simulations for Post-Flight Reconstruction of Spacecraft Trajectory

Parallelizing software to execute on multi-core central processing units (CPUs) and graphics processing units (GPUs) can be challenging. For some fields outside of Computer Science, this transition comes with new issues. For example, memory limitations can require modifications to code not initially developed to run on GPUs. This work applies the Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) directive-based parallelization strategies on a Monte Carlo simulation approach for trajectory reconstruction enabling it to run on multi-core CPUs and GPUs. Large matrix operations are the most common use of GPUs, which are not present in this algorithm; however, the natural parallelism of independent trajectories in Monte Carlo simulations is exploited. Benchmarking data are presented comparing execution times of the software for single-thread CPUs, multi-thread CPUs with OpenMP, and multi-thread GPUs using OpenACC. These data were collected using nodes with Intel® Xeon® E5-2670 (Sandy Bridge) CPUs enhanced with NVIDIA® Tesla® K40 GPUs on the Pleiades Supercomputer cluster at the National Aeronautics and Space Administration (NASA) Ames Research Center (ARC) and a local Intel® Xeon Phi™ node at NASA Langley Research Center (LaRC).

Williams, R. Anthony↗

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Bailey, David H.↗

Performance and Accuracy Assessment of Line Marching Algorithm Computations Utilizing GPUs Within a Predictive GNSS Quality Service

This paper presents a detailed analysis of the accuracy and performance of line marching algorithms executing on a GPU. In the context of an accurate Global Navigation Satellite System(GNSS) quality of service simulation, horizon sky-plots are a useful tool to determine satellite visibility in the presence of obstructions from objects, such as buildings or dense foliage. In order to accurately model satellite visibility at a point of interest on a map, a horizon plot can identify the viewing angles at which objects are blocking the sky. This computation requires traversing a line starting at the point of interest on a 2D altitude map, moving outward for every azimuth angle. To explore the performance of this computation, we propose a new dynamic stopping condition for the traversal of the line, benefiting from objects close to the point of interest. We compare the accuracy of common line marching algorithms, and consider their parallel performance when developed in CUDA. We find that our proposed stopping condition for line marching provides a significant improvement in performance in urban canyon sky-plots, as compared to previous work. Additionally, these results show that simpler algorithms, such as the digital differential analyzer line algorithm, are better suited for GPUs than more sophisticated schemes such as Bresenham’s algorithm, specifically in the context of sky-plothorizon computations. The trade-off between accuracy and performance is analyzed and providing guidance that depends on the targeted goal of the GNSS application.

GNSS↗

Real-Time Adaptive Lossless Hyperspectral Image Compression using CCSDS on Parallel GPGPU and Multicore Processor Systems

The proposed CCSDS (Consultative Committee for Space Data Systems) Lossless Hyperspectral Image Compression Algorithm was designed to facilitate a fast hardware implementation. This paper analyses that algorithm with regard to available parallelism and describes fast parallel implementations in software for GPGPU and Multicore CPU architectures. We show that careful software implementation, using hardware acceleration in the form of GPGPUs or even just multicore processors, can exceed the performance of existing hardware and software implementations by up to 11x and break the real-time barrier for the first time for a typical test application.

realtime↗

Computation and parallel implementation for early vision

The problem of early vision is to transform one or more retinal illuminance images-pixel arrays-to image representations built out of such primitive visual features such as edges, regions, disparities, and clusters. These transformed representations form the input to later vision stages that perform higher level vision tasks including matching and recognition. Researchers developed algorithms for: (1) edge finding in the scale space formulation; (2) correlation methods for computing matches between pairs of images; and (3) clustering of data by neural networks. These algorithms are formulated for parallel implementation of SIMD machines, such as the Massively Parallel Processor, a 128 x 128 array processor with 1024 bits of local memory per processor. For some cases, researchers can show speedups of three orders of magnitude over serial implementations.

Gualtieri, J. Anthony↗

The LSBmax algorithm for boosting resilience of electric grids post (N‐2) contingencies

Abstract A computationally improved algorithm is presented to find the best transmission switching (TS) candidate for boosting resilience of electricity grids subject to ( N ‐2) contingencies. Here, resilience is computed as the reduction in load shed after the above‐mentioned ( N‐ ) contingencies. TS is a planned line outage, and past research shows that changing the transmission system's topology changes the power flow and removes post contingency violations. Finding the best TS candidate in a computationally suitable time for effectively boosting resilience is a challenge. The best TS candidate is found using a novel heuristic method by decreasing the search space based on proximity to the bus with the maximum load shedding (LSB). The LSB algorithm is faster than existing algorithms in the literature; and, it is compatible with both the AC and DC optimal power flow formulations. To validate the authors' claims of speedup and accuracy, two metrics are used to analyze the results from the IEEE 39‐bus and 118‐bus systems. Finally, the inherent parallelism of the LSB algorithm is leveraged on a high‐performance computing platform and applied to the large‐scale Polish 2383‐bus test system to validate scalability in both size and speedup in computation time.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The nondeterministic divide

The nondeterministic divide partitions a vector into two non-empty slices by allowing the point of division to be chosen nondeterministically. Support for high-level divide-and-conquer programming provided by the nondeterministic divide is investigated. A diva algorithm is a recursive divide-and-conquer sequential algorithm on one or more vectors of the same range, whose division point for a new pair of recursive calls is chosen nondeterministically before any computation is performed and whose recursive calls are made immediately after the choice of division point; also, access to vector components is only permitted during activations in which the vector parameters have unit length. The notion of diva algorithm is formulated precisely as a diva call, a restricted call on a sequential procedure. Diva calls are proven to be intimately related to associativity. Numerous applications of diva calls are given and strategies are described for translating a diva call into code for a variety of parallel computers. Thus diva algorithms separate logical correctness concerns from implementation concerns.

Charlesworth, Arthur↗

Multichannel Analysis of Surface Waves Accelerated (MASWAccelerated): Software for efficient surface wave inversion using MPI and GPUs

Multichannel Analysis of Surface Waves (MASW) is a technique frequently used in geotechnical engineering and engineering geophysics to infer 1D layered models of seismic shear wave velocities in the top tens to hundreds of meters of the subsurface. We aim to accelerate MASW calculations by capitalizing on modern computer hardware available in the workstations of most engineers: multiple cores and graphics processing units (GPUs). We propose new parallel and GPU accelerated algorithms for computing 1D MASW inversion, and provide software implementations in C using Message Passing Interface (MPI) and CUDA. These algorithms take advantage of sparsity that arises in the problem, and the work balance between processes considers typical data trends. We compare our methods to an existing open source Matlab MASW tool. Our serial C implementation achieves a 2x speedup over the Matlab software, and we continue to see improvements by parallelizing the problem with MPI. Here we see nearly perfect strong and weak scaling for uniform data, and improve strong scaling for realistic data by repartitioning the problem to process mapping. By utilizing GPUs available on most modern workstations, we observe an additional 1.3x speedup over the serial C implementation on the first use of the method. We typically repeatedly evaluate theoretical dispersion curves as part of an optimization procedure, and on the GPU the kernel can be cached for faster reuse on later runs. We observe a 3.2x speedup on the cached GPU runs compared to the serial C runs. This work is the first open-source parallel or GPU-accelerated software tool for MASW imaging, and should enable geotechnical engineers to fully utilize all computer hardware at their disposal.

58 GEOSCIENCES↗

Contextual classification on PASM

The use of N microprocessors in the SIMD mode of parallel processing to do classifications almost N times faster than a single microprocessor is discussed. Examples of contextual classifiers are given, uniprocessor algorithms for performing contextual classifications are presented, and their computational complexity is analyzed. The SIMD mode of parallel processing is defined and PASM is overviewed. The presented uniprocessor algorithms are used as a basis for developing parallel algorithms for performing computationally intensive contextual classifications.

Siegel, H. J.↗

Efficient solution of parabolic equations by Krylov approximation methods

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Gallopoulos, E.↗

Parallel computing for power system climate resiliency: Solving a large-scale stochastic capacity expansion problem with mpi-sppy

Here we propose a nodal stochastic generation and transmission expansion planning model that incorporates the output from high-resolution global climate models through load and generation availability scenarios. We implement our model in Pyomo and perform computational studies on a realistically-sized test case of the California electric grid in a high performance computing environment. We propose model reformulations and algorithm tuning to efficiently solve this large problem using a variant of the Progressive Hedging Algorithm. We utilize the parallelization capabilities and overall versatility of mpi-sppy, exploiting its hub-and-spoke architecture to concurrently obtain inner and outer bounds on an optimal expansion plan. Initial results show that instances with 360 representative days on a system with over 8,000 buses can be solved to within 5% of optimality in under 4 h of wall clock time, a first step towards solving a large-scale power system expansion planning problem across a wide range of climate-informed operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Parallel adaptive mesh refinement techniques for plasticity problems

The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.

Barry, W. J.↗

Parallel-vector unsymmetric Eigen-Solver on high performance computers

The popular QR algorithm for solving all eigenvalues of an unsymmetric matrix is reviewed. Among the basic components in the QR algorithm, it was concluded from this study, that the reduction of an unsymmetric matrix to a Hessenberg form (before applying the QR algorithm itself) can be done effectively by exploiting the vector speed and multiple processors offered by modern high-performance computers. Numerical examples of several test cases have indicated that the proposed parallel-vector algorithm for converting a given unsymmetric matrix to a Hessenberg form offers computational advantages over the existing algorithm. The time saving obtained by the proposed methods is increased as the problem size increased.

Nguyen, Duc T.↗

EXAGRAPH: Graph and combinatorial methods for enabling exascale applications

Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to implement on parallel systems. With tens of billions of hardware threads and deep memory hierarchies, the exascale computing systems in particular pose extreme challenges in scaling graph algorithms. The codesign center on combinatorial algorithms, ExaGraph, was established to design and develop methods and techniques for efficient implementation of key combinatorial (graph) algorithms chosen from a diverse set of exascale applications. Algebraic and combinatorial methods have a complementary role in the advancement of computational science and engineering, including playing an enabling role on each other. In this paper, we survey the algorithmic and software development activities performed under the auspices of ExaGraph from both a combinatorial and an algebraic perspective. In particular, we detail our recent efforts in porting the algorithms to manycore accelerator (GPU) architectures. We also provide a brief survey of the applications that have benefited from the scalable implementations of different combinatorial algorithms to enable scientific discovery at scale. We believe that several applications will benefit from the algorithmic and software tools developed by the ExaGraph team.

97 MATHEMATICS AND COMPUTING↗

Speed challenge: a case for hardware implementation in soft-computing

For over a decade, JPL has been actively involved in soft computing research on theory, architecture, applications, and electronics hardware. The driving force in all our research activities, in addition to the potential enabling technology promise, has been creation of a niche that imparts orders of magnitude speed advantage by implementation in parallel processing hardware with algorithms made especially suitable for hardware implementation. We review our work on neural networks, fuzzy logic, and evolvable hardware with selected application examples requiring real time response capabilities.

neural networks fuzzy logic evolvable hardware sof↗

GronOR: Massively Parallel and GPU-Accelerated Non-Orthogonal Configuration Interaction for Large Molecular Systems

GronOR is a program package for non-orthogonal configuration interaction calculations for an electronic wave function built in terms of anti-symmetrized products of multi-configuration molecular fragment wave functions. The two-electron integrals that have to be processed may be expressed in terms of atomic orbitals or in terms of an orbital basis determined from the molecular orbitals of the fragments. The code has been specifically designed for execution on distributed memory massively parallel and Graphics Processing Unit (GPU)-accelerated computer architectures, using an MPI+OpenACC/OpenMP programming approach. The task-based execution model used in the implementation allows for linear scaling with the number of nodes on the largest pre-exascale architectures available, provides hardware fault resiliency, and enables effective execution on systems with distinct central processing unit-only and GPU-accelerated partitions. The code interfaces with existing multi-configuration electronic structure codes that provide optimized molecular fragment orbitals, configuration interaction coefficients, and the required integrals. Algorithm and implementation details, parallel and accelerated performance benchmarks, and an analysis of the sensitivity of the accuracy of results and computational performance to thresholds used in the calculations are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