Multilevel Techniques in Large Scale Computation

First-order system least squares (FOSLS) is a methodology that offers an alternative to standard methods for solving partial differential equations. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. In a companion paper [M. Berndt, T. A. Manteuffel, S. F. McCormick, and G. Starke, Analysis of first-order system least squares ({FOSLS}) for elliptic problems with discontinuous coefficients: Part I, SIAM J. Numer. Anal., 43 (2005), pp. 386--408], ellipticity of an appropriately scaled least-squares bilinear form is established in a natural norm. For some geometries this ellipticity is independent of the size of the jumps in the coefficients. The occurrence of singularities at interface corners, cross-points, reentrant corners, and irregular boundary points is discussed, and a basis of singular functions with local support around singular points is established. This paper describes a method for including discrete versions of the singular basis functions together with standard finite element spaces in a least-squares format at little additional computational cost. The singular basis functions are constructed to match the jump conditions that arise at interfaces between regions of continuity of the diffusion coefficient. Because these basis functions must be approximated in practice, the resulting discretization is by nature nonconforming. This necessitates the establishment here of a general error estimate for FOSLS L2 minimization problems discretized by nonconforming finite elements. An advantage of the FOSLS formulation is that this estimate does not involve the consistency error term usually present in bounds for other methods. Based on this general estimate, error bounds are derived for the finite element space that includes singular basis functions. Numerical tests are included that confirm these discretization error bounds. Finally, a multilevel method is developed for solving the discrete system that uses singular basis functions on all levels, and its efficiency is demonstrated by the numerical results.

SUMMARY We present an inversion algorithm tailored for point gravity data. As the data are from multiple surveys, it is inconsistent with regards to spacing and accuracy. An algorithm design objective is the exact placement of gravity observations to ensure no interpolation of the data is needed prior to any inversion. This is accommodated by discretization using an unstructured tetrahedral finite-element mesh for both gravity and density with mesh nodes located at all observation points and a first-order system least-squares (FOSLS) formulation for the gravity modelling equations. Regularization follows the Bayesian framework where we use a differential operator approximation of an exponential covariance kernel, avoiding the usual requirement of inverting large dense covariance matrices. Rather than using higher order basis functions with continuous derivatives across element faces, regularization is also implemented with a FOSLS formulation using vector-valued property function (density and its gradient). Minimization of the cost function, comprised of data misfit and regularization, is achieved via a Lagrange multiplier method with the minimum of the gravity FOSLS functional as a constraint. The Lagrange variations are combined into a single equation for the property function and solved using an integral form of the pre-conditioned conjugate gradient method (I-PCG). The diagonal entries of the regularization operator are used as the pre-conditioner to minimize computational costs and memory requirements. Discretization of the differential operators with the finite-element method (FEM) results in matrix systems that are solved with smoothed aggregation algebraic multigrid pre-conditioned conjugate gradient (AMG-PCG). After their initial setup, the AMG-PCG operators and coarse grid solvers are reused in each iteration step, further reducing computation time. The algorithm is tested on data from 23 surveys with a total of 6519 observation points in the Mt Isa–Cloncurry region in north–west Queensland, Australia. The mesh had about 2.5 million vertices and 16.5 million cells. A synthetic case was also tested using the same mesh and error measures for localized concentrations of high and low densities. The inversion results for different parameters are compared to each other as well as to lower order smoothing. Final inversion results are shown with and without depth weighting and compared to previous geological studies for the Mt Isa–Cloncurry region.

