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At least 73 records · Page 4

Parallel peak pruning for scalable SMP contour tree computation

As data sets grow to exascale, automated data analysis and visualisation are increasingly important, to intermediate human understanding and to reduce demands on disk storage via in situ analysis. Trends in architecture of high performance computing systems necessitate analysis algorithms to make effective use of combinations of massively multicore and distributed systems. One of the principal analytic tools is the contour tree, which analyses relationships between contours to identify features of more than local importance. Unfortunately, the predominant algorithms for computing the contour tree are explicitly serial, and founded on serial metaphors, which has limited the scalability of this form of analysis. While there is some work on distributed contour tree computation, and separately on hybrid GPU-CPU computation, there is no efficient algorithm with strong formal guarantees on performance allied with fast practical performance. Here in this paper, we report the first shared SMP algorithm for fully parallel contour tree computation, withfor-mal guarantees of O(lgnlgt) parallel steps and O(n lgn) work, and implementations with up to 10x parallel speed up in OpenMP and up to 50x speed up in NVIDIA Thrust.

97 MATHEMATICS AND COMPUTING↗

Snowmass Computational Frontier: Topical Group Report on Experimental Algorithm Parallelization

The substantial increase in data volume and complexity expected from future experiments will require significant investment to prepare experimental algorithms. These algorithms include physics object reconstruction, calibrations, and processing of observational data. In addition, the changing computing architecture landscape, which will be primarily composed of heterogeneous resources, will continue to pose major challenges with regard to algorithmic migration. Portable tools need to be developed that can be shared among the frontiers (e.g., for code execution on different platforms) and opportunities, such as forums or cross-experimental working groups, need to be provided where experiences and lessons learned can be shared between experiments and frontiers. At the same time, individual experiments also need to invest considerable resources to develop algorithms unique to their needs (e.g., for facilities dedicated to the experiment), and ensure that their specific algorithms will be able to efficiently exploit external heterogeneous computing facilities. Common software tools represent a cost-effective solution, providing ready-to-use software solutions as well as a platform for R&D work. These are particularly important for small experiments which typically do not have dedicated resources needed to face the challenges imposed by the evolving computing technologies. Workforce development is a key concern across frontiers and experiments, and additional support is needed to provide career opportunities for researchers working in the field of experimental algorithm development. Finally, cross-discipline collaborations going beyond high-energy physics are a key ingredient to address the challenges ahead and more support for such collaborations needs to be created. This report targets future experiments, observations and experimental algorithm development for the next 10-15 years.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

PAGANI: a parallel adaptive GPU algorithm for numerical integration

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core utilization is difficult to achieve because the adaptive work-load can vary greatly across the integration space and is impossible to predict a priori. Existing parallel algorithms utilize sequential computations on independent processors, which results in bottlenecks due to the need for data redistribution and processor synchronization. Our algorithm employs a high-throughput approach in which all existing sub-regions are processed and sub-divided in parallel. Repeated sub-region classification and filtering improves upon a brute-force approach and allows the algorithm to make efficient use of computation and memory resources. A CUDA implementation shows orders of magnitude speedup over the fastest open-source CPU method and extends the achievable accuracy for difficult integrands. Our algorithm typically outperforms other existing deterministic parallel methods.

Sakiotis, Ioannis↗

Algorithms for Balanced Graph Colorings with Applications in Parallel Computing

Graph coloring is used to identify subsets of independent tasks in parallel scientific computing applications. Traditional coloring heuristics aim to reduce the number of colors used as that number also corresponds to the number of parallel steps in the application. However, if the color classes produced have a skew in their sizes, utilization of hardware resources becomes inefficient, especially for the smaller color classes. Equitable coloring is a theoretical formulation of coloring that guarantees a perfect balance among color classes, and its practical relaxation is referred to as balanced coloring. In this paper, we revisit the problem of balanced coloring in the context of parallel computing. The goal is to achieve a balanced coloring of an input graph without increasing the number of colors that an algorithm oblivious to balance would have used. We propose and study multiple heuristics that aim to achieve such a balanced coloring for two variants of coloring problem, distance-1 coloring and partial distance-2 coloring (defined on a bipartite graph). We present parallelization approaches for multi-core and manycore architectures, and cross-evaluate their effectiveness with respect to the quality of balance achieved and performance. Furthermore, we study the impact of the proposed balanced coloring heuristics on a concrete application - viz. parallel community detection, which is an example of an irregular application. In addition, we propose several extensions to our balancing schemes and evaluate their balancing efficacy and performance characteristics. The thorough treatment of balanced coloring presented in this paper from algorithms to application is expected to serve as a valuable resource to parallel application developers who seek to improve parallel performance of their applications using coloring.

graph coloring, multithreaded algorithms↗

Frog: Asynchronous Graph Processing on GPU with Hybrid Coloring Model

GPUs have been increasingly used to accelerate graph processing for complicated computational problems regarding graph theory. Many parallel graph algorithms adopt the asynchronous computing model to accelerate the iterative convergence. Unfortunately, the consistent asynchronous computing requires locking or atomic operations, leading to significant penalties/overheads when implemented on GPUs. As such, coloring algorithm is adopted to separate the vertices with potential updating conflicts, guaranteeing the consistency/correctness of the parallel processing. Common coloring algorithms, however, may suffer from low parallelism because of a large number of colors generally required for processing a large-scale graph with billions of vertices. We propose a light-weight asynchronous processing framework called Frog with a preprocessing/hybrid coloring model. The fundamental idea is based on Pareto principle (or 80-20 rule) about coloring algorithms as we observed through masses of realworld graph coloring cases. We find that a majority of vertices (about 80%) are colored with only a few colors, such that they can be read and updated in a very high degree of parallelism without violating the sequential consistency. Accordingly, our solution separates the processing of the vertices based on the distribution of colors. In this work, we mainly answer three questions: (1) how to partition the vertices in a sparse graph with maximized parallelism, (2) how to process large-scale graphs that cannot fit into GPU memory, and (3) how to reduce the overhead of data transfers on PCIe while processing each partition. Here, we conduct experiments on real-world data (Amazon, DBLP, YouTube, RoadNet-CA, WikiTalk and Twitter) to evaluate our approach and make comparisons with well-known non-preprocessed (such as Totem, Medusa, MapGraph and Gunrock) and preprocessed (Cusha) approaches, by testing four classical algorithms (BFS, PageRank, SSSP and CC). On all the tested applications and datasets, Frog is able to significantly outperform existing GPU-based graph processing systems except Gunrock and MapGraph. MapGraph gets better performance than Frog when running BFS on RoadNet-CA. The comparison between Gunrock and Frog is inconclusive. Frog can outperform Gunrock more than 1.04X when running PageRank and SSSP, while the advantage of Frog is not obvious when running BFS and CC on some datasets especially for RoadNet-CA.

97 MATHEMATICS AND COMPUTING↗

Avoiding excess computation in asynchronous evolutionary algorithms

Abstract Asynchronous evolutionary algorithms are becoming increasingly popular as a means of making full use of many processors while solving computationally expensive search and optimization problems. These algorithms excel at keeping large clusters fully utilized, but may sometimes inefficiently sample an excess of fast‐evaluating solutions at the expense of higher‐quality, slow‐evaluating ones. We have previously introduced a steady‐state parent selection strategy, SWEET (“Selection whilE EvaluaTing”), that sometimes selects individuals that are still being evaluated and allows them to reproduce early. We perform a takeover‐time analysis that confirms that this strategy gives slow‐evaluating individuals that have higher fitnesses an increased ability to multiply in the population. We also find that SWEET appears effective at improving optimization performance on problems in which solution quality is positively correlated with evaluation time. We evaluate our approach on six simulated real‐valued optimization problems and three real‐world applications: an autonomous vehicle controller problem that involves tuning a spiking neural network and two adversarial EA problems. We further evaluate SWEET versus a basic asynchronous process in a simulated setting. We present evidence that SWEET outperforms basic asynchronous processes in a use‐case in which performance is positively correlated with evaluation time, and performs comparably (and often better) than basic asynchronous processes in several use‐cases where performance is negatively correlated with evaluation time. That said, in the cases where performance and evaluation time are negatively correlated the variance of outcomes for SWEET is notably high.

97 MATHEMATICS AND COMPUTING↗

Comparative Implementation of High Performance Computing for Power System Dynamic Simulations

Dynamic simulation for transient stability assessment is one of the most important, but intensive, computations for power system planning and operation. Present commercial software is mainly designed for sequential computation to run a single simulation, which is very time consuming with a single processer. The application of High Performance Computing (HPC) to dynamic simulations is very promising in accelerating the computing process by parallelizing its kernel algorithms while maintaining the same level of computation accuracy. This paper describes the comparative implementation of four parallel dynamic simulation schemes in two state-of-the-art HPC environments: Message Passing Interface (MPI) and Open Multi-Processing (OpenMP). These implementations serve to match the application with dedicated multi-processor computing hardware and maximize the utilization and benefits of HPC during the development process.

