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Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.
Unique in content and approach, this book covers all the topics that are usually covered in an introduction to scientific computing--but folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate the "connection" between continuous mathematics and computing. "MATLAB 5" is used "throughout" to encourage experimentation, and each chapter focuses on a different important theorem--allowing readers to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a "hard" problem that involves ill-conditioning, high dimension, etc.; 2)at least one theorem with both a rigorous proof and a "proof by MATLAB" experiment to bolster intuition; 3)at least one recursive algorithm; and 4)at least one connection to a real-world application. The book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing. Power Tools of the Trade. Polynomial Interpolation. Piecewise Polynomial Interpolation. Numerical Integration. Matrix Computations. Linear Systems. The QR and Cholesky Factorizations. Nonlinear Equations and Optimization. The Initial Value Problem. For engineers and mathematicians.
This easy-to-read textbook/reference presents an essential guide to object-oriented C++ programming for scientific computing. With a practical focus on learning by example, the theory is supported by numerous exercises. Features: provides a specific focus on the application of C++ to scientific computing, including parallel computing using MPI; stresses the importance of a clear programming style to minimize the introduction of errors into code; presents a practical introduction to procedural programming in C++, covering variables, flow of control, input and output, pointers, functions, and reference variables; exhibits the efficacy of classes, highlighting the main features of object-orientation; examines more advanced C++ features, such as templates and exceptions; supplies useful tips and examples throughout the text, together with chapter-ending exercises, and code available to download from Springer.
This textbook provides an introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression-based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. The codes used for most of the computational examples in the text are available on GitHub. This new edition includes material necessary for an upper division course in computational linear algebra.
Designed for undergraduates, An Introduction to High-Performance Scientific Computing assumes a basic knowledge of numerical computation and proficiency in Fortran or C programming and can be used in any science, computer science, applied mathematics, or engineering department or by practicing scientists and engineers, especially those associated with one of the national laboratories or supercomputer centers. This text evolved from a new curriculum in scientific computing that was developed to teach undergraduate science and engineering majors how to use high-performance computing systems (supercomputers) in scientific and engineering applications. Designed for undergraduates, An Introduction to High-Performance Scientific Computing assumes a basic knowledge of numerical computation and proficiency in Fortran or C programming and can be used in any science, computer science, applied mathematics, or engineering department or by practicing scientists and engineers, especially those associated with one of the national laboratories or supercomputer centers. The authors begin with a survey of scientific computing and then provide a review of background (numerical analysis, IEEE arithmetic, Unix, Fortran) and tools (elements of MATLAB, IDL, AVS). Next, full coverage is given to scientific visualization and to the architectures (scientific workstations and vector and parallel supercomputers) and performance evaluation needed to solve large-scale problems. The concluding section on applications includes three problems (molecular dynamics, advection, and computerized tomography) that illustrate the challenge of solving problems on a variety of computer architectures as well as the suitability of a particular architecture to solving a particular problem. Finally, since this can only be a hands-on course with extensive programming and experimentation with a variety of architectures and programming paradigms, the authors have provided a laboratory manual and supporting software via anonymous ftp. Scientific and Engineering Computation series
The International Workshop on "The Use of Supercomputers in Theoretical Science" took place on November 29 and 30, 1989 at the University of Antwerp (UIA), Antwerpen, Belgium. It was the fifth in a series of workshops, the first of which took place in 1984. The principal aim of these workshops is to present the state-of-the-art in scientific large scale and high speed computation. Computational science has developed into a third methodology equally important now as its theoretical and experimental companions. Gradually academic researchers acquired access to a variety of supercomputers and as a consequence computational science has become a major tool for their work. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) and the Ministry of Scientific Affairs for sponsoring the workshop. It was organized both in the framework of the Third Cycle "Vectorization, Parallel Processing and Supercomputers" and the "Governemental Program in Information Technology"~ We also very much would like to thank the University of Antwerp (Universitaire Instelling Antwerpen - UIA) for financial and material support. Special thanks are due to Mrs. H. Evans for the typing and editing of the manuscripts and for the preparation of the author and subject index.
In this text, students of applied mathematics, science and engineering are introduced to fundamental ways of thinking about the broad context of parallelism. The authors begin by giving the reader a deeper understanding of the issues through a general examination of timing, data dependencies, and communication. These ideas are implemented with respect to shared memory, parallel and vector processing, and distributed memory cluster computing. Threads, OpenMP, and MPI are covered, along with code examples in Fortran, C, and Java. The principles of parallel computation are applied throughout as the authors cover traditional topics in a first course in scientific computing. Building on the fundamentals of floating point representation and numerical error, a thorough treatment of numerical linear algebra and eigenvector/eigenvalue problems is provided. By studying how these algorithms parallelize, the reader is able to explore parallelism inherent in other computations, such as Monte Carlo methods.
The International Workshops on "The Use of Supercomputers in Theoretical Science" have become a tradition at the Univer sity of Antwerp, Belgium. The first one took place in 1984. This volume combines the proceedings of the second work shop (December 12, 1985), of the third (June 16, 1987) and of the fourth (June 9, 1988). The principal aim of the International Workshops is to present the state-of-the-art in scientific high speed computa tion. Indeed, during the past ten years computational science has become a third methodology with merits equal to the theo retical and experimental sciences. Regretfully, access to supercomputers remains limited for academic researchers. None theless, supercomputers have become a major tool for scientists in a wide variety of scientific fields, and they lead to a realistic solution of problems that could not be solved a decade ago. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) for the sponsoring of all the workshops. These workshops are organized in the framework of the Third Cy cle "Vectorization, Parallel Processing and Supercomputers", which is also funded by the NFWO-FNRS. The other sponsor I want to thank is the University of Antwerp, where the workshops took place. The University of Antwerp (UIA), together with the NFWO-FNRS, are also the main sponsors of the ALPHA-project, which gives the scientists of Belgium the opportunity to obtain an easy supercomputer connection.
This is a textbook that teaches the bridging topics between numerical analysis, parallel computing, code performance, large scale applications.
This book is a complete introduction to vector analysis, especially within the context of computer graphics. The author shows why vectors are useful and how it is possible to develop analytical skills in manipulating vector algebra. Even though vector analysis is a relatively recent development in the history of mathematics, it has become a powerful and central tool in describing and solving a wide range of geometric problems. The book is divided into eleven chapters covering the mathematical foundations of vector algebra and its application to, among others, lines, planes, intersections, rotating vectors, and vector differentiation.