The parabolic equation (PE) method is widely used in radiowave propagation predictions. It has the advantages of high efficiency and stability, but it will lead to greater predicting errors in some situations, because the effects of transverse terrain gradients are not modeled. This problem can be solved by extending the 2D PE to the three-dimensional (3D) PE. However, the computing efficiency will degrade because of large scale matrix operations. In this paper, a new method is presented, in which the 3D PE is decomposed into two 2D PEs. It increases the computational efficiency and accuracy effectively. To verify the capability of the proposed method in radiowave propagation prediction, an experiment platform was set up. The computational results using this new method are compared with the experimental and Method of Moment (MoM) numerical computational results. Good agreements are achieved in the comparison. The study of radiowave propagation under complex environments is vitally important for improving the effective signal coverage in wireless communication and television broadcasting with plenty of urban buildings as well as mountainous terrains. It presents a big challenge due to the multiple wave propagation mechanisms involving the line of sight, diffraction and scattering propagation and the characteristic of large scale computation. The major issues refer to how to keep the computational accuracy and conducting the large scale computation at the same time. To meet the request for large scale computation of actual engineering problems, the modified empirical formulas are often used for analysis and computation with the drawback of poor computational accuracy, and the variance of the predicted propagation loss is generally 2 to 5 dB for the flat terrain, but for the complex terrain, the variance of the predicted propagation loss is usually about 5 to 10 dB. Many computational methods have been developed to improve the predicted accuracy. The commonly used methods are geometric diffraction methods, path integration methods and FDTD. It is hard to meet the requirement of engineering computation because these methods are computationally expensive and require high data accuracy of the terrain database at the same time (1). The Parabolic Equation (PE) method is a computational method for radiowave propagation loss besides the full wave method and ray tracing method, and has become a research focus. The PE method has high potential in radiowave propagation of mobile communication and broadcasting and television signal coverage as it can not only deal with complex terrain boundary conditions accurately, but also deal with complex atmosphere waveguide structure. Compared with the full wave method, the PE method deals with an unidirectional wave propagation, in which the equation can be solved by the step marching method in the propagation direction. The PE method can reduce the computational complexity of the full wave equation.

The least-squares pseudo-spectral method for Navier–Stokes equations

Deep least-squares methods: An unsupervised learning-based numerical method for solving elliptic PDEs

A project team involved in large scale computer system development usually has a prescribed or traditional approach to guide them in accomplishing their task. This approach is influenced by system development standards. There are situations though, where business requirements dictate the need to revise the approach. The present paper addresses both the traditional and non-traditional methods of approach for the large scale computer project. It also describes the key role the human factors specialist plays in either approach.

BEM for wave interaction with structures and low storage accelerated methods for large scale computation

The comparative performance characteristics of COBOL programs in a small versus large computer systems are investigated. The vehicle consists of a set of synthetic benchmark COBOL programs, each measuring a particular aspect of COBOL proigrams; and in addition a large actual COBOL program. Measurement of the CPU execution time and the elapsed clock time for various COBOL computations, data manipulation, and input/output is made on both a large scale computer (IBM 370/158) and a minicomputer (Texas Instruments TI980). Results of a number of such experiments are presented and comparisons made between results gotten from the two systems.

Cloud computing is now a well-adopted computing paradigm. With unprecedented scalability and flexibility, the computational cloud is able to carry out large scale computing tasks in parallel. The datacenter cloud is a new cloud computing model that uses multi-datacenter architectures for large scale massive data processing or computing. In datacenter cloud computing, the overall efficiency of the cloud depends largely on the workload scheduler, which allocates clients’ tasks to different Cloud datacenters. Developing high performance workload scheduling techniques in Cloud computing imposes a great challenge which has been extensively studied. Most previous works aim only at minimizing the completion time of all tasks. However, timeliness is not the only concern, reliability and security are also very important. In this work, a comprehensive Quality of Service (QoS) model is proposed to measure the overall performance of datacenter clouds. An advanced Cross-Entropy based stochastic scheduling (CESS) algorithm is developed to optimize the accumulative QoS and sojourn time of all tasks. Experimental results show that our algorithm improves accumulative QoS and sojourn time by up to 56.1 and 25.4 percent respectively compared to the baseline algorithm. The runtime of our algorithm grows only linearly with the number of Cloud datacenters and tasks. Given the same arrival rate and service rate ratio, our algorithm steadily generates scheduling solutions with satisfactory QoS without sacrificing sojourn time.

The first-order system least-squares (FOSLS) finite element method for solving partial differential equations has many advantages, including the construction of symmetric positive definite algebraic linear systems that can be solved efficiently with multilevel iterative solvers. However, one drawback of the method is the potential lack of conservation of certain properties. One such property is conservation of mass. This paper describes a strategy for achieving mass conservation for a FOSLS system by changing the minimization process to that of a constrained minimization problem. If the space of corresponding Lagrange multipliers contains the piecewise constants, then local mass conservation is achieved similarly to the standard mixed finite-element method. To make the strategy more robust and not add too much computational overhead to solving the resulting saddle-point system, an overlapping Schwarz process is used.KeywordsConservationFirst-order system least-squaresFinite elementsDomain decompositionTwo-level

A secure, reliable and economic power supply is closely linked to a fast, efficient and dependable communications infrastructure. The appliance of the cloud computing model meets the requirements of data and computing intensive smart grid applications. Using internal network improves the calculation, storage capacity, data security of the overall system, reducing the system expansion investment, thus providing ideas and strong technical support in smart grid and large scale computing can be achieved over existing network. In this paper, we have focused to distributed verification protocol to guaranty the data storage security in cloud computing. This article also introduces the application field the merit of cloud computing, such as to reduce the users' cost. It provide secure and dependable data storage center. The intelligent control techniques lift the level of energy efficient and security lowering the level of the pollution and greenhouse gas emission. In this paper, we have proposed a internet connectivity device model instead of having C.P.U. and discs, for cloud computing.

