Structure-Preserving Algorithms for Oscillatory Differential Equations

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Dietmar Hildenbrand

<p>The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics.</p><p><p>This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications.</p><p>The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

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Alexandre Ern, Jean-Luc Guermond

This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering.

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Joseph L. Zachary

"Introduction to Computational Science" was developed over a period of two years at the University of Utah Department of Computer Science in conjunction with the U.S. Department of Energy-funded Undergraduate Computation in Engineering Science (UCES) program. Each chapter begins by introducing a problem and then guiding the student through its solution. The computational techniques needed to solve the problem are developed as necassary, making the motivation for learning the computing alwasy apparent. Each chapter will introduce a single problem that will be used to motivate a single computing concept. The notes currently consist of 15 chapters. The first seven chapters deal with Maple and the last eight with C. The textbook will contain 20 to 30 chapters covering a similar mix of concepts at a finer level of detail.

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Jean-Claude Geffroy, Gilles Motet

Today computing systems are more and more complex and they assume more and more responsibilities in all sectors of human activity. Unfortunately, many faults can harm the development or the use of these products. Destructive mechanisms transform faults into errors and finally failures altering the delivered service. For critical systems, the consequences of these failures can be catastrophic, but for most non-critical systems, failures are nowadays unacceptable. Hence, it is necessary to take dependability attributes into account, along the product lifecycle. This book aims at providing a general overview of the dependability of computing systems: impairments and protective means. Issues, concepts and techniques are considered from a system point of view, and are illustrated by both hardware and software technologies. An important pedagogical effort has been made: the explanations are illustrated by 370 figures, 80 examples, and 97 exercises with complete answers. A glossary of more than 500 entries defines the important terms.