97 MATHEMATICS AND COMPUTING↗

Optimization and Augmentation for Data Parallel Contour Trees

Contour trees are used for topological data analysis in scientific visualization. While originally computed with serial algorithms, recent work has introduced a vector-parallel algorithm. Furthermore, this algorithm is relatively slow for fully augmented contour trees which are needed for many practical data analysis tasks. We therefore introduce a representation called the hyperstructure that enables efficient searches through the contour tree and use it to construct a fully augmented contour tree in data parallel, with performance on average 6 times faster than the state-of-the-art parallel algorithm in the TTK topological toolkit.

97 MATHEMATICS AND COMPUTING↗

Parallel Asynchronous Distributed-Memory Maximal Independent Set Algorithm with Work Ordering

The maximal independent set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of graph data suggests the use of distributed memory hardware as a cost-effective approach to providing necessary compute and memory resources. Existing distributed memory parallel MIS algorithms rely on synchronous communication and use techniques such as subgraph computations. In this paper, we present an asynchronous distributed-memory parallel graph algorithm that relies on a virtual directed acyclic graph (DAG) that is created during the algorithm execution. We introduce two additional algorithms that save computations by ordering generated work. The first algorithm applies ordering globally to reduce computations, and the second algorithm applies ordering locally at the level of threads to minimize the synchronization overhead. We use two different implementations of Luby’s algorithm variants as baseline to compare the performance of the presented algorithms: (1) vertex-centric Luby A and Luby B implementations, and (2) the CombBLAS linear-algebra Luby A implementation. Results show that proposed algorithms outperform both implementations of Luby algorithms, especially in distributed execution. Furthermore, we show that for low-diameter graphs the algorithm that applies global ordering scales better than other algorithms and for high diameter graphs the original asynchronous algorithm and thread-level ordering algorithm show better performance.

maximal independent set (MIS), distributed memory ↗

Regularized Finite Element Formulations for Shear Band Instabilities in Metals

In my research I have addressed several fundamental issues of dynamic fracture: 1. established the role of heat conduction as a natural regularizing mechanism in shearband problems (i.e. using the correct physics for this problem), 2. developed a unified model to incorporate fracture through a modified phase field formulation, 3. developed stability analysis tools to determine the onset of localization, 4. developed discretization methods and solvers to solve this problem (on parallel computers) that lead to mesh insensitive results and fast convergence. For such difficult problems, the physics and numerics are strongly coupled. To accurately model the physics, one must develop reliable numerics but reliable numerics depends on correct description of the physics. To this end, we have already made significant progress in the field showing that a fully-coupled implicit solution with heat conduction is the key to obtain reliable results for shear bands (see the next sections for more details). This research fits well within the mission of DOE ASCR program on all aspects: from governing equations to discretization to solvers to parallel computers to applications problems. It also relies on the computational tools developed through the SciDAC institutes FASTMath and SDAV, such as PETSc (and SLEPc), ParaView, Trilinos and Masquite.

97 MATHEMATICS AND COMPUTING↗

Extension of the high-resolution thermal-hydraulics code ESCOT to hexagonal core geometries for multi-physics calculations

The extension of the capabilities of the pin-level nuclear reactor core thermal-hydraulics (T/H) code ESCOT to analyze hexagonal fueled cores and its performance are presented. ESCOT is an accurate yet fast core thermal-hydraulics solution aiming at high-fidelity and high-resolution multi-physics core analysis in the framework of massively parallel computing platforms. Its algorithm solution is based on the four-equation drift-flux model for two-phase calculations, these are numerically solved by applying the Finite Volume Method (FVM) and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE)-like algorithm in a staggered grid system. Constitutive models such as turbulent mixing, pressure drop, and vapor generation are employed to simulate key phenomena in subchannel-scale analysis. ESCOT is parallelized by a double (radial and axial) domain decomposition that enables its highly parallelized execution. The coupling of the code with the neutronics whole core solver for hexagonal geometries nTRACER is described. The newly implemented ESCOT features are validated by comparing single assembly and full core steady state nTRACER-ESCOT solutions with nTRACER standalone internal one-dimensional T/H solver results. The validation problems are based on the VVER 440 and VVER 1000 cores. ESCOT results show differences within an acceptable range with respect to the simple 1D nTRACER built-in solver. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A new augmentation based algorithm for extracting maximal chordal subgraphs

If every cycle of a graph is chordal length greater than three then it contains an edge between non-adjacent vertices. Chordal graphs are of interest both theoretically, since they admit polynomial time solutions to a range of NP-hard graph problems, and practically, since they arise in many applications including sparse linear algebra, computer vision, and computational biology. A maximal chordal subgraph is a chordal subgraph that is not a proper subgraph of any other chordal subgraph. Existing algorithms for computing maximal chordal subgraphs depend on dynamically ordering the vertices, which is an inherently sequential process and therefore limits the algorithms’ parallelizability. In our paper we explore techniques to develop a scalable parallel algorithm for extracting a maximal chordal subgraph. We demonstrate that an earlier attempt at developing a parallel algorithm may induce a non-optimal vertex ordering and is therefore not guaranteed to terminate with a maximal chordal subgraph. We then give a new algorithm that first computes and then repeatedly augments a spanning chordal subgraph. After proving that the algorithm terminates with a maximal chordal subgraph, we then demonstrate that this algorithm is more amenable to parallelization and that the parallel version also terminates with a maximal chordal subgraph. That said, the complexity of the new algorithm is higher than that of the previous parallel algorithm, although the earlier algorithm computes a chordal subgraph which is not guaranteed to be maximal. Finally, we experimented with our augmentation-based algorithm on both synthetic and real-world graphs. We provide scalability results and also explore the effect of different choices for the initial spanning chordal subgraph on both the running time and on the number of edges in the maximal chordal subgraph.

97 MATHEMATICS AND COMPUTING↗

Quantum Hamiltonian Physics with Supercomputers

The vision of solving the nuclear many-body problem in a Hamiltonian framework with fundamental interactions tied to QCD via Chiral Perturbation Theory is gaining support. The goals are to preserve the predictive power of the underlying theory, to test fundamental symmetries with the nucleus as laboratory and to develop new understandings of the full range of complex quantum phenomena. Advances in theoretical frameworks (renormalization and many-body methods) as well as in computational resources (new algorithms and leadership-class parallel computers) signal a new generation of theory and simulations that will yield profound insights into the origins of nuclear shell structure, collective phenomena and complex reaction dynamics. Fundamental discovery opportunities also exist in such areas as physics beyond the Standard Model of Elementary Particles, the transition between hadronic and quark–gluon dominated dynamics in nuclei and signals that characterize dark matter. I will review some recent achievements and present ambitious consensus plans along with their challenges for a coming decade of research that will build new links between theory, simulations and experiment. Opportunities for graduate students to embark upon careers in the fast developing field of supercomputer simulations is also discussed.

Physics↗

On-the-fly Doppler Broadening with Probability Table Interpolation for Unresolved Resonance Region in RMC

With the rapid development of computational power and parallel algorithms, Monte Carlo method has been widely investigated and used in neutron transport simulations due to its advantages in geometry modelling and usage of continuous energy point-wise cross sections. Nowadays the road has been paved to couple Monte Carlo codes with thermal-hydraulics codes to make multi-physics calculations. One of the most important aspects of thermal-hydraulics feedback is the detailed temperature distribution, which demands temperature dependent cross sections in neutron transport simulations. The conventional pre-generated cross section libraries at each temperature point are no longer feasible for detailed temperature distributions because of tremendous memory footprint. Hence, different on-the-fly Doppler broadening methods have been proposed for resolved resonance energy region and thermal energy region, such as the interpolation, regress model fitting, multipole representation (MPR), target motion sampling (TMS) and different integration algorithms based on Doppler broadening equation. Compared to resolved resonance energy region and thermal energy region, the representation of cross sections in unresolved resonance region is slightly different. As a result of the limitation of experiment measurements, the overlapped resonances cannot be distinguished from each other and the statistic average resonance parameters are given in the evaluated nuclear data file. In early applications, infinite-dilute pointwise cross sections were obtained from average parameters and were directly used in neutron simulations. However, it was proven that these infinite-dilute pointwise cross sections cannot capture the energy self-shielding effect, thus leading to an overestimate of reaction rates and usually an underestimate of k{sub eff} owing to the increased absorption rates and increased scattering probability to energy below unresolved resonance region where the capture-to-fission ratio is typically higher. This phenomenon is of great importance especially for problems where there is a considerable flux in unresolved resonance region. Then the probability table method was put forward by Levitt to take energy self-shielding effect into account, which provides probability distribution function of cross sections in unresolved resonance region instead of specific cross section values. The probability distribution function is presented in the form of tables and the mean values are equal to the infinite dilution cross sections. To obtain the temperature dependent cross sections in unresolved energy region, there are two different methods. One is to calculate cross sections directly from average resonance parameters and their statistical distributions , which is effective and precise but time-consuming. The other is to interpolate between pre-generated probability table files, which is much more efficient. In this paper, on-the-fly Doppler broadening of cross sections in unresolved resonance regions based on probability tables interpolation was implemented in RMC codes as a supplement to on-the-fly Doppler broadening for resolved resonance energy region and thermal region, which is based on the integration of Doppler broadening equation. The results of criticality calculation and depletion calculation show that on-the-fly Doppler broadening for the whole energy region is accurate and efficient. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

GentenMPI: Distributed Memory Sparse Tensor Decomposition

GentenMPl is a toolkit of sparse canonical polyadic (CP) tensor decomposition algorithms that is designed to run effectively on distributed-memory high-performance computers. Its use of distributed-memory parallelism enables it to efficiently decompose tensors that are too large for a single compute node's memory. GentenMPl leverages Sandia's decades-long investment in the Trilinos solver framework for much of its parallel-computation capability. Trilinos contains numerical algorithms and linear algebra classes that have been optimized for parallel simulation of complex physical phenomena. This work applies these tools to the data science problem of sparse tensor decomposition. In this report, we describe the use of Trilinos in GentenMPl, extensions needed for sparse tensor decomposition, and implementations of the CP-ALS (CP via alternating least squares) and GCP-SGD (generalized CP via stochastic gradient descent) sparse tensor decomposition algorithms. We show that GentenMPl can decompose sparse tensors of extreme size, e.g., a 12.6-terabyte tensor on 8192 computer cores. We demonstrate that the Trilinos backbone provides good strong and weak scaling of the tensor decomposition algorithms.

97 MATHEMATICS AND COMPUTING↗

PeleLMeX: an AMR Low Mach Number Reactive Flow Simulation Code without level sub-cycling

PeleLMeX simulates chemically reacting low Mach number flows with block-structured adaptive mesh refinement (AMR). The code is built upon the AMReX library, which provides the underlying data structures and tools to manage and operate on them across massively parallel computing architectures. PeleLMeX algorithmic features are inherited from its predecessor PeleLM but key improvements allow representation of more complex physical processes. Together with its compressible flow counterpart PeleC, the thermo-chemistry library PelePhysics and the multi-physics library PeleMP, it forms the Pele suite of open-source reactive flow simulation codes.

97 MATHEMATICS AND COMPUTING↗

Acceleration of the Particle Swarm Optimization for Peierls–Nabarro modeling of dislocations in conventional and high-entropy alloys

Dislocations are among the most important defects in determining the mechanical properties of both conventional alloys and high-entropy alloys. The Peierls-Nabarro model supplies an efficient pathway to their geometries and mobility. The difficulty in solving the integro-differential Peierls-Nabarro equation is how to effectively avoid the local minima in the energy landscape of a dislocation core. Among the other methods to optimize the dislocation core structures, we choose the algorithm of Particle Swarm Optimization, an algorithm that simulates the social behaviors of organisms. By employing more particles (bigger swarm) and more iterative steps (allowing them to explore for longer time), the local minima can be effectively avoided. But this would require more computational cost. The advantage of this algorithm is that it is readily parallelized in modern high computing architecture. We demonstrate the performance of our parallelized algorithm scales linearly with the number of employed cores.

36 MATERIALS SCIENCE↗

Parallel Algorithms and Patterns

This is a powerpoint presentation on parallel algorithms and patterns. A parallel algorithm is a well-defined, step-by-step computational procedure that emphasizes concurrency to solve a problem. Examples of problems include: Sorting, searching, optimization, matrix operations. A parallel pattern is a computational step in a sequence of independent, potentially concurrent operations that occurs in diverse scenarios with some frequency. Examples are: Reductions, prefix scans, ghost cell updates. We only touch on parallel patterns in this presentation. It really deserves its own detailed discussion which Gabe Rockefeller would like to develop.

97 MATHEMATICS AND COMPUTING↗