Idle Period Propagation in Message-Passing Applications

Idle periods on different processes of Message Passing applications are unavoidable. While the origin of idle periods on a single process is well understood as the effect of system and architectural random delays, yet it is unclear how these idle periods propagate from one process to another. It is important to understand idle period propagation in Message Passing applications as it allows application developers to design communication patterns avoiding idle period propagation and the consequent performance degradation in their applications. To understand idle period propagation, we introduce a methodology to trace idle periods when a process is waiting for data from a remote delayed process in MPI applications. We apply this technique in an MPI application that solves the heat equation to study idle period propagation on three different systems. We confirm that idle periods move between processes in the form of waves and that there are different stages in idle period propagation. Our methodology enables us to identify a self-synchronization phenomenon that occurs on two systems where some processes run slower than the other processes.Comment: 18th International Conference on High Performance Computing and Communications, IEEE, 201

Performance Modeling and Prediction for the Scalable Solution of Partial Differential Equations on Unstructured Grids

This dissertation studies the sources of poor performance in scientific computing codes based on partial differential equations (PDEs), which typically perform at a computational rate well below other scientific simulations (e.g., those with dense linear algebra or N-body kernels) on modern architectures with deep memory hierarchies. We identify that the primary factors responsible for this relatively poor performance are: insufficient available memory bandwidth, low ratio of work to data size (good algorithmic efficiency), and nonscaling cost of synchronization and gather/scatter operations (for a fixed problem size scaling). This dissertation also illustrates how to reuse the legacy scientific and engineering software within a library framework. Specifically, a three-dimensional unstructured grid incompressible Euler code from NASA has been parallelized with the Portable Extensible Toolkit for Scientific Computing (PETSc) library for distributed memory architectures. Using this newly instrumented code (called PETSc-FUN3D) as an example of a typical PDE solver, we demonstrate some strategies that are effective in tolerating the latencies arising from the hierarchical memory system and the network. Even on a single processor from each of the major contemporary architectural families, the PETSc-FUN3D code runs from 2.5 to 7.5 times faster than the legacy code on a medium-sized data set (with approximately 105 degrees of freedom). The major source of performance improvement is the increased locality in data reference patterns achieved through blocking, interlacing, and edge reordering. To explain these performance gains, we provide simple performance models based on memory bandwidth and instruction issue rates. Experimental evidence, in terms of translation lookaside buffer (TLB) and data cache miss rates, achieved memory bandwidth, and graduated floating point instructions per memory reference, is provided through accurate measurements with hardware counters. The performance models and experimental results motivate algorithmic and software practices that lead to improvements in both parallel scalability and per-node performance. We identify the bottlenecks to scalability (algorithmic as well as implementation) for a fixed-size problem when the number of processors grows to several thousands (the expected level of concurrency on terascale architectures). We also evaluate the hybrid programming model (mixed distributed/shared) from a performance standpoint

21st Century Simulation: Exploiting High Performance Computing and Data Analysis

This paper identifies, defines, and analyzes the limitations imposed on Modeling and Simulation by outmoded paradigms in computer utilization and data analysis. The authors then discuss two emerging capabilities to overcome these limitations: High Performance Parallel Computing and Advanced Data Analysis. First, parallel computing, in supercomputers and Linux clusters, has proven effective by providing users an advantage in computing power. This has been characterized as a ten-year lead over the use of single-processor computers. Second, advanced data analysis techniques are both necessitated and enabled by this leap in computing power. JFCOM's JESPP project is one of the few simulation initiatives to effectively embrace these concepts. The challenges facing the defense analyst today have grown to include the need to consider operations among non-combatant populations, to focus on impacts to civilian infrastructure, to differentiate combatants from non-combatants, and to understand non-linear, asymmetric warfare. These requirements stretch both current computational techniques and data analysis methodologies. In this paper, documented examples and potential solutions will be advanced. The authors discuss the paths to successful implementation based on their experience. Reviewed technologies include parallel computing, cluster computing, grid computing, data logging, OpsResearch, database advances, data mining, evolutionary computing, genetic algorithms, and Monte Carlo sensitivity analyses. The modeling and simulation community has significant potential to provide more opportunities for training and analysis. Simulations must include increasingly sophisticated environments, better emulations of foes, and more realistic civilian populations. Overcoming the implementation challenges will produce dramatically better insights, for trainees and analysts. High Performance Parallel Computing and Advanced Data Analysis promise increased understanding of future vulnerabilities to help avoid unneeded mission failures and unacceptable personnel losses. The authors set forth road maps for rapid prototyping and adoption of advanced capabilities. They discuss the beneficial impact of embracing these technologies, as well as risk mitigation required to ensure success

An evaluation of parallel job scheduling for ASCI Blue-Pacific

In this paper we analyze the behavior of a gang-scheduling strategy that we are developing for the ASCI Blue-Pacific machines. Using actual job logs for one of the ASCI machines we generate a statistical model of the current workload with hyper Erlang distributions. We then vary the parameters of those distributions to generate various workloads, representative of different operating points of the machine. Through simulation we obtain performance parameters for three different scheduling strategies: (i) first-come first-serve, (ii) gang-scheduling, and (iii) backfilling. Our results show that backfilling, can be very effective for the common operating points in the 60-70% utilization range. However, for higher utilization rates, time-sharing techniques such as gang-scheduling offer much better performance

An error estimate of Gaussian Recursive Filter in 3Dvar problem

Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with a very large covariance matrix having Gaussian correlation structure. This operation may be interpreted as a Gaussian convolution, that is a very expensive numerical kernel. Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively applied in the meteorology, in the oceanography and in forecast models. In this paper, we deal with an oceanographic 3D-Var data assimilation scheme, named OceanVar, where the linear system is solved by using the Conjugate Gradient (GC) method by replacing, at each step, the Gaussian convolution with RFs. Here we give theoretical issues on the discrete convolution approximation with a first order (1st-RF) and a third order (3rd-RF) recursive filters. Numerical experiments confirm given error bounds and show the benefits, in terms of accuracy and performance, of the 3-rd RF.Comment: 9 page

New Sequential and Scalable Parallel Algorithms for Incomplete Factor Preconditioning

The solution of large, sparse, linear systems of equations Ax = b is an important kernel, and the dominant term with regard to execution time, in many applications in scientific computing. The large size of the systems of equations being solved currently (millions of unknowns and equations) requires iterative solvers on parallel computers. Preconditioning, which is the process of translating a linear system into a related system that is easier to solve, is widely used to reduce solution time and is sometimes required to ensure convergence. Level-based preconditioning (ILU(ℓ)) has long been used in serial contexts and is widely recognized as robust and effective for a wide range of problems. However, the method has long been regarded as an inherently sequential technique. Parallelism, it has been thought, can be achieved primarily at the expense of increased iterations. We dispute these claims. The first half of this dissertation takes an in-depth look at structurally based ILU(ℓ) symbolic factorization. There are two definitions of fill level, “sum” and “max,” that have been proposed. Hitherto, these definitions have been cast in terms of matrix terminology. We develop a sequence of lemmas and theorems that provide graph theoretic characterizations of both definitions; these characterizations are based on the static graph of a matrix, G(A). Our Incomplete Fill Path Theorem characterizes fill levels per the sum definition; this is the definition that is used in most library implementations of the “classic” ILU(ℓ) factorization algorithm. Our theorem leads to several new graph-search algorithms that compute factors identical, or nearly identical, to those computed by the “classic” algorithm. Our analyses shows that the new algorithms have lower run time complexity than that of the previously existing algorithms for certain classes of matrices that are commonly encountered in scientific applications. The second half of this dissertation presents a Parallel ILU algorithmic framework (PILU). This framework enables scalable parallel ILU preconditioning by combining concepts from domain decomposition and graph ordering. The framework can accommodate ILU(ℓ) factorization as well as threshold-based ILUT methods. A model implementation of the framework, the Euclid library, was developed as part of this dissertation. This library was used to obtain experimental results for Poisson\u27s equation, the Convection-Diffusion equation, and a nonlinear Radiative Transfer problem. The experiments, which were conducted on a variety of platforms with up to 400 CPUs, demonstrate that our approach is highly scalable for arbitrary ILU(ℓ) fill levels