Browsing by Subject "Parallel computing"
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Item The Graph 500 Benchmark on a Medium-Size Distributed-Memory Cluster with High-Performance Interconnect(2012-12-17) Angel, Jordan B.; Flores, Amy M.; Heritage, Justine S.; Wardrip, Nathan C.; Raim, Andrew M.; Gobbert, Matthias K.; Murphy, Richard C.; Mountain, David J.While traditional performance benchmarks for high-performance computers measure the speed of arithmetic operations, memory access time is a more useful performance gauge for many large problems today. The Graph 500 benchmark has been developed to measure a computer’s performance in memory retrieval. The Graph 500 implementation considers large, randomly generated graphs, which may be spread across many nodes on a distributed memory cluster. The benchmark conducts breadth-first searches on these graphs, and measures performance in billions of traversed edges per second (GTEPS). We present our experience implementing and running the Graph 500 benchmark on the medium-size distributed-memory cluster tara in the UMBC High Performance Computing Facility (www.umbc.edu/hpcf). The cluster tara has 82 compute nodes, each with two quad-core Intel Nehalem X5550 CPUs and 24 GB of memory, connected by a high-performance quad-data rate InfiniBand interconnect. Results are explained in detail in terms of the machine architecture, which demonstrates that the Graph 500 benchmark indeed provides a measure of memory access as the chief bottleneck for many applications. Our best run to date was of scale 31 using 64 nodes and achieved a GTEPS rate that placed tara at rank 98 on the November 2012 Graph 500 list.Item Hidden Markov Models for High Dimensional Data with Geostatistical Applications(2021-01-01) Majumder, Reetam; Neerchal, Nagaraj K; Mathematics and Statistics; StatisticsStochastic precipitation generators (SPGs) are a class of statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. In this thesis, we construct SPGs for daily precipitation data that is specified as a semi-continuous distribution with a point mass at zero for no precipitation and a mixture of Exponential or Gamma distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMMs) where the underlying climate conditions form the states.Maximum likelihood estimation of an HMM's parameters has historically relied on the Baum-Welch algorithm, which is a modification of the Expectation Maximization algorithm. We implement variational Bayes (VB) as an alternative estimation procedure for HMMs with semi-continuous emissions. Stochastic optimization in the form of stochastic variational Bayes (SVB) has been employed for computational speedup in practical cases. A univariate state process is often unable to adequately capture the underlying weather conditions over large watersheds, since different areas can have local weather regimes. We extend the HMM to a linked HMM (LHMM) where locations are divided into clusters. Each cluster's emissions are assumed to arise from a cluster-specific state process; the state processes are correlated and together form a multivariate Markov chain (MMC). The MMC provides more flexibility to accommodate heterogeneity that might be present in larger geographical areas. A Gaussian copula is constructed to capture the correlation structure of the MMC. Finally, we also construct a Gaussian copula for the emissions of the HMM to explicitly parameterize the pairwise correlations of observed positive precipitation. Daily precipitation data over the Chesapeake Bay watershed in the Eastern coast of the USA is used as a demonstrative case study. Remote sensing precipitation data is sourced from the GPM-IMERG dataset for the wet season between July to September from 2000-2019. Synthetic data generated from the clustered LHMM can reproduce the monthly precipitation statistics as well as the spatial correlations present in the historical GPM-IMERG data.Item A Memory-Efficient Finite Volume Method for Advection-Diffusion-Reaction Systems with Non-Smooth Sources(Wiley, 2014-06-20) Schafer, Jonas; Huang, Xuan; Kopecz, Stefan; Birken, Philipp; Gobbert, Matthias K.; Meister, AndreasWe present a parallel matrix-free implicit finite volume scheme for the solution of unsteady three-dimensional advection-diffusion-reaction equations with smooth and Dirac-Delta source terms. The scheme is formally second order in space and a Newton-Krylov method is employed for the appearing nonlinear systems in the implicit time integration. The matrix-vector product required is hardcoded without any approximations, obtaining a matrix-free method that needs little storage and is well suited for parallel implementation. We describe the matrix-free implementation of the method in detail and give numerical evidence of its second order convergence in the presence of smooth source terms. For non-smooth source terms the convergence order drops to one half. Furthermore, we demonstrate the method’s applicability for the long time simulation of calcium flow in heart cells and show its parallel scaling.