Methods In Computational Science

Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory.

The book is designed to serve as a textbook for courses offered to graduate and upper-undergraduate students enrolled in mechanical engineering. The book attempts to make students with mathematical backgrounds comfortable with numerical methods. The book also serves as a handy reference for practicing engineers who are interested in applications. The book is written in an easy-to-understand manner, with the essence of each numerical method clearly stated. This makes it easy for professional engineers, students, and early career researchers to follow the material presented in the book. The structure of the book has been modeled accordingly. It is divided into four modules: i) solution of a system of equations and eigenvalues which includes linear equations, determining eigenvalues, and solution of nonlinear equations; ii) function approximations: interpolation, data fit, numerical differentiation, and numerical integration; iii) solution of ordinary differential equations—initial value problems and boundary value problems; and iv) solution of partial differential equations—parabolic, elliptic, and hyperbolic PDEs. Each section of the book includes exercises to reinforce the concepts, and problems have been added at the end of each chapter. Exercise problems may be solved by using computational tools such as scientific calculators, spreadsheet programs, and MATLAB codes. The detailed coverage and pedagogical tools make this an ideal textbook for students, early career researchers, and professionals.

Offers students a practical knowledge of modern techniques in scientific computing.

This book provides a theoretical background in computation to scientists who use computational methods. It explains how computing is used in the natural sciences, and provides a high-level overview of those aspects of computer science and software engineering that are most relevant for computational science. The focus is on concepts, results, and applications, rather than on proofs and derivations. The unique feature of this book is that it “connects the dots between computational science, the theory of computation and information, and software engineering. The book should help scientists to better understand how they use computers in their work, and to better understand how computers work. It is meant to compensate a bit for the general lack of any formal training in computer science and information theory. Readers will learn something they can use throughout their careers.

"In 1946 John von Neumann stated that science is stagnant along the entire front of complex problems, proposing the use of largescale computing machines to overcome this stagnation. In other words, Neumann advocated replacing analytical methods with numerical ones. The invention of the computer in the 1940s allowed scientists to realise numerical simulations of increasingly complex problems like weather forecasting, and climate and molecular modelling. Today, computers are widely used as computational laboratories, shifting science toward the computational sciences. By replacing analytical methods with numerical ones, they have expanded theory and experimentation by simulation. During the last decades hundreds of computational departments have been established all over the world and countless computer-based simulations have been conducted. This volume explores the epoch-making influence of automatic computing machines on science, in particular as simulation tools."--Back cover.

This refereed volume arose from the editors' recognition that physical scientists, engineers, and applied mathematicians are developing, in parallel, solutions to problems of parallelization. The cross-disciplinary field of scientific computation is bringing about better communication between heterogeneous computational groups, as they face this common challenge. This volume is one attempt to provide cross-disciplinary communication. Problem decomposition and the use of domain-based parallelism in computational science and engineering was the subject addressed at a workshop held at the University of Minnesota Supercomputer Institute in April 1994. The authors were subsequently able to address the relationships between their individual applications and independently developed approaches. This book is written for an interdisciplinary audience and concentrates on transferable algorithmic techniques, rather than the scientific results themselves. Cross-disciplinary editing was employed to identify jargon that needed further explanation and to ensure provision of a brief scientific background for each chapter at a tutorial level so that the physical significance of the variables is clear and correspondences between fields are visible.

This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.

Computational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. This textbook provides students with a versatile and accessible introduction to the subject. It assumes only a background in high school algebra, enables instructors to follow tailored pathways through the material, and is the only textbook of its kind designed specifically for an introductory course in the computational science and engineering curriculum. While the text itself is generic, an accompanying website offers tutorials and files in a variety of software packages. This fully updated and expanded edition features two new chapters on agent-based simulations and modeling with matrices, ten new project modules, and an additional module on diffusion. Besides increased treatment of high-performance computing and its applications, the book also includes additional quick review questions with answers, exercises, and individual and team projects. The only introductory textbook of its kind—now fully updated and expanded Features two new chapters on agent-based simulations and modeling with matrices Increased coverage of high-performance computing and its applications Includes additional modules, review questions, exercises, and projects An online instructor's manual with exercise answers, selected project solutions, and a test bank and solutions (available only to professors) An online illustration package is available to professors