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$H(\mathrm {div})$ preconditioning for a mixed finite element formulation of the diffusion problem with random data

Mathematics of Computation 2010年第270期79卷 733-760页

作者： Elman, Howard Furnival, Darran Powell, Catherine Department of Computer Science and Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 Applied Mathematics and Scientific Computing Program University of Maryland College Park Maryland 20742 National Oceanographic Centre Southampton S014 32H School of Mathematics University of Manchester Oxford Road Manchester M13 9PL United Kingdom

Abstract: We study $H(\mathrm {div})$ preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an $H(\mathrm {div})$ operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the Arnold-Falk-Winther multigrid algorithm presented in 1997 by varying the spatial discretization from grid to grid whilst keeping the stochastic discretization fixed. We extend the deterministic analysis to accommodate the modified $H(\mathrm {div})$ operator and establish spectral equivalence bounds with a new multigrid V-cycle operator that are independent of the spatial and stochastic discretization parameters. We implement multigrid within a block-diagonal preconditioner for the full saddle-point problem, derive eigenvalue bounds for the preconditioned system matrices and investigate the impact of all the discretization parameters on the convergence rate of preconditioned minres.

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Maximizing adaptivity in hierarchical topological models using cancellation trees

Maximizing adaptivity in hierarchical topological models usi...

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Workshop on Mathematical Foundations of scientific Visualization, computer Graphics, and Massive Data Exploration, 2004

作者： Bremer, Peer-Timo Pascucci, Valerio Hamann, Bernd Department of Computer Science University of Illinois Urbana-Champaign United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Institute for Data Analysis and Visualization Department of Computer Science University of California Davis United States

ISBN: (纸本)9783642543005

We present a highly adaptive hierarchical representation of the topology of functions defined over two-manifold domains. Guided by the theory of Morse–Smale complexes, we encode dependencies between cancellations of critical points using two independent structures: a traditional mesh hierarchy to store connectivity information and a new structure called cancellation trees to encode the configuration of critical points. Cancellation trees provide a powerful method to increase adaptivity while using a simple, easy-to-implement data structure. The resulting hierarchy is significantly more flexible than the one previously reported (IEEE Trans. Vis. Comput. Graph. 10(4):385–396, 2004). In particular, the resulting hierarchy is guaranteed to be of logarithmic height. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： Trees (mathematics)

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New expansions of numerical eigenvalues by Wilson's element

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Journal of Computational and applied Mathematics 2009年第1期225卷 213-226页

作者： Lin, Qun Huang, Hung-Tsai Li, Zi-Cai Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences P.O. Box 2719 Beijing 1000080 China Department of Applied Mathematics I-Shou University 840 Taiwan Department of Applied Mathematics National Sun Yat-sen University Kaohsiung 80424 Taiwan Department of Computer Science and Engineering National Sun Yat-sen University Kaohsiung 80424 Taiwan

The paper explores new expansions of eigenvalues for - Δ u = λ ρ u in S with Dirichlet boundary conditions by Wilson's element. The expansions indicate that Wilson's element provides lower bounds of the eigenvalues. By the extrapolation or the splitting extrapolation, the O (h4) convergence rate can be obtained, where h is the maximal boundary length of uniform rectangles. Numerical experiments are carried to verify the theoretical analysis made. It is worth pointing out that these results are new, compared with the recent book, Lin and Lin [Q. Lin, J. Lin, Finite Element Methods;Accuracy and Improvement, science Press, Beijing, 2006]. © 2009.

关键词： Extrapolation

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Compression and occlusion culling for fast isosurface extraction from massive datasets

Compression and occlusion culling for fast isosurface extrac...

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Workshop on Mathematical Foundations of scientific Visualization, computer Graphics, and Massive Data Exploration, 2004

作者： Gregorski, Benjamin Senecal, Joshua Duchaineau, Mark Joy, Kenneth I. Center for Applied Scientific Computing Lawrence Livermore National Laboratory 7000 East Avenue LivermoreCA94551 United States Institute for Data Analysis and Visualization Department of Computer Science University of California Davis One Shields Avenue DavisCA95616 United States

ISBN: (纸本)9783642543005

We present two algorithms for data compression and occlusion culling that improve interactive, adaptive isosurface extraction from large volume datasets. Our algorithm, based on hierarchical tetrahedral meshes defined by longest edge bisection, allows arbitrary isosurfaces to be adaptively extracted at interactive rates from losslessly compressed volumes where the region of interest, determined at runtime by user interaction, is decompressed on-the-fly. For interactive applications, we exploit frame-to-frame coherence between consecutive views to simplify the mesh structure in occluded regions and eliminate occluded triangles significantly reducing the complexity of the visualized surface and the underlying multiresolution volume representation. We extend the use of hardware accelerated occlusion queries to adaptive isosurface extraction applications where the surface geometry and topology change with the level-of-detail and view-point and the user can select an arbitrary isovalue for visualization. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： Extraction

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Machine learning based online performance prediction for runtime parallelization and task scheduling

Machine learning based online performance prediction for run...

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International Symposium on Performance Analysis of Systems and Software, ISPASS 2009

作者： Li, Jiangtian Ma, Xiaosong Singh, Karan Schulz, Martin De Supinski, Bronis McKee, Sally A. Dept. of Computer Science North Carolina State University Raleigh NC 27606 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge TN 37831 United States Computer Systems Laboratory Cornell University Ithaca NY 14850 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore CA 94550 United States Department of Computer Science and Engineering Chalmers University of Technology Göteborg Sweden

ISBN: (纸本)9781424441846

With the emerging many-core paradigm, parallel programming must extend beyond its traditional realm of scientific applications. Converting existing sequential applications as well as developing next-generation software requires assistance from hardware, compilers and runtime systems to exploit parallelism transparently within applications. These systems must decompose applications into tasks that can be executed in parallel and then schedule those tasks to minimize load imbalance. However, many systems lack a priori knowledge about the execution time of all tasks to perform effective load balancing with low scheduling overhead. In this paper, we approach this fundamental problem using machine learning techniques first to generate performance models for all tasks and then applying those models to perform automatic performance prediction across program executions. We also extend an existing scheduling algorithm to use generated task cost estimates for online task partitioning and scheduling. We implement the above techniques in the pR framework, which transparently parallelizes scripts in the popular R language, and evaluate their performance and overhead with both a realworld application and a large number of synthetic representative test scripts. Our experimental results show that our proposed approach significantly improves task partitioning and scheduling, with maximum improvements of 21.8%, 40.3% and 22.1% and average improvements of 15.9%, 16.9% and 4.2% for LMM (a real R application) and synthetic test cases with independent and dependent tasks, respectively. © 2009 IEEE.

关键词： Scheduling algorithms

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Image-based automatic object localisation in iSpace environment

Image-based automatic object localisation in iSpace environm...

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10th International Symposium of Hungarian Researchers on Computational Intelligence and Informatics, CINTI 2009

作者： Zanaty, Péter Korondi, Péter Sziebig, Gábor Jeni, László A. Department of Scientific Computing Narvik University College Electrical Engineering and Space technology Hungary Department of Mechatronics Budapest University of Technology and Economics Optics and Applied Informatics Hungary Computer and Automation Research Institute Japan Department of Industrial Engineering Narvik University College Norway Institute of Industrial Science University of Tokyo Japan

Localization is a fundamental task in mobile robotics and in indoor environments we can use various sensors to solve this problem. In the Intelligent Space environment we can use laser range finders or ultrasonic positioning systems to localize and track mobile robots. Nevertheless, our final goal is to substitute these sensors and accomplish this task using just cameras. In this paper, we show the feasibility of determining the robot's location based on the images received from a single camera. In our experimental room we used a surveillance camera, which can be controlled to pan/tilt in order to change the point of view. The camera had been mounted on the ceiling and six preset positions were selected to cover the whole area. The object recognition is based on colour space filtering and contour detection. Finally, the contours of the detected objects are transformed from the image space to the world coordinate system and the polygons are reduced to simpler ones. The system is able to detect not only the position of the objects, but their orientations.

关键词： Cameras

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Architectural implications for spatial object association algorithms

Architectural implications for spatial object association al...

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International Symposium on Parallel and Distributed Processing (IPDPS)

作者： Vijay S. Kumar Tahsin Kurc Joel Saltz Ghaleb Abdulla Scott R. Kohn Celeste Matarazzo Department of Computer Science and Engineering Ohio State Uinversity USA Center for Comprehensive Informatics Emory University USA Center for Applied Scientific Computing Lawrence Livemore National Laboratory USA

Spatial object association, also referred to as crossmatch of spatial datasets, is the problem of identifying and comparing objects in two or more datasets based on their positions in a common spatial coordinate system. In this work, we evaluate two crossmatch algorithms that are used for astronomical sky surveys, on the following database system architecture configurations: (1) Netezza Performance Server reg , a parallel database system with active disk style processing capabilities, (2) MySQL Cluster, a high-throughput network database system, and (3) a hybrid configuration consisting of a collection of independent database system instances with data replication support. Our evaluation provides insights about how architectural characteristics of these systems affect the performance of the spatial crossmatch algorithms. We conducted our study using real use-case scenarios borrowed from a large-scale astronomy application known as the large synoptic survey telescope (LSST).

关键词： Database systems Astronomy Telescopes Catalogs Clustering algorithms Distributed databases computer science Data engineering Informatics scientific computing

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Towards realization of scientific dataspaces for the breath gas analysis research community

Towards realization of scientific dataspaces for the breath ...

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1st International Workshop on Portals for Life sciences, IWPLS 2009

作者： Elsayed, Ibrahim Ludescher, Thomas Schwarz, Konrad Feilhauer, Thomas Amann, Anton Brezany, Peter Department of Scientific Computing Faculty of Computer Science University of Vienna Nordbergstrasse 15/C/3 1090 Vienna Austria Research Center for Process and Product Engineering Vorarlberg University of Applied Sciences Hochschulstrasse 1 6850 Dornbirn Austria Austria and Breath Research Institute of Austrian Academy of Sciences Department of Operative Medicine Innsbruck Medical University Innsbruck Austria

Motivation: scientific dataspaces aim at providing associated mechanisms for managing semantically rich relationships among scientific data sources (primary data) and its corresponding findings (derived data). The latter result from a set of activities defining concrete preprocessing and analysis methods (background data) that were applied to a source dataset. To keep track of scientific experiments that are being conducted by members of a scientific community these experiments should be linked with user information i.e. institutional affiliation, email address, working field, etc. of the scientist who conducted the experiment. This paper deals with the development of a scientific dataspace for the breath gas analysis community. Breath gas analysis is an emerging new scientific field with a growing international scientific community addressing many different breath gas studies in terms of investigating and screening for hundreds of compounds in exhaled breath gas. The purpose of breath gas analysis scientific dataspaces is to enable collaborating scientists and institutions several important activities, which include: (a) access to distributed breath gas data and analytical resources collected and developed at different research institutions around the world and (b) to easily contribute to and leverage the resources of an international- And national-scale, multi-institutional environment. Results: This paper describes the conception and prototypical implementation of the scientific dataspace paradigm for breath gas analysis. The scientific dataspace is evaluated on top of applications from breath gas analysis. Availability: We discuss the scientific dataspace paradigm in the context of applications from breath gas analysis, however the concepts introduced can also be deployed in other research domains.

关键词： Gases

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Machine learning based online performance prediction for runtime parallelization and task scheduling

Machine learning based online performance prediction for run...

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IEEE International Symposium on Performance Analysis of Systems and Software

作者： Jiangtian Li Xiaosong Ma Karan Singh Martin Schulz Bronis R. de Supinski Sally A. McKee Department of Computer Science North Carolina State University Raleigh NC USA Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge TN USA Computer Systems Laboratory Cornell University Ithaca NY USA Center of Applied Scientific Computing Lawrence Livemore National Laboratory Livermore CA USA Department of Computer Science and Engineering Chalmers University of Technology Goteborg Sweden

ISBN: (纸本)9781424441853

With the emerging many-core paradigm, parallel programming must extend beyond its traditional realm of scientific applications. Converting existing sequential applications as well as developing next-generation software requires assistance from hardware, compilers and runtime systems to exploit parallelism transparently within applications. These systems must decompose applications into tasks that can be executed in parallel and then schedule those tasks to minimize load imbalance. However, many systems lack a priori knowledge about the execution time of all tasks to perform effective load balancing with low scheduling overhead. In this paper, we approach this fundamental problem using machine learning techniques first to generate performance models for all tasks and then applying those models to perform automatic performance prediction across program executions. We also extend an existing scheduling algorithm to use generated task cost estimates for online task partitioning and scheduling. We implement the above techniques in the pR framework, which transparently parallelizes scripts in the popular R language, and evaluate their performance and overhead with both a real-world application and a large number of synthetic representative test scripts. Our experimental results show that our proposed approach significantly improves task partitioning and scheduling, with maximum improvements of 21.8%, 40.3% and 22.1% and average improvements of 15.9%, 16.9% and 4.2% for LMM (a real R application) and synthetic test cases with independent and dependent tasks, respectively.

关键词： Machine learning Runtime Application software Predictive models Testing Parallel programming Hardware Load management Scheduling algorithm Costs

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Preserving time in large-scale communication traces

Preserving time in large-scale communication traces

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22nd ACM International Conference on Supercomputing, ICS'08

作者： Ratn, Prasun Mueller, Frank De Supinski, Bronis R. Schulz, Martin North Carolina State University Department of Computer Science Raleigh NC 27695-7534 United States Lawrence Livermore National Laboratory Center for Applied Scientific Computing Livermore CA 94551 United States

ISBN: (纸本)9781605581583

Analyzing the performance of large-scale scientific applications is becoming increasingly difficult due to the sheer size of performance data gathered. Recent work on scalable communication tracing applies online interprocess compression to address this problem. Yet, analysis of communication traces requires knowledge about time progression that cannot trivially be encoded in a scalable manner during compression. We develop scalable time stamp encoding schemes for communication traces. At the same time, our work contributes novel insights into the scalable representation of time stamped data. We show that our representations capture sufficient information to enable what-if explorations of architectural variations and analysis for path-based timing irregularities while not requiring excessive disk space. We evaluate the ability of several time-stamped compressed MPI trace approaches to enable accurate timed replay of communication events. Our lossless traces are orders of magnitude smaller, if not near constant size, regardless of the number of nodes while preserving timing information suitable for application tuning or assessing requirements of future procurements. Our results prove timepreserving tracing without loss of communication information can scale in the number of nodes and time steps, which is a result without precedent. Copyright 2008 Association for computing Machinery.

关键词： Message passing

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