This book deals with the analysis and development of numerical methods for the time-domain analysis of multiphysical effects in superconducting circuits of particle accelerator magnets. An important challenge is the simulation of “quenching”, i.e. the transition of a material from the superconducting to the normally electrically conductive state. The book analyses complex mathematical structures and presents models to simulate such quenching events in the context of generalized circuit elements. Furthermore, it proposes efficient parallelized algorithms with guaranteed convergence properties for the simulation of multiphysical problems. Spanning from theoretical concepts to applied research, and featuring rigorous mathematical presentations on one side, as well as simplified explanations of many complex issues, on the other side, this book provides graduate students and researchers with a comprehensive introduction on the state of the art and a source of inspiration for future research. Moreover, the proposed concepts and methods can be extended to the simulation of multiphysical phenomena in different application contexts.

This book deals with efficient estimation and optimization methods to improve the design of electrotechnical devices under uncertainty. Uncertainties caused by manufacturing imperfections, natural material variations, or unpredictable environmental influences, may lead, in turn, to deviations in operation. This book describes two novel methods for yield (or failure probability) estimation. Both are hybrid methods that combine the accuracy of Monte Carlo with the efficiency of surrogate models. The SC-Hybrid approach uses stochastic collocation and adjoint error indicators. The non-intrusive GPR-Hybrid approach consists of a Gaussian process regression that allows surrogate model updates on the fly. Furthermore, the book proposes an adaptive Newton-Monte-Carlo (Newton-MC) method for efficient yield optimization. In turn, to solve optimization problems with mixed gradient information, two novel Hermite-type optimization methods are described. All the proposed methods have been numerically evaluated on two benchmark problems, such as a rectangular waveguide and a permanent magnet synchronous machine. Results showed that the new methods can significantly reduce the computational effort of yield estimation, and of single- and multi-objective yield optimization under uncertainty. All in all, this book presents novel strategies for quantification of uncertainty and optimization under uncertainty, with practical details to improve the design of electrotechnical devices, yet the methods can be used for any design process affected by uncertainties.

This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques.

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

Modeling and Simulation in Python teaches readers how to analyze real-world scenarios using the Python programming language, requiring no more than a background in high school math. Modeling and Simulation in Python is a thorough but easy-to-follow introduction to physical modeling—that is, the art of describing and simulating real-world systems. Readers are guided through modeling things like world population growth, infectious disease, bungee jumping, baseball flight trajectories, celestial mechanics, and more while simultaneously developing a strong understanding of fundamental programming concepts like loops, vectors, and functions. Clear and concise, with a focus on learning by doing, the author spares the reader abstract, theoretical complexities and gets right to hands-on examples that show how to produce useful models and simulations.

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.

From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography