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Differential Algebraic Systems Analytical Aspects And Circuit Applications
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Book Synopsis Differential-Algebraic Systems by : Ricardo Riaza
Download or read book Differential-Algebraic Systems written by Ricardo Riaza and published by World Scientific. This book was released on 2008 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.
Book Synopsis Surveys in Differential-Algebraic Equations I by : Achim Ilchmann
Download or read book Surveys in Differential-Algebraic Equations I written by Achim Ilchmann and published by Springer Science & Business Media. This book was released on 2013-03-19 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need for a rigorous mathematical theory for Differential-Algebraic Equations (DAEs) has its roots in the widespread applications of controlled dynamical systems, especially in mechanical and electrical engineering. Due to the strong relation to (ordinary) differential equations, the literature for DAEs mainly started out from introductory textbooks. As such, the present monograph is new in the sense that it comprises survey articles on various fields of DAEs, providing reviews, presentations of the current state of research and new concepts in - Controllability for linear DAEs - Port-Hamiltonian differential-algebraic systems - Robustness of DAEs - Solution concepts for DAEs - DAEs in circuit modeling. The results in the individual chapters are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.
Book Synopsis Differential-algebraic Systems: Analytical Aspects And Circuit Applications by : Ricardo Riaza
Download or read book Differential-algebraic Systems: Analytical Aspects And Circuit Applications written by Ricardo Riaza and published by World Scientific. This book was released on 2008-05-29 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential-algebraic equations (DAEs) provide an essential tool for system modeling and analysis within different fields of applied sciences and engineering. This book addresses modeling issues and analytical properties of DAEs, together with some applications in electrical circuit theory.Beginning with elementary aspects, the author succeeds in providing a self-contained and comprehensive presentation of several advanced topics in DAE theory, such as the full characterization of linear time-varying equations via projector methods or the geometric reduction of nonlinear systems. Recent results on singularities are extensively discussed. The book also addresses in detail differential-algebraic models of electrical and electronic circuits, including index characterizations and qualitative aspects of circuit dynamics. In particular, the reader will find a thorough discussion of the state/semistate dichotomy in circuit modeling. The state formulation problem, which has attracted much attention in the engineering literature, is cleverly tackled here as a reduction problem on semistate models.
Book Synopsis Surveys in Differential-Algebraic Equations IV by : Achim Ilchmann
Download or read book Surveys in Differential-Algebraic Equations IV written by Achim Ilchmann and published by Springer. This book was released on 2017-03-08 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE aspects of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.
Book Synopsis Differential-Algebraic Equations: A Projector Based Analysis by : René Lamour
Download or read book Differential-Algebraic Equations: A Projector Based Analysis written by René Lamour and published by Springer Science & Business Media. This book was released on 2013-01-19 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential algebraic equations (DAEs), including so-called descriptor systems, began to attract significant research interest in applied and numerical mathematics in the early 1980s, no more than about three decades ago. In this relatively short time, DAEs have become a widely acknowledged tool to model processes subjected to constraints, in order to simulate and to control processes in various application fields such as network simulation, chemical kinematics, mechanical engineering, system biology. DAEs and their more abstract versions in infinite-dimensional spaces comprise a great potential for future mathematical modeling of complex coupled processes. The purpose of the book is to expose the impressive complexity of general DAEs from an analytical point of view, to describe the state of the art as well as open problems and so to motivate further research to this versatile, extra-ordinary topic from a broader mathematical perspective. The book elaborates a new general structural analysis capturing linear and nonlinear DAEs in a hierarchical way. The DAE structure is exposed by means of special projector functions. Numerical integration issues and computational aspects are treated also in this context.
Book Synopsis Numerical Analysis of Nonlinear Partial Differential-algebraic Equations by : Michael Matthes
Download or read book Numerical Analysis of Nonlinear Partial Differential-algebraic Equations written by Michael Matthes and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various mathematical models in many application areas give rise to systems of so called partial or abstract differential-algebraic equations (ADAEs). A substantial mathematical treatment of nonlinear ADAEs is still at an initial stage.In this thesis two approaches for treating nonlinear ADAEs are presented. The first one represents an extension of an approach by Tischendorf for the treatment of a specific class of linear ADAEs to the nonlinear case. It is based on the Galerkin approach and the theory of monotone operators for evolution equations. Unique solvability of the ADAE and strong convergence of the Galerkin solutions is proven. Furthermore it is shown that this class of ADAEs has Perturbation Index 1 and at most ADAE Index 1. In the second approach we formulate two prototypes of coupled systems where a semi-explicit differential-algebraic equation is coupled to an infinite dimensional algebraic operator equation or an evolution equation. For both prototypes unique solvability, strong convergence of Galerkin solutions and a Perturbation Index 1 result is shown. Both prototypes can be applied to concrete coupled systems in circuit simulation relying on a new global solvability result for the nonlinear equations of the Modified Nodal Analysis under suitable topological assumptions.
Book Synopsis Applications of Differential-Algebraic Equations: Examples and Benchmarks by : Stephen Campbell
Download or read book Applications of Differential-Algebraic Equations: Examples and Benchmarks written by Stephen Campbell and published by Springer. This book was released on 2019-06-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text. Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful.
Book Synopsis Surveys in Differential-Algebraic Equations III by : Achim Ilchmann
Download or read book Surveys in Differential-Algebraic Equations III written by Achim Ilchmann and published by Springer. This book was released on 2015-10-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Flexibility of DAE formulations - Reachability analysis and deterministic global optimization - Numerical linear algebra methods - Boundary value problems The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.
Book Synopsis The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods by : Ernst Hairer
Download or read book The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods written by Ernst Hairer and published by Lecture Notes in Mathematics. This book was released on 1989-11-28 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.
Book Synopsis Progress in Differential-Algebraic Equations II by : Timo Reis
Download or read book Progress in Differential-Algebraic Equations II written by Timo Reis and published by Springer Nature. This book was released on 2020-10-10 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains articles presented at the 9th Workshop on Differential-Algebraic Equations held in Paderborn, Germany, from 17–20 March 2019. The workshop brought together more than 40 mathematicians and engineers from various fields, such as numerical and functional analysis, control theory, mechanics and electromagnetic field theory. The participants focussed on the theoretical and numerical treatment of “descriptor” systems, i.e., differential-algebraic equations (DAEs). The book contains 14 contributions and is organized into four parts: mathematical analysis, numerics and model order reduction, control as well as applications. It is a useful resource for applied mathematicians with interest in recent developments in the field of differential algebraic equations but also for engineers, in particular those interested in modelling of constraint mechanical systems, thermal networks or electric circuits.
Book Synopsis Scientific Computing in Electrical Engineering SCEE 2010 by : Bastiaan Michielsen
Download or read book Scientific Computing in Electrical Engineering SCEE 2010 written by Bastiaan Michielsen and published by Springer Science & Business Media. This book was released on 2012-01-06 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected from papers presented at the 8th Scientific Computation in Electrical Engineering conference in Toulouse in 2010, the contributions to this volume cover every angle of numerically modelling electronic and electrical systems, including computational electromagnetics, circuit theory and simulation and device modelling. On computational electromagnetics, the chapters examine cutting-edge material ranging from low-frequency electrical machine modelling problems to issues in high-frequency scattering. Regarding circuit theory and simulation, the book details the most advanced techniques for modelling networks with many thousands of components. Modelling devices at microscopic levels is covered by a number of fundamental mathematical physics papers, while numerous papers on model order reduction help engineers and systems designers to bring their modelling of industrial-scale systems within the reach of present-day computational power. Complementing these more specific papers, the volume also contains a selection of mathematical methods which can be used in any application domain.
Book Synopsis Coupled Electromagnetic Field/Circuit Simulation. Modeling and Numerical Analysis by : Sascha Baumanns
Download or read book Coupled Electromagnetic Field/Circuit Simulation. Modeling and Numerical Analysis written by Sascha Baumanns and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today's most commonly used circuit models increasingly tend to lose their validity in circuit simulation due to rapid technological developments, miniaturization and increased complexity of integrated circuits. The starting point of this thesis was to tackle these challenges by refining the critical parts of the circuit by combining circuit simulation directly with distributed device models. The approach set out in this thesis couples partial differential equations for electromagnetic devices - modeled by Maxwell's equations -, to differential-algebraic equations, which describe basic circuit elements including memristors and the circuit's topology. First, Maxwell's equations are spatially discretized and a potential formulation is derived, the coupled system is then formulated as a differential-algebraic equation with a properly stated leading term and analyzed. Topological and modeling conditions are presented to guarantee the tractability index of these differential-algebraic equations to be no greater than two. Finally, local solvability, perturbation results and an algorithm to calculate consistent initializations are derived for a general class of differential-algebraic equations with a properly stated leading term having tractability index-2.
Book Synopsis Index-aware Model Order Reduction Methods by : N. Banagaaya
Download or read book Index-aware Model Order Reduction Methods written by N. Banagaaya and published by Springer. This book was released on 2016-03-05 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.
Book Synopsis Large-Scale Networks in Engineering and Life Sciences by : Peter Benner
Download or read book Large-Scale Networks in Engineering and Life Sciences written by Peter Benner and published by Springer. This book was released on 2014-10-21 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume provides insights into and tools for the modeling, analysis, optimization, and control of large-scale networks in the life sciences and in engineering. Large-scale systems are often the result of networked interactions between a large number of subsystems, and their analysis and control are becoming increasingly important. The chapters of this book present the basic concepts and theoretical foundations of network theory and discuss its applications in different scientific areas such as biochemical reactions, chemical production processes, systems biology, electrical circuits, and mobile agents. The aim is to identify common concepts, to understand the underlying mathematical ideas, and to inspire discussions across the borders of the various disciplines. The book originates from the interdisciplinary summer school “Large Scale Networks in Engineering and Life Sciences” hosted by the International Max Planck Research School Magdeburg, September 26-30, 2011, and will therefore be of interest to mathematicians, engineers, physicists, biologists, chemists, and anyone involved in the network sciences. In particular, due to their introductory nature the chapters can serve individually or as a whole as the basis of graduate courses and seminars, future summer schools, or as reference material for practitioners in the network sciences.
Book Synopsis Progress in Differential-Algebraic Equations by : Sebastian Schöps
Download or read book Progress in Differential-Algebraic Equations written by Sebastian Schöps and published by Springer. This book was released on 2014-11-13 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 8th Workshop on Coupled Descriptor Systems held March 2013 in the Castle of Eringerfeld, Geseke in the neighborhood of Paderborn, Germany. It examines the wide range of current research topics in descriptor systems, including mathematical modeling, index analysis, wellposedness of problems, stiffness and different time-scales, cosimulation and splitting methods and convergence analysis. In addