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At least 415 records · Page 23

An extension to V ORO ++ for multithreaded computation of Voronoi cells

V ORO ++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. V ORO ++ was released in 2009 and is based on computing the Voronoi cell for each particle individually. Here, we take advantage of modern computer hardware, and extend the original serial version to allow for multithreaded computation of Voronoi cells via the OpenMP application programming interface. We test the performance of the code, and demonstrate that it can achieve parallel efficiencies greater than 95% in many cases. Further, the multithreaded extension follows standard OpenMP programming paradigms, allowing it to be incorporated into other programs. We provide an example of this using the VoroTop software library, performing a multithreaded Voronoi cell topology analysis of up to 102.4 million particles.

97 MATHEMATICS AND COMPUTING↗

Argo NodeOS: Toward Unified Resource Management for Exascale

Exascale systems are expected to feature hundreds of thousands of compute nodes with hundreds of hardware threads and complex memory hierarchies with a mix of on-package and persistent memory modules. In this context, the Argo project is developing a new operating system for exascale machines. Targeting production workloads using workflows or coupled codes, we improve the Linux kernel on several fronts. We extend the memory management of Linux to be able to subdivide NUMA memory nodes, allowing better resource partitioning among processes running on the same node. We also add support for memory-mapped access to node- local, PCIe-attached NVRAM devices and introduce a new scheduling class targeted at parallel runtimes supporting user- level load balancing.

Perarnau, Swann↗

Automatic Differentiation of C++ Codes on Emerging Manycore Architectures with Sacado

Automatic differentiation (AD) is a well-known technique for evaluating analytic derivatives of calculations implemented on a computer, with numerous software tools available for incorporating AD technology into complex applications. However, a growing challenge for AD is the efficient differentiation of parallel computations implemented on emerging manycore computing architectures such as multicore CPUs, GPUs, and accelerators as these devices become more pervasive. In this work, we explore forward mode, operator overloading-based differentiation of C++ codes on these architectures using the widely available Sacado AD software package. In particular, we leverage Kokkos, a C++ tool providing APIs for implementing parallel computations that is portable to a wide variety of emerging architectures. Here we describe the challenges that arise when differentiating code for these architectures using Kokkos, and two approaches for overcoming them that ensure optimal memory access patterns as well as expose additional dimensions of fine-grained parallelism in the derivative calculation. We describe the results of several computational experiments that demonstrate the performance of the approach on a few contemporary CPU and GPU architectures. We then conclude with applications of these techniques to the simulation of discretized systems of partial differential equations.

97 MATHEMATICS AND COMPUTING↗

Thermal stability analysis of the fine structure of solar prominences

The linear thermal stability of a 2D periodic structure (alternatively hot and cold) in a uniform magnetic field is analyzed. The energy equation includes wave heating (assumed proportional to density), radiative cooling and both conduction parallel and orthogonal to magnetic lines. The equilibrium is perturbed at constant gas pressure. With parallel conduction only, it is found to be unstable when the length scale 1// is greater than 45 Mn. In that case, orthogonal conduction becomes important and stabilizes the structure when the length scale is smaller than 5 km. On the other hand, when the length scale is greater than 5 km, the thermal equilibrium is unstable, and the corresponding time scale is about 10,000 s: this result may be compared to observations showing that the lifetime of the fine structure of solar prominences is about one hour; consequently, our computations suggest that the size of the unresolved threads could be of the order of 10 km only.

Demoulin, Pascal↗

Optimizing the Accelerated Recursive Doubling Algorithm for Block Tridiagonal Systems of Equations

The need to solve block tridiagonal systems with hundreds or thousands of right-hand sides for the same block tridiagonal matrix is common in a variety of disciplines. To meet this need, the Accelerated Recursive Doubling Algorithm was developed. After a right-hand side independent phase, the algorithm allows for the quick, online calculation of solutions for different right-hand sides. In this work, we present methods to optimize the Accelerated Recursive Doubling Algorithm in memory usage and computation time in a hybrid parallelization model. The right-hand side independent phase of the naïve implementation takes ≥ 11/3 the amount of memory required to store the tridiagonal matrix, while our implementation reduces the fraction to ≈ 5/3 . The right-hand side dependent phase of the naïve implementation takes ≥ 6 times the amount of memory required to store the right-hand side, while our implementation reduces the fraction to ≈ 3. The computation time for the independent phase is reduced to ≈ 2/3 times that of the naïve implementation, while the computation time for the dependent phase is reduced to ≈ 5/9 . With increasing numbers of shared-memory threads q on every distributed processing element, we have O(q) theoretical speedup.

97 MATHEMATICS AND COMPUTING↗

Enabling communication concurrency through flexible MPI endpoints

MPI defines a one-to-one relationship between MPI processes and ranks. This model captures many use cases effectively; however, it also limits communication concurrency and interoperability between MPI and programming models that utilize threads. This paper describes the MPI endpoints extension, which relaxes the longstanding one-to-one relationship between MPI processes and ranks. Using endpoints, an MPI implementation can map separate communication contexts to threads, allowing them to drive communication independently. Endpoints also enable threads to be addressable in MPI operations, enhancing interoperability between MPI and other programming models. These characteristics are illustrated through several examples and an empirical study that contrasts current multithreaded communication performance with the need for high degrees of communication concurrency to achieve peak communication performance.

Communication↗

Optimizing Approximate Weighted Matching on Nvidia Kepler K40

Matching is a fundamental graph problem with numerous applications in science and engineering. While algorithms for computing optimal matchings are difficult to parallelize, approximation algorithms on the other hand generally compute high quality solutions and are amenable to parallelization. In this paper, we present efficient implementations of the current best algorithm for half-approximate weighted matching, the Suitor algorithm, on Nvidia Kepler K-40 platform. We develop four variants of the algorithm that exploit hardware features to address key challenges for a GPU implementation. We also experiment with different combinations of work assigned to a warp. Using an exhaustive set of $269$ inputs, we demonstrate that the new implementation outperforms the previous best GPU algorithm by $10$ to $100\times$ for over $100$ instances, and from $100$ to $1000\times$ for $15$ instances. We also demonstrate up to $20\times$ speedup relative to $2$ threads, and up to $5\times$ relative to $16$ threads on Intel Xeon platform with $16$ cores for the same algorithm. The new algorithms and implementations provided in this paper will have a direct impact on several applications that repeatedly use matching as a key compute kernel. Further, algorithm designs and insights provided in this paper will benefit other researchers implementing graph algorithms on modern GPU architectures.

GPU↗

Parallel implementation and performance optimization of the configuration-interaction method

The configuration-interaction (CI) method, long a popular approach to describe quantum many-body systems, is cast as a very large sparse matrix eigenpair problem with matrices whose dimension can exceed one billion. Such formulations place high demands on memory capacity and memory bandwidth - - two quantities at a premium today. In this paper, we describe an efficient, scalable implementation, BIGSTICK, which, by factorizing both the basis and the interaction into two levels, can reconstruct the nonzero matrix elements on the fly, reduce the memory requirements by one or two orders of magnitude, and enable researchers to trade reduced resources for increased computational time. We optimize BIGSTICK on two leading HPC platforms - - the Cray XC30 and the IBM Blue Gene/Q. Specifically, we not only develop an empirically-driven load balancing strategy that can evenly distribute the matrix-vector multiplication across 256K threads, we also developed techniques that improve the performance of the Lanczos reorthogonalization. Combined, these optimizations improved performance by 1.3-8× depending on platform and configuration.

97 MATHEMATICS AND COMPUTING↗

Communication-Avoiding and Memory-Constrained Sparse Matrix-Matrix Multiplication at Extreme Scale

Sparse matrix-matrix multiplication (SpGEMM) is a widely used kernel in various graph, scientific computing and machine learning algorithms. In this paper, we consider SpGEMMs performed on hundreds of thousands of processors generating trillions of nonzeros in the output matrix. Distributed SpGEMM at this extreme scale faces two key challenges: (1) high communication cost and (2) inadequate memory to generate the output. Furthermore, we address these challenges with an integrated communication-avoiding and memory-constrained SpGEMM algorithm that scales to 262,144 cores (more than 1 million hardware threads) and can multiply sparse matrices of any size as long as inputs and a fraction of output fit in the aggregated memory. As we go from 16,384 cores to 262,144 cores on a Cray XC40 supercomputer, the new SpGEMM algorithm runs 10x faster when multiplying large-scale protein-similarity matrices.

97 MATHEMATICS AND COMPUTING↗

A Methodology for the Rapid Development of Scalable HPC Data Services

There is growing evidence in the scientifc computing community that parallel file systems are not sufficient for all HPC storage workloads. This realization has motivated extensive research in new storage system designs. The question of which alternative we should turn towards implies that there could be a single answer satisfying a wide range of very diverse applications. We argue that such a generic solution does not exist. Instead, custom data services should be designed and tailored to the needs of specific applications on specific hardware. Furthermore, custom data services should be designed in close collaboration with users. In this paper, we present a methodology for the rapid development of such data services. This methodology promotes the design of reusable building blocks that can be composed together efficiently through a runtime based on high-performance threading, tasking, and remote procedure calls. We illustrate the success of our methodology by showcasing three examples of data services designed from the same building blocks, yet targeting entirely different applications.

Dorier, Mattieu↗

Three point lead screw positioning apparatus for a cavity tuning plate

Three lead screws are provided for adjusting the position of a traversing plate. Each of the three lead screws is threaded through a collar that is press fitted through the center of one of three pinion gears. A sun gear meshes with all three pinion gears and transversely moves the three lead screws upon actuation of a drive gear. The drive gear meshes with the sun gear and is driven by a handle or servomotor. When the handle or servomotor rotates the drive gear, the sun gear rotates causing the three pinion gears to rotate, thus, causing transverse movement of the three lead screws and, accordingly, transverse movement of the transversing plate. When the drive gear rotates, the traversing plate is driven in and out of a microwave cavity. Thus, the length or size of the cavity can be tuned while maintaining the traversing plate in an exact parallel relationship with an opposing plate on another end of the cavity.

Calco, Frank S.↗

Implementing Arbitrary/Common Concurrent Writes of CRCW PRAM

The Parallel Random Access Machines (PRAM) abstraction is the simplest and most elegant algorithmic model for the design and analysis of parallel algorithms. It consists of different models categorized based on the underlying memory access mode used, the most powerful of which is the Concurrent Read Concurrent Write (CRCW) model. A PRAM algorithm describes a series of rounds, each of which consists of a collection of operations that can be executed concurrently within the same time step. However, the lack of support for concurrent memory accesses and the prevalence of asynchronous programming models led to the belief that implementing CRCW PRAM algorithms is unattainable and prompted many to avoid this model except for theoretical studies of optimal performance.In this work, we study the arbitrary and common concurrent writes in the CRCW PRAM model and explore implementation challenges on general-purpose systems. Moreover, we examine current practices for implementing common/arbitrary concurrent writes and propose a new efficient lightweight and thread-safe method to implement concurrent writes through leveraging atomic instructions. To demonstrate the efficacy of our method, we developed OpenMP kernels for classical CRCW PRAM algorithms and provide experimental results and comparisons based on run time performance measured over the x86 multicore architecture. Our results show a performance speedup compared to current practices up to 4.5x across all our benchmarks.

Ghanim, Fady↗

Exploiting communication concurrency on high performance computing systems

Although logically available, applications may not exploit enough instantaneous communication concurrency to maximize hardware utilization on HPC systems. This is exacerbated in hybrid programming models such as SPMD+OpenMP. We present the design of a "multi-threaded" runtime able to transparently increase the instantaneous network concurrency and to provide near saturation bandwidth, independent of the application configuration and dynamic behavior. The runtime forwards communication requests from application level tasks to multiple communication servers. Our techniques alleviate the need for spatial and temporal application level message concurrency optimizations. Experimental results show improved message throughput and bandwidth by as much as 150% for 4KB bytes messages on InfiniBand and by as much as 120% for 4KB byte messages on Cray Aries. For more complex operations such as all-to-all collectives, we observe as much as 30% speedup. This translates into 23% speedup on 12,288 cores for a NAS FT implemented using FFTW. We also observe as much as 76% speedup on 1,500 cores for an already optimized UPC+OpenMP geometric multigrid application using hybrid parallelism.

97 MATHEMATICS AND COMPUTING↗

Direction-optimizing Label Propagation Framework for Structure Detection in Graphs: Design, Implementation, and Experimental Analysis

Label Propagation is not only a well-known machine learning algorithm for classification but also an effective method for discovering communities and connected components in networks. We propose a new Direction-optimizing Label Propagation Algorithm (DOLPA) framework that enhances the performance of the standard Label Propagation Algorithm (LPA), increases its scalability, and extends its versatility and application scope. As a central feature, the DOLPA framework relies on the use of frontiers and alternates between label push and label pull operations to attain high performance. It is formulated in such a way that the same basic algorithm can be used for finding communities or connected components in graphs by only changing the objective function used. Additionally, DOLPA has parameters for tuning the processing order of vertices in a graph to reduce the number of edges visited and improve the quality of solution obtained. We present the design and implementation of the enhanced algorithm as well as our shared-memory parallelization of it using OpenMP. We also present an extensive experimental evaluation of our implementations using the LFR benchmark and real-world networks drawn from various domains. Compared with an implementation of LPA for community detection available in a widely used network analysis software, we achieve at most five times the F-Score while maintaining similar runtime for graphs with overlapping communities. We also compare DOLPA against an implementation of the Louvain method for community detection using the same LFR-graphs and show that DOLPA achieves about three times the F-Score at just 10% of the runtime. For connected component decomposition, our algorithm achieves orders of magnitude speedups over the basic LP-based algorithm on large-diameter graphs, up to 13.2× speedup over the Shiloach-Vishkin algorithm, and up to 1.6× speedup over Afforest on an Intel Xeon processor using 40 threads.

97 MATHEMATICS AND COMPUTING↗

The scheme machine: A case study in progress in design derivation at system levels

The Scheme Machine is one of several design projects of the Digital Design Derivation group at Indiana University. It differs from the other projects in its focus on issues of system design and its connection to surrounding research in programming language semantics, compiler construction, and programming methodology underway at Indiana and elsewhere. The genesis of the project dates to the early 1980's, when digital design derivation research branched from the surrounding research effort in programming languages. Both branches have continued to develop in parallel, with this particular project serving as a bridge. However, by 1990 there remained little real interaction between the branches and recently we have undertaken to reintegrate them. On the software side, researchers have refined a mathematically rigorous (but not mechanized) treatment starting with the fully abstract semantic definition of Scheme and resulting in an efficient implementation consisting of a compiler and virtual machine model, the latter typically realized with a general purpose microprocessor. The derivation includes a number of sophisticated factorizations and representations and is also deep example of the underlying engineering methodology. The hardware research has created a mechanized algebra supporting the tedious and massive transformations often seen at lower levels of design. This work has progressed to the point that large scale devices, such as processors, can be derived from first-order finite state machine specifications. This is roughly where the language oriented research stops; thus, together, the two efforts establish a thread from the highest levels of abstract specification to detailed digital implementation. The Scheme Machine project challenges hardware derivation research in several ways, although the individual components of the system are of a similar scale to those we have worked with before. The machine has a custom dual-ported memory to support garbage collection. It consists of four tightly coupled processes--processor, collector, allocator, memory--with a very non-trivial synchronization relationship. Finally, there are deep issues of representation for the run-time objects of a symbolic processing language. The research centers on verification through integrated formal reasoning systems, but is also involved with modeling and prototyping environments. Since the derivation algebra is basd on an executable modeling language, there is opportunity to incorporate design animation in the design process. We are looking for ways to move smoothly and incrementally from executable specifications into hardware realization. For example, we can run the garbage collector specification, a Scheme program, directly against the physical memory prototype, and similarly, the instruction processor model against the heap implementation.

Johnson, Steven D.↗

Virtual Machine Language 2.1

VML (Virtual Machine Language) is an advanced computing environment that allows spacecraft to operate using mechanisms ranging from simple, time-oriented sequencing to advanced, multicomponent reactive systems. VML has developed in four evolutionary stages. VML 0 is a core execution capability providing multi-threaded command execution, integer data types, and rudimentary branching. VML 1 added named parameterized procedures, extensive polymorphism, data typing, branching, looping issuance of commands using run-time parameters, and named global variables. VML 2 added for loops, data verification, telemetry reaction, and an open flight adaptation architecture. VML 2.1 contains major advances in control flow capabilities for executable state machines. On the resource requirements front, VML 2.1 features a reduced memory footprint in order to fit more capability into modestly sized flight processors, and endian-neutral data access for compatibility with Intel little-endian processors. Sequence packaging has been improved with object-oriented programming constructs and the use of implicit (rather than explicit) time tags on statements. Sequence event detection has been significantly enhanced with multi-variable waiting, which allows a sequence to detect and react to conditions defined by complex expressions with multiple global variables. This multi-variable waiting serves as the basis for implementing parallel rule checking, which in turn, makes possible executable state machines. The new state machine feature in VML 2.1 allows the creation of sophisticated autonomous reactive systems without the need to develop expensive flight software. Users specify named states and transitions, along with the truth conditions required, before taking transitions. Transitions with the same signal name allow separate state machines to coordinate actions: the conditions distributed across all state machines necessary to arm a particular signal are evaluated, and once found true, that signal is raised. The selected signal then causes all identically named transitions in all present state machines to be taken simultaneously. VML 2.1 has relevance to all potential space missions, both manned and unmanned. It was under consideration for use on Orion.

Riedel, Joseph E.↗

Magnetohydrodynamic simulations of outflows from accretion disks

Magnetohydrodynamic simulations have been made of the formation of outflows from a Keplerian disk threaded by a magnetic field. The disk is treated as a boundary condition, where matter is ejected with Keplerian azimuthal speed and poloidal speed less than the slow magnetosonic velocity, and where boundary conditions on the magnetic field correspond to a highly conducting disk. Initially, the space above the disk, the corona, is filled with high specific entropy plasma in thermal equilibrium in the gravitational potential of the central object. The initial magnetic field is poloidal and is represented by a superposition of monopoles located below the plane of the disk. The rotation of the disk twists the initial poloidal magnetic field, and this twist propagates into the corona pushing and collimating matter into jetlike outflow in a cylindrical region. Matter outflowing from the disk flows and accelerates in the z-direction owing to both the magnetic and pressure gradient forces. The flow accelerates through the slow magnetosonic and Alfven surfaces and at larger distances through the fast magnetosonic surface. The flow velocity of the jet is approximately parallel to the z-axis, and the collimation results from the pinching force of the toroidal magnetic field. For a nonrotating disk no collimation is observed.

Ustyugova, G. V.↗

Radiative Heat Transfer Calculation on 16384 GPUs Using a Reverse Monte Carlo Ray Tracing Approach with Adaptive Mesh Refinement

Modeling thermal radiation is computationally challenging in parallel due to its all-to-all physical and resulting computational connectivity, and is also the dominant mode of heat transfer in practical applications such as next-generation clean coal boilers, being modeled by the Uintah framework. However, a direct all-to-all treatment of radiation is prohibitively expensive on large computers systems whether homogeneous or heterogeneous. DOE Titan and the planned DOE Summit and Sierra machines are examples of current and emerging GPU-based heterogeneous systems where the increased processing capability of GPUs over CPUs exacerbates this problem. These systems require that computational frameworks like Uintah leverage an arbitrary number of on-node GPUs, while simultaneously utilizing thousands of GPUs within a single simulation. We show that radiative heat transfer problems can be made to scale within Uintah on heterogeneous systems through a combination of reverse Monte Carlo ray tracing (RMCRT) techniques combined with AMR, to reduce the amount of global communication. In particular, significant Uintah infrastructure changes, including a novel lock and contention-free, thread-scalable data structure for managing MPI communication requests and improved memory allocation strategies were necessary to achieve excellent strong scaling results to 16384 GPUs on Titan.

Computer Science↗