We present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem, our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.
We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia's agile software components toolkit. The latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.
As supercomputers move to exascale, the number of cores per node continues to increase, but the I/O bandwidth between nodes is increasing more slowly. This leads to computational power outstripping I/O bandwidth. This growth, in turn, encourages moving as much of an HPC workflow as possible onto the node in order to minimize data movement. One particular method of application composition, enclaves, co-locates different operating systems and runtimes on the same node where they communicate by in situ communication mechanisms. In this work, we describe a mechanism for communicating between composed applications. We implement a mechanism using Copy onWrite cooperating with XEMEM shared memory to provide consistent, implicitly unsynchronized communication across enclaves. We then evaluate this mechanism using a composed application and analytics between the Kitten Lightweight Kernel and Linux on top of the Hobbes Operating System and Runtime. These results show a 3% overhead compared to an application running in isolation, demonstrating the viability of this approach.
We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result, the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.
Formulation of locally conservative least-squares finite element methods (LSFEMs) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require non-standard boundary conditions (Bochev and Gunzburger, 2009 [3]), while methods that admit the no-slip condition satisfy the incompressibility equation only approximately (Bochev and Gunzburger, 2009 [4, Chapter 7]). Here we address this problem by proving a new non-standard stability bound for the velocity-vorticity-pressure Stokes system augmented with a no-slip boundary condition. This bound gives rise to a norm-equivalent least-squares functional in which the velocity can be approximated by div-conforming finite element spaces, thereby enabling a locally-conservative approximations of this variable. We also provide a practical realization of the new LSFEM using high-order spectral mimetic finite element spaces (Kreeft et al., 2011) and report several numerical tests, which confirm its mimetic properties.
Optical networks hold great promise for improving the performance of supercomputers, yet they have always proven just out of reach. This talk will examine the potential of optical interconnects, barriers to adoption, and possible solutions from hardware/software co-design.
As supercomputers move to exascale, the number of cores per node continues to increase, but the I/O bandwidth between nodes is increasing more slowly. This leads to computational power outstripping I/O bandwidth. This growth, in turn, encourages moving as much of an HPC workflow as possible onto the node in order to minimize data movement. One particular method of application composition, enclaves, co-locates different operating systems and runtimes on the same node where they communicate by in situ communication mechanisms. In this work, we describe a mechanism for communicating between composed applications. We implement a mechanism using Copy onWrite cooperating with XEMEM shared memory to provide consistent, implicitly unsynchronized communication across enclaves. We then evaluate this mechanism using a composed application and analytics between the Kitten Lightweight Kernel and Linux on top of the Hobbes Operating System and Runtime. These results show a 3% overhead compared to an application running in isolation, demonstrating the viability of this approach.
The considerable interest in the high performance computing (HPC) community regarding analyzing and visualization data without first writing to disk, i. e., in situ processing, is due to several factors. First is an I/O cost savings, where data is analyzed/visualized while being generated, without first storing to a filesystem. Second is the potential for increased accuracy, where fine temporal sampling of transient analysis might expose some complex behavior missed in coarse temporal sampling. Third is the ability to use all available resources, CPU's and accelerators, in the computation of analysis products. This STAR paper brings together researchers, developers and practitioners using in situ methods in extreme-scale HPC with the goal to present existing methods, infrastructures, and a range of computational science and engineering applications using in situ analysis and visualization.
Proceedings of the International Conference on Supercomputing
Fiala, David; Mueller, Frank; Ferreira, Kurt B.; Engelmann, Christian
Concern is growing in the high-performance computing (HPC) community on the reliability of future extreme- scale systems. Current efforts have focused on appli- cation fault-tolerance rather than the operating system (OS), despite the fact that recent studies have suggested that failures in OS memory may be more likely. The OS is critical to a system's correct and efficient operation of the node and processes it governs-and the parallel na- ture of HPC applications means any single node failure generally forces all processes of this application to ter- minate due to tight communication in HPC. Therefore, the OS itself must be capable of tolerating failures in a robust system. In this work, we introduce mini-ckpts, a framework which enables application survival despite the occurrence of a fatal OS failure or crash. minickpts achieves this tolerance by ensuring that the crit- ical data describing a process is preserved in persistent memory prior to the failure. Following the failure, the OS is rejuvenated via a warm reboot and the applica- tion continues execution effectively making the failure and restart transparent. The mini-ckpts rejuvenation and recovery process is measured to take between three to six seconds and has a failure-free overhead of between 3-5% for a number of key HPC workloads. In contrast to current fault-tolerance methods, this work ensures that the operating and runtime systems can continue in the presence of faults. This is a much finer-grained and dynamic method of fault-tolerance than the current coarse-grained application-centric methods. Handling faults at this level has the potential to greatly reduce overheads and enables mitigation of additional faults.
Fault tolerance is a key challenge to building the first exascale system. To understand the potential impacts of failures on next-generation systems, significant effort has been devoted to collecting, characterizing and analyzing failures on current systems. These studies require large volumes of data and complex analysis. Because the occurrence of failures in large-scale systems is unpredictable, failures are commonly modeled as a stochastic process. Failure data from current systems is examined in an attempt to identify the underlying probability distribution and its statistical properties. In this paper, we use modeling to examine the impact of failure distributions on the time-to-solution and the optimal checkpoint interval of applications that use coordinated checkpoint/restart. Using this approach, we show that as failures become more frequent, the failure distribution has a larger influence on application performance. We also show that as failure times are less tightly grouped (i.e., as the standard deviation increases) the underlying probability distribution has a greater impact on application performance. Finally, we show that computing the checkpoint interval based on the assumption that failures are exponentially distributed has a modest impact on application performance even when failures are drawn from a different distribution. Our work provides critical analysis and guidance to the process of analyzing failure data in the context of coordinated checkpoint/restart. Specifically, the data presented in this paper helps to distinguish cases where the failure distribution has a strong influence on application performance from those cases when the failure distribution has relatively little impact.
We present a study of the 'snap-back' regime of resistive switching hysteresis in bipolar TaOx memristors, identifying power signatures in the electronic transport. Using a simple model based on the thermal and electric field acceleration of ionic mobilities, we provide evidence that the 'snap-back' transition represents a crossover from a coupled thermal and electric-field regime to a primarily thermal regime, and is dictated by the reconnection of a ruptured conducting filament. We discuss how these power signatures can be used to limit filament radius growth, which is important for operational properties such as power, speed, and retention.
2016 IEEE/ACES International Conference on Wireless Information Technology, ICWITS 2016 and System and Applied Computational Electromagnetics, ACES 2016 - Proceedings
We explore how reliable the ALEGRA MHD code is in its static limit. Also, we explore (in the quasi-static approximation) the process of evolution of the magnetic fields inside and outside an inclusion and the parameters for which the quasi-static approach provides for self-consistent results.
Measuring and controlling the power and energy consumption of high performance computing systems by various components in the software stack is an active research area [13, 3, 5, 10, 4, 21, 19, 16, 7, 17, 20, 18, 11, 1, 6, 14, 12]. Implementations in lower level software layers are beginning to emerge in some production systems, which is very welcome. To be most effective, a portable interface to measurement and control features would significantly facilitate participation by all levels of the software stack. We present a proposal for a standard power Application Programming Interface (API) that endeavors to cover the entire software space, from generic hardware interfaces to the input from the computer facility manager.
This reports describes extensions of DEDICOM (DEcomposition into DIrectional COMponents) data models [3] that incorporate bound and linear constraints. The main purpose of these extensions is to investigate the use of improved data models for unsupervised part-of-speech tagging, as described by Chew et al. [2]. In that work, a single domain, two-way DEDICOM model was computed on a matrix of bigram fre- quencies of tokens in a corpus and used to identify parts-of-speech as an unsupervised approach to that problem. An open problem identi ed in that work was the com- putation of a DEDICOM model that more closely resembled the matrices used in a Hidden Markov Model (HMM), speci cally through post-processing of the DEDICOM factor matrices. The work reported here consists of the description of several models that aim to provide a direct solution to that problem and a way to t those models. The approach taken here is to incorporate the model requirements as bound and lin- ear constrains into the DEDICOM model directly and solve the data tting problem as a constrained optimization problem. This is in contrast to the typical approaches in the literature, where the DEDICOM model is t using unconstrained optimization approaches, and model requirements are satis ed as a post-processing step.
Remote sensing systems produce large volumes of high-resolution images that are difficult to search. The GeoGraphy (pronounced Geo-Graph-y) framework [2, 20] encodes remote sensing imagery into a geospatial-temporal semantic graph representation to enable high level semantic searches to be performed. Typically scene objects such as buildings and trees tend to be shaped like blocks with few holes, but other shapes generated from path networks tend to have a large number of holes and can span a large geographic region due to their connectedness. For example, we have a dataset covering the city of Philadelphia in which there is a single road network node spanning a 6 mile x 8 mile region. Even a simple question such as "find two houses near the same street" might give unexpected results. More generally, nodes arising from networks of paths (roads, sidewalks, trails, etc.) require additional processing to make them useful for searches in GeoGraphy. We have assigned the term Path Network Recovery to this process. Path Network Recovery is a three-step process involving (1) partitioning the network node into segments, (2) repairing broken path segments interrupted by occlusions or sensor noise, and (3) adding path-aware search semantics into GeoQuestions. This report covers the path network recovery process, how it is used, and some example use cases of the current capabilities.
High-performance computing (HPC) systems enable scientists to numerically model complex phenomena in many important physical systems. The next major milestone in the development of HPC systems is the construction of the rst supercomputer capable executing more than an exa op, 1018 oating point operations per second. On systems of this scale, failures will occur much more frequently than on current systems. As a result, resilience is a key obstacle to building next-generation extremescale systems. Coordinated checkpointing is currently the most widely-used mechanism for handling failures on HPC systems. Although coordinated checkpointing remains e ective on current systems, increasing the scale of today's systems to build next-generation systems will increase the cost of fault tolerance as more and more time is taken away from the application to protect against or recover from failure. Rollback avoidance techniques seek to mitigate the cost of checkpoint/restart by allowing an application to continue its execution rather than rolling back to an earlier checkpoint when failures occur. These techniqes include failure prediction and preventive migration, replicated computation, fault-tolerant algorithms, and softwarebased memory fault correction. In this thesis, we examine how rollback avoidance techniques can be used to address failures on extreme-scale systems. Using a combination of analytic modeling and simulation, we evaluate the potential impact of rollback avoidance on these systems. We then present a novel rollback avoidance technique that exploits similarities in application memory. Finally, we examine the feasibility of using this technique to protect against memory faults in kernel memory.
This is the definitive user manual for the I FPACK 2 package in the Trilinos project. I FPACK 2 pro- vides implementations of iterative algorithms (e.g., Jacobi, SOR, additive Schwarz) and processor- based incomplete factorizations. I FPACK 2 is part of the Trilinos T PETRA solver stack, is templated on index, scalar, and node types, and leverages node-level parallelism indirectly through its use of T PETRA kernels. I FPACK 2 can be used to solve to matrix systems with greater than 2 billion rows (using 64-bit indices). Any options not documented in this manual should be considered strictly experimental .