The eleven papers in this special section focus on both system- and circuit-level aspects of emerging memory and storage technologies. The overwhelmingly increasing demand for both storage and computation necessitates revisiting the traditional memory subsystems used in processors and storage systems to take advantage of emerging memory technologies. Dynamic Random Access Memory (DRAM) and Static Random Access Memory (SRAM) have been ubiquitously used for decades as main memory and as on-chip cache, respectively. Scaling and power issues of these traditional memory technologies have led to significant investment in emerging memory technologies. On the other hand, fundamental limitations of mechanical disk drives have brought great attention to further explore the design space of solid-state drives (SSDs). The promising features of emerging memory technologies such as low power consumption, increased performance, lower susceptibility to particle strikes, and higher bit density have prompted researchers to seek new organizations in the different memory-hierarchy levels, to propose new circuitry and algorithms to improve performance and reduce power consumption, and to develop new schemes to enhance system reliability.

Environment configuration is a significant challenge in large scale computing. An application that runs correctly on one carefully-prepared machine may fail completely on another machine, creating wasted effort and serious concerns about long-term reproducibility. Virtual machines and system containers provide a partial solution to this problem, in that they allow for the accurate reconstruction of an entire computing environment. However, when used directly, they have the dual problems of significant overhead and a lack of portability. To avoid this problem, we present Umbrella, a tool for specifying and materializing comprehensive execution environments from the hardware all the way up to software and data. A user simply invokes Umbrella with the desired task, and Umbrella determines the minimum mechanism necessary to run the task - direct execution, a system container, a local virtual machine, or submission to a cloud or grid environment. We present the overall design of Umbrella and demonstrate its use to precisely execute a high energy physics application across many platforms using combinations of chroot, Docker, Parrot, Condor, and Amazon EC2.

IThe National Energy Research Scientific Computing Center (NERSC) is the primary computing center for the DOE Office of Science, serving approximately 4,000 users and hosting some 550 projects that involve nearly 700 codes for a wide variety of scientific disciplines. In addition to large-scale computing resources NERSC provides critical staff support and expertise to help scientists make the most efficient use of these resources to advance the scientific mission of the Office of Science. In May 2011, NERSC, DOE’s Office of Advanced Scientific Computing Research (ASCR) and DOE’s Office of Nuclear Physics (NP) held a workshop to characterize HPC requirements for NP research over the next three to five years. The effort is part of NERSC’s continuing involvement in anticipating future user needs and deploying necessary resources to meet these demands. The workshop revealed several key requirements, in addition to achieving its goal of characterizing NP computing. The key requirements include: 1. Larger allocations of computational resources at NERSC; 2. Visualization and analytics support; and 3. Support at NERSC for the unique needs of experimental nuclear physicists. This report expands upon these key points and adds others. The results are based upon representative samples, called “case studies,” of the needs of science teams within NP. The case studies were prepared by NP workshop participants and contain a summary of science goals, methods of solution, current and future computing requirements, and special software and support needs. Participants were also asked to describe their strategy for computing in the highly parallel, “multi-core” environment that is expected to dominate HPC architectures over the next few years. The report also includes a section with NERSC responses to the workshop findings. NERSC has many initiatives already underway that address key workshop findings and all of the action items are aligned with NERSC strategic plans.

This paper describes a speech recognition system developed as a voice-input programming system. A modified version of BASIC which we call 'SPOKEN-BASIC-1' is selected as a task for speech recognition. The system consists of four major components: acoustic, lexical matching, syntactic and semantic processors. 71 sentences spoken by each of four speakers have been applied to the system for gathering several statistics on system performance. The system have achieved a sentence recognition rate of 85.5 %. The average time required to recognize an utterance is from 1/4 to 1/5 times real time on the large scale computer. The two space search strategies, depth-first method and best-first method have been compared quantitatively in their effectiveness. Further, various types of knowledge sources have been investigated in their contribution to the system performance.