Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

ElGENANALYSlS OF LARGE ELECTRIC POWER SYSTEMS

Modern electric power systems are large and complicated, and, in many regions, the generation and transmission systems are operating near their limits. Eigenanalysis is one of the tools used to analyze the behavior of these systems. Standard eigenvalue methods require that simplified models be used for these analyses; however, these simplified models do not adequately model all of the characteristics of large power systems. Thus, new eigenanalysis methods that can analyze detailed power system models are required. The primary objectives of the work described in this report were I) to determine the availability of eigenanalysis algorithms that are better than methods currently being applied and that could be used an large power systems and 2) to determine if vector supercomputers could be used to significantly increase the size of power systems that can be analyzed by a standard power system eigenanalysis code. At the request of the Bonneville Power Administration, the Pacific Northwest Laboratory (PNL) conducted a literature review of methods currently used for the eigenanalysis of large electric power systems, as well as of general eigenanalysis algorithms that are applicable to large power systems. PNL found that a number of methods are currently being used for the this purpose, and all seem to work fairly well. Furthermore, most of the general eigenanalysis techniques that are applicable to power systems have been tried on these systems, and most seem to work fairly well. One of these techniques, a variation of the Arnoldi method, has been incorporated into a standard power system eigenanalysis package. Overall, it appears that the general purpose eigenanalysis methods are more versatile than most of the other methods that have been used for power systems eigenanalysis. In addition, they are generally easier to use. For some problems, however, it appears that some of the other eigenanalysis methods may be better. Power systems eigenanalysis requires the computation of eigenvalues of nonsymmetric matrices. Such computations are fairly difficult, however, and they constitute an area of active research. Thus, research in this area should be closely monitored, and, as new methods become available, they should be tested on large power systems. PNL also investigated the use of vector supercomputers to enlarge the size of power systems that can be analyzed by MASS, a standard power system eigenanalysis code. MASS was converted to run on a Cray supercomputer. On a conventional computer, MASS is limited to power system problems with about 500 states because of computer time constraints. Running MASS on a Cray X-MP EA/232, however, PNL found that a problem with about 2200 states could be solved in about 26 minutes. Furthermore, by moving to a larger Cray, it should be possible to use MASS to analyze power systems with 5,000 to 10,000 states. Problems with 5,000 states would probably take about 5 Cray hours, while a problem with 10,000 states would probably take about 43 Cray hours, though the actual execution times will depend on the type of Cray used. Problems requiring 5 Cray hours are not uncommon. Problems requiring 43 Cray hours, however, would be fairly expensive. Thus, power systems with about 5000 states probably represent an upper limit on the size of problems that one would want to routinely solve using a Cray version of MASS

High Performance Computing Facility Operational Assessment, FY 2011 Oak Ridge Leadership Computing Facility

Oak Ridge National Laboratory's Leadership Computing Facility (OLCF) continues to deliver the most powerful resources in the U.S. for open science. At 2.33 petaflops peak performance, the Cray XT Jaguar delivered more than 1.4 billion core hours in calendar year (CY) 2011 to researchers around the world for computational simulations relevant to national and energy security; advancing the frontiers of knowledge in physical sciences and areas of biological, medical, environmental, and computer sciences; and providing world-class research facilities for the nation's science enterprise. Users reported more than 670 publications this year arising from their use of OLCF resources. Of these we report the 300 in this review that are consistent with guidance provided. Scientific achievements by OLCF users cut across all range scales from atomic to molecular to large-scale structures. At the atomic scale, researchers discovered that the anomalously long half-life of Carbon-14 can be explained by calculating, for the first time, the very complex three-body interactions between all the neutrons and protons in the nucleus. At the molecular scale, researchers combined experimental results from LBL's light source and simulations on Jaguar to discover how DNA replication continues past a damaged site so a mutation can be repaired later. Other researchers combined experimental results from ORNL's Spallation Neutron Source and simulations on Jaguar to reveal the molecular structure of ligno-cellulosic material used in bioethanol production. This year, Jaguar has been used to do billion-cell CFD calculations to develop shock wave compression turbo machinery as a means to meet DOE goals for reducing carbon sequestration costs. General Electric used Jaguar to calculate the unsteady flow through turbo machinery to learn what efficiencies the traditional steady flow assumption is hiding from designers. Even a 1% improvement in turbine design can save the nation billions of gallons of fuel

Speeding up Energy System Models - a Best Practice Guide

Background Energy system models (ESM) are widely used in research and industry to analyze todays and future energy systems and potential pathways for the European energy transition. Current studies address future policy design, analysis of technology pathways and of future energy systems. To address these questions and support the transformation of today’s energy systems, ESM have to increase in complexity to provide valuable quantitative insights for policy makers and industry. Especially when dealing with uncertainty and in integrating large shares of renewable energies, ESM require a detailed implementation of the underlying electricity system. The increased complexity of the models makes the application of ESM more and more difficult, as the models are limited by the available computational power of today’s decentralized workstations. Severe simplifications of the models are common strategies to solve problems in a reasonable amount of time – naturally significantly influencing the validity of results and reliability of the models in general. Solutions for Energy-System Modelling Within BEAM-ME a consortium of researchers from different research fields (system analysis, mathematics, operations research and informatics) develop new strategies to increase the computational performance of energy system models and to transform energy system models for usage on high performance computing clusters. Within the project, an ESM will be applied on two of Germany’s fastest supercomputers. To further demonstrate the general application of named techniques on ESM, a model experiment is implemented as part of the project. Within this experiment up to six energy system models will jointly develop, implement and benchmark speed-up methods. Finally, continually collecting all experiences from the project and the experiment, identified efficient strategies will be documented and general standards for increasing computational performance and for applying ESM to high performance computing will be documented in a best-practice guide

NASA Tech Briefs, May 1990

Topics: New Product Ideas; NASA TU Services; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences

Cell mechanics in flow: algorithms and applications

The computer simulations are pervasively used to improve the knowledge about biophysical phenomena and to quantify effects which are difficult to study experimentally. Generally, the numerical methods and models are desired to be as accurate as possible on the chosen length and time scales, but, at the same time, affordable in terms of computations. Until recently, the cell mechanics and blood flow phenomena on the sub-micron resolution could not be rigorously studied using computer simulations. However, within the last decade, advances in methods and hardware catalyzed the development of models for cells mechanics and blood flow modeling which, previously, were considered to be not feasible. In this context, a model should accurately describe a phenomenon, be computationally affordable, and be flexible to be applied to study different biophysical changes. This thesis focuses on the development of the new methods, models, and high-performance software implementation that expand the class of problems which can be studied numerically using particle-based methods. Microvascular networks have complex geometry, often without any symmetry, and to study them we need to tackle computational domains with several inlets and outlets. However, an absence of appropriate boundary conditions for particle- based methods hampers study of the blood flow in these domains. Another obstacle to model complex blood flow problems is the absence the highperformance software. This problem restricts the applicability of the of particlebased cell flow models to relatively small systems. Although there are several validated red blood cell models, to date, there are no models for suspended eukaryotic cells. The present thesis addresses these issues. We introduce new open boundary conditions for particle-based systems and apply them to study blood flow in a part of a microvascular network. We develop a software demonstrating outstanding performance on the largest supercomputers and used it to study blood flow in microfluidic devices. Finally, we present a new eukaryotic cell model which helps in quantifying the effect of sub-cellular components on the cell mechanics during deformations in microfluidic devices

The ICON-A model for direct QBO simulations on GPUs (version icon-cscs:baf28a514)

Classical numerical models for the global atmosphere, as used for numerical weather forecasting or climate research, have been developed for conventional central processing unit (CPU) architectures. This hinders the employment of such models on current top-performing supercomputers, which achieve their computing power with hybrid architectures, mostly using graphics processing units (GPUs). Thus also scientific applications of such models are restricted to the lesser computer power of CPUs. Here we present the development of a GPU-enabled version of the ICON atmosphere model (ICON-A), motivated by a research project on the quasi-biennial oscillation (QBO), a global-scale wind oscillation in the equatorial stratosphere that depends on a broad spectrum of atmospheric waves, which originates from tropical deep convection. Resolving the relevant scales, from a few kilometers to the size of the globe, is a formidable computational problem, which can only be realized now on top-performing supercomputers. This motivated porting ICON-A, in the specific configuration needed for the research project, in a first step to the GPU architecture of the Piz Daint computer at the Swiss National Supercomputing Centre and in a second step to the JUWELS Booster computer at the Forschungszentrum Jülich. On Piz Daint, the ported code achieves a single-node GPU vs. CPU speedup factor of 6.4 and allows for global experiments at a horizontal resolution of 5 km on 1024 computing nodes with 1 GPU per node with a turnover of 48 simulated days per day. On JUWELS Booster, the more modern hardware in combination with an upgraded code base allows for simulations at the same resolution on 128 computing nodes with 4 GPUs per node and a turnover of 133 simulated days per day. Additionally, the code still remains functional on CPUs, as is demonstrated by additional experiments on the Levante compute system at the German Climate Computing Center. While the application shows good weak scaling over the tested 16-fold increase in grid size and node count, making also higher resolved global simulations possible, the strong scaling on GPUs is relatively poor, which limits the options to increase turnover with more nodes. Initial experiments demonstrate that the ICON-A model can simulate downward-propagating QBO jets, which are driven by wave–mean flow interaction

NASA Tech Briefs, October 1988

Topics include: New Product Ideas; NASA TU Services; Electronic Components and Circuits; Electronic Systems; Physical Sciences Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences

Mixed integer programming on transputers

Mixed Integer Programming (MIP) problems occur in many industries and their practical solution can be challenging in terms of both time and effort. Although faster computer hardware has allowed the solution of more MIP problems in reasonable times, there will come a point when the hardware cannot be speeded up any more. One way of improving the solution times of MIP problems without further speeding up the hardware is to improve the effectiveness of the solution algorithm used. The advent of accessible parallel processing technology and techniques provides the opportunity to exploit any parallelism within MIP solving algorithms in order to accelerate the solution of MIP problems. Many of the MIP problem solving algorithms in the literature contain a degree of exploitable parallelism. Several algorithms were considered as candidates for parallelisation within the constraints imposed by the currently available parallel hardware and techniques. A parallel Branch and Bound algorithm was designed for and implemented on an array of transputers hosted by a PC. The parallel algorithm was designed to operate as a process farm, with a master passing work to various slave processors. A message-passing harness was developed to allow full control of the slaves and the work sent to them. The effects of using various node selection techniques were studied and a default node selection strategy decided upon for the parallel algorithm. The parallel algorithm was also designed to take full advantage of the structure of MIP problems formulated using global entities such as general integers and special ordered sets. The presence of parallel processors makes practicable the idea of performing more than two branches on an unsatisfied global entity. Experiments were carried out using multiway branching strategies and a default branching strategy decided upon for appropriate types of MIP problem