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At least 343 records · Page 19

Parallel PIPS-SBB: multi-level parallelism for stochastic mixed-integer programs

PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch & Bound (B&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B&B tree search that has been sucessfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores.

97 MATHEMATICS AND COMPUTING↗

Performance analysis of data intensive cloud systems based on data management and replication: a survey

As we delve deeper into the ‘Digital Age’, we witness an explosive growth in the volume, velocity, and variety of the data available on the Internet. For example, in 2012 about 2.5 quintillion bytes of data was created on a daily basis that originated from myriad of sources and applications including mobiledevices, sensors, individual archives, social networks, Internet of Things, enterprises, cameras, software logs, etc. Such ‘Data Explosions’ has led to one of the most challenging research issues of the current Information and Communication Technology era: how to optimally manage (e.g., store, replicated, filter, and the like) such large amount of data and identify new ways to analyze large amounts of data for unlocking information. It is clear that such large data streams cannot be managed by setting up on-premises enterprise database systems as it leads to a large up-front cost in buying and administering the hardware and software systems. Therefore, next generation data management systems must be deployed on cloud. The cloud computing paradigm provides scalable and elastic resources, such as data and services accessible over the Internet Every Cloud Service Provider must assure that data is efficiently processed and distributed in a way that does not compromise end-users’ Quality of Service (QoS) in terms of data availability, data search delay, data analysis delay, and the like. In the aforementioned perspective, data replication is used in the cloud for improving the performance (e.g., read and write delay) of applications that access data. Through replication a data intensive application or system can achieve high availability, better fault tolerance, and data recovery. In this paper, we survey data management and replication approaches (from 2007 to 2011) that are developed by both industrial and research communities. The focus of the survey is to discuss and characterize the existing approaches of data replication and management that tackle the resource usage and QoS provisioning with different levels of efficiencies. Moreover, the breakdown of both influential expressions (data replication and management) to provide different QoS attributes is deliberated. Furthermore, the performance advantages and disadvantages of data replication and management approaches in the cloud computing environments are analyzed. Open issues and future challenges related to data consistency, scalability, load balancing, processing and placement are also reported.

Malik, Saif Ur Rehman↗

DeStager: feature guided in-situ data management in distributed deep memory hierarchies

In-situ analytics have been increasingly adopted by leadership scientific applications to gain fast insights into massive output data of simulations. With the current practice, systems buffer the output data in DRAM for analytics processing, constraining it to DRAM capacity un-used by the simulation. The rapid growth of data size requires alternative approaches to accommodating data-rich analytics, such as using solid-state disks to increase effective memory capacity. For this purpose, this paper explores software solutions for exploring the deep memory hierarchies expected on future high-end machines. Leveraging the fact that many analytics are sensitive to data features (regions-of-interest) hidden in the data being processed, the approach incorporates the knowledge of the data features into in-situ data management. It uses adaptive index creation/refinement to reduce the overhead of index management. In addition, it uses data features to predict data skew and improve load balance through controlling data distribution and placement on distributed staging servers. The experimental results show that such feature-guided optimizations achieve substantial improvements over state-of-the-art approaches for managing output data in-situ.

Computer Science↗

Spatial decomposition of structured grids for nuclear reactor simulations

Spatial decomposition methods based on graph partitioning are developed and implemented in the high fidelity neutron transport code MPACT. These graph-based spatial decomposition methods are more general than previous decomposition methods and typically provide better load balance and reduced runtimes due to their improved parallel efficiency. Correlations are drawn between simulation runtime and the balance of the partition for 2D simulations. Comparisons are made using partition balance metrics for different decomposition schemes in 2D and 3D simulations. Finally, for typical ranges of subdomains, graph-based partitioning methods offer significant reductions to runtimes. However, for highly decomposed problems, these graph-based methods may decrease convergence rates, thus reducing parallel efficiency compared to older methods.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Domain decomposition in the GPU-accelerated Shift Monte Carlo code

The GPU solver within the Shift continuous-energy Monte Carlo neutron transport code has been extended to provide domain decomposition in addition to domain replication to enable the solution of problems with memory requirements exceeding the capacity of a single GPU. The strategy follows the Multiple Set, Overlapping Domain (MSOD) approach that is used in Shift’s CPU solver and integrates into the event-based algorithm used for Shift’s GPU solver. Furthermore, the ability to assign processors to spatial domains non-uniformly has been maintained. In this work, two different approaches for communicating particle data between domains are considered, and multiple criteria for load balancing problems have been investigated. Numerical results are presented for both fresh and depleted small modular nuclear reactor (SMR) cores. A parallel efficiency of approximately 80% was achieved with up to 16 spatial domains measured relative to full domain replication. A scaling study on the Summit supercomputer demonstrates a weak scaling parallel efficiency of over 90% on over 24000 GPUs.

97 MATHEMATICS AND COMPUTING↗

A generalized massively parallel ultra-high order FFT-based Maxwell solver

Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser–matter interactions with Particle-In-Cell (PIC) codes. To enable a massively parallel scaling of these solvers, a novel parallelization technique was recently proposed, which consists in splitting the simulation domain into several processor sub-domains, with guard regions appended at each sub-domain boundary. Maxwell's equations are advanced independently on each sub-domain using local shared-memory FFTs (instead of a single distributed global FFT). This implies small truncation errors at sub-domain boundaries, the amplitude of which depends on guard regions sizes and order of the Maxwell solver. For moderate guard region sizes, this ’local’ technique proved to be highly scalable on up to a million cores and notably enabled the 3D modeling of so-called plasma mirrors, for which 8 guard cells only were enough to prevent truncation error growth. Yet, for other applications, the required number of guard cells might be much higher, which would severely limit the parallel efficiency of this technique due to the large volume of guard cells to be exchanged between sub-domains. In this context, we propose a novel parallelization technique that ensures very good scaling of FFT-based solvers with an arbitrarily high number of guard cells. Our ’hybrid’ technique consists in performing distributed FFTs on local groups of processors with guard regions now appended to boundaries of each group of processors. It uses a dual domain decomposition method for the Maxwell solver and other parts of the PIC cycle to keep the simulation load-balanced. This ’hybrid’ technique was implemented in the open source exascale library PICSAR. Benchmarks show that for a large number of guard cells (>16), the ’hybrid’ technique offers up to ×3 speed-up and ×8 memory savings compared to the ’local’ one.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC

In this work, we present an efficient implementation of polynomial filtering methods in PARSEC, a real-space pseudopotential based Kohn–Sham density functional theory solver. The implementation described here improves upon a Chebyshev-filtered subspace iteration algorithm used in the previous version of PARSEC. We present a hybrid polynomial filtering scheme that combines Chebyshev-filtered subspace iteration and a spectrum slicing method that partitions the spectrum into several spectral slices and uses bandpass-filtered subspace iteration to compute approximate eigenpairs within each interior slice simultaneously. We describe a procedure to partition a spectrum and construct polynomial filters. We also discuss a number of practical issues such as the use of appropriate data layouts for carrying out the computation on a two-dimensional process grid and how to achieve good load balance by allocating an appropriate number of process groups to each spectral slice. Numerical examples are presented to demonstrate the effectiveness of the hybrid polynomial filtering method as well as the superior parallel scalability of spectrum slicing in comparison to that of Chebyshev-filtered subspace iteration.

97 MATHEMATICS AND COMPUTING↗

A code-independent generalized actuator line model for wind farm aerodynamics over simple and complex terrain

Actuator line model representations of wind turbines reduce the simulation cost of wind farm aerodynamics relative to blade geometry resolving simulations. However, most implementations are code specific and may not have proper load balancing when run in parallel. Here, a generalized actuator line model (GALM) is developed to overcome this implementation drawback of existing approaches. The GALM can be coupled to any existing microscale solver with minimal or no modifications. The coupling of our GALM model with the open-source microscale code CgWind is used to demonstrate both its ease of use and fidelity. The results obtained from the coupled-model simulations are validated for both isolated turbine in wind tunnel experiments and measurements in offshore wind farm. Finally, an operational wind farm over complex terrain is demonstrated. The simulations show that wake meandering and power production are strongly influenced by terrain impacts. Access information for obtaining the code is provided.

17 WIND ENERGY↗

An accelerated approach to inline non-LTE modeling

A goal across many physics and engineering disciplines is to use radiation-hydrodynamics codes to accurately simulate systems that are expected to deviate from local thermodynamic equilibrium (LTE), such as laser-driven hohlraums, stellar coronae, and supernova ejecta. The computational expense of traditional non-LTE (NLTE) opacity calculations can dominate the cost of simulating these systems and render NLTE physics untenable in most cases. In this paper, we present a new parallel implementation for NLTE opacity calculations that employs advanced load balancing, vectorization, and memory management to significantly reduce the computational costs of these calculations. Using the radiation-hydrodynamics code xRAGE , we demonstrate this new implementation on three test problems and present order-of-magnitude speed improvements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Energy-efficient cooperative resource allocation and task scheduling for Internet of Things environments

Offloading Internet of Things (IoT) tasks to the cloud for further processing might not always lead to an optimal execution time, particularly in situations such as resource contention, under-provisioning, over-provisioning, and fragmentation. In addition, dynamically optimizing the number of Virtual Machines (VMs) for resource scheduling in order to meet application requirements remains a major research challenge. Further, existing resource scheduling algorithms focus primarily on minimizing operational costs while maximizing resource sharing and utilization. Considering energy utilization as part of the resource allocation and scheduling process as an optimization objective for maintaining load balancing has often been neglected. To address these challenges and more, we propose a cooperative energy-aware resource allocation and scheduling strategy based on a Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) multi-criteria decision-making method. Here we used the Grid Workloads Archive dataset to evaluate our proposed approach named TOPREAL. Experimental results with respect to the allocation of VM resources when considering processing a large segment of tasks indicate that TOPREAL outperforms existing algorithms in terms of energy savings, with an average improvement of 40.25%, while maintaining an average improvement of 16.21% when it comes to execution time. Results also demonstrate that our method can save an average of 78.06 processing hours and 63,215kJ of energy when compared to existing scheduling algorithms. These results demonstrate the effectiveness of our proposed model and the viability of using multi-criteria decision-making techniques such as TOPSIS to solve the resource allocation and scheduling problem in edge environments.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Fast analysis of molecular dynamics trajectories with graphics processing units-Radial distribution function histogramming

The calculation of radial distribution functions (RDFs) from molecular dynamics trajectory data is a common and computationally expensive analysis task. The rate limiting step in the calculation of the RDF is building a histogram of the distance between atom pairs in each trajectory frame. Here we present an implementation of this histogramming scheme for multiple graphics processing units (GPUs). The algorithm features a tiling scheme to maximize the reuse of data at the fastest levels of the GPU's memory hierarchy and dynamic load balancing to allow high performance on heterogeneous configurations of GPUs. Several versions of the RDF algorithm are presented, utilizing the specific hardware features found on different generations of GPUs. We take advantage of larger shared memory and atomic memory operations available on state-of-the-art GPUs to accelerate the code significantly. The use of atomic memory operations allows the fast, limited-capacity on-chip memory to be used much more efficiently, resulting in a fivefold increase in performance compared to the version of the algorithm without atomic operations. The ultimate version of the algorithm running in parallel on four NVIDIA GeForce GTX 480 (Fermi) GPUs was found to be 92 times faster than a multithreaded implementation running on an Intel Xeon 5550 CPU. On this multi-GPU hardware, the RDF between two selections of 1,000,000 atoms each can be calculated in 26.9 s per frame. The multi-GPU RDF algorithms described here are implemented in VMD, a widely used and freely available software package for molecular dynamics visualization and analysis.

97 MATHEMATICS AND COMPUTING↗

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.

97 MATHEMATICS AND COMPUTING↗

Π4U: A high performance computing framework for Bayesian uncertainty quantification of complex models

We present Π4U,{sup 1} an extensible framework, for non-intrusive Bayesian Uncertainty Quantification and Propagation (UQ+P) of complex and computationally demanding physical models, that can exploit massively parallel computer architectures. The framework incorporates Laplace asymptotic approximations as well as stochastic algorithms, along with distributed numerical differentiation and task-based parallelism for heterogeneous clusters. Sampling is based on the Transitional Markov Chain Monte Carlo (TMCMC) algorithm and its variants. The optimization tasks associated with the asymptotic approximations are treated via the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). A modified subset simulation method is used for posterior reliability measurements of rare events. The framework accommodates scheduling of multiple physical model evaluations based on an adaptive load balancing library and shows excellent scalability. In addition to the software framework, we also provide guidelines as to the applicability and efficiency of Bayesian tools when applied to computationally demanding physical models. Theoretical and computational developments are demonstrated with applications drawn from molecular dynamics, structural dynamics and granular flow.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimization and large scale computation of an entropy-based moment closure

We present computational advances and results in the implementation of an entropy-based moment closure, M N , in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as P N , but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the M N algorithm that do not appear for the P N algorithm. We also observe that in weak scaling tests, the ratio in time to solution of M N to P N decreases.

97 MATHEMATICS AND COMPUTING↗

Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.

97 MATHEMATICS AND COMPUTING↗

A hybrid incremental projection method for thermal-hydraulics applications

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

97 MATHEMATICS AND COMPUTING↗

A novel partitioning method for block-structured adaptive meshes

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

97 MATHEMATICS AND COMPUTING↗

A physics-motivated Centroidal Voronoi Particle domain decomposition method

In this paper, we propose a novel domain decomposition method for large-scale simulations in continuum mechanics by merging the concepts of Centroidal Voronoi Tessellation (CVT) and Voronoi Particle dynamics (VP). The CVT is introduced to achieve a high-level compactness of the partitioning subdomains by the Lloyd algorithm which monotonically decreases the CVT energy. The number of computational elements between neighboring partitioning subdomains, which scales the communication effort for parallel simulations, is optimized implicitly as the generated partitioning subdomains are convex and simply connected with small aspect-ratios. Moreover, Voronoi Particle dynamics employing physical analogy with a tailored equation of state is developed, which relaxes the particle system towards the target partition with good load balance. Since the equilibrium is computed by an iterative approach, the partitioning subdomains exhibit locality and the incremental property. Numerical experiments reveal that the proposed Centroidal Voronoi Particle (CVP) based algorithm produces high-quality partitioning with high efficiency, independently of computational-element types. Thus it can be used for a wide range of applications in computational science and engineering.

97 MATHEMATICS AND COMPUTING↗