Advanced computing capabilities are used to tackle a rapidly growing range of challenging science and engineering problems, many of which are compute- and data-intensive as well. Demand for advanced computing has been growing for all types and capabilities of systems, from large numbers of single commodity nodes to jobs requiring thousands of cores; for systems with fast interconnects; for systems with excellent data handling and management; and for an increasingly diverse set of applications that includes data analytics as well as modeling and simulation. Since the advent of its supercomputing centers, the National Science Foundation (NSF) has provided its researchers with state-of-the-art computing systems. The growth of new models of computing, including cloud computing and publically available by privately held data repositories, opens up new possibilities for NSF. In order to better understand the expanding and diverse requirements of the science and engineering community and the importance of a new broader range of advanced computing infrastructure, the NSF requested that the National Research Council carry out a study examining anticipated priorities and associated tradeoffs for advanced computing. Future Directions for NSF Advanced Computing Infrastructure to Support U.S. Science and Engineering in 2017-2020 provides a framework for future decision-making about NSF's advanced computing strategy and programs. It offers recommendations aimed at achieving four broad goals: (1) position the U.S. for continued leadership in science and engineering, (2) ensure that resources meet community needs, (3) aid the scientific community in keeping up with the revolution in computing, and (4) sustain the infrastructure for advanced computing.

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

Mathematics of Computing -- Numerical Analysis.

Geosciences particularly numerical weather predication, are demanding the highest levels of computer power available. The European Centre for Medium-Range Weather Forecasts, with its experience in using supercomputers in this field, organizes a workshop every other year bringing together manufacturers, computer scientists, researchers and operational users to share their experiences and to learn about the latest developments. This volume provides an excellent overview of the latest achievements and plans for the use of new parallel techniques in the fields of meteorology, climatology and oceanography.

This is a fully revised edition of the best-selling Introduction to Maple. The book presents the modern computer algebra system Maple, teaching the reader not only what can be done by Maple, but also how and why it can be done. The book also provides the necessary background for those who want the most of Maple or want to extend its built-in knowledge. Emphasis is on understanding the Maple system more than on factual knowledge of built-in possibilities. To this end, the book contains both elementary and more sophisticated examples as well as many exercises. The typical reader should have a background in mathematics at the intermediate level. Andre Heck began developing and teaching Maple courses at the University of Nijmegen in 1987. In 1989 he was appointed managing director of the CAN Expertise Center in Amsterdam. CAN, Computer Algebra in the Netherlands, stimulates and coordinates the use of computer algebra in education and research. In 1996 the CAN Expertise Center was integrated into the Faculty of Science at the University of Amsterdam, into what became the AMSTEL Institute. The institute program focuses on the innovation of computer activities in mathematics and science education on all levels of education. The author is actively involved in the research and development aimed at the integrated computer learning environment Coach for mathematics and science education at secondary school level.

Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

The aim of this book is to present important software tools, basic concepts, methods, and highly sophisticated applications of computerized symbolic manipulation to mechanics problems. An overview about general-purpose symbolic software is followed by general guidelines how to develop and implement high-quality computer algebra code. The theoretical background including modeling techniques for mechanical systems is provided which allows for the computer aided generation of the symbolic equation of motion for multibody systems. It is shown how the governing equations for different types of problems in structural mechanics can be automatically derived and how to implement finite element techniques via computer algebra software. Perturbation methods as a very powerful approach for nonlinear problems are discussed in detail and are demonstrated for a number of applications. The applications covered in this book represent some of the most advanced topics in the rapidly growing field of research on symbolic computation.

Praise for the Series:"This book will be a useful reference to control engineers and researchers. The papers contained cover well the recent advances in the field of modern control theory."-IEEE Group Correspondence"This book will help all those researchers who valiantly try to keep abreast of what is new in the theory and practice of optimal control."--Control