Finite Computational Structures and Implementations

What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only partial answers to these questions. In order to make these problems more precise, we describe an abstract algebraic definition of classical computation, generalizing traditional models to semigroups. The mathematical abstraction also allows the investigation of different computing paradigms (e.g. cellular automata, reversible computing) in the same framework. Here we summarize the main questions and recent results of the research of finite computation.Comment: 12 pages, 3 figures, will be presented at CANDAR'16 and final version published by IEEE Computer Societ

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Computing infrastructure issues in distributed communications systems : a survey of operating system transport system architectures

The performance of distributed applications (such as file transfer, remote login, tele-conferencing, full-motion video, and scientific visualization) is influenced by several factors that interact in complex ways. In particular, application performance is significantly affected both by communication infrastructure factors and computing infrastructure factors. Several communication infrastructure factors include channel speed, bit-error rate, and congestion at intermediate switching nodes. Computing infrastructure factors include (among other things) both protocol processing activities (such as connection management, flow control, error detection, and retransmission) and general operating system factors (such as memory latency, CPU speed, interrupt and context switching overhead, process architecture, and message buffering). Due to a several orders of magnitude increase in network channel speed and an increase in application diversity, performance bottlenecks are shifting from the network factors to the transport system factors.This paper defines an abstraction called an "Operating System Transport System Architecture" (OSTSA) that is used to classify the major components and services in the computing infrastructure. End-to-end network protocols such as TCP, TP4, VMTP, XTP, and Delta-t typically run on general-purpose computers, where they utilize various operating system resources such as processors, virtual memory, and network controllers. The OSTSA provides services that integrate these resources to support distributed applications running on local and wide area networks.A taxonomy is presented to evaluate OSTSAs in terms of their support for protocol processing activities. We use this taxonomy to compare and contrast five general-purpose commercial and experimental operating systems including System V UNIX, BSD UNIX, the x-kernel, Choices, and Xinu

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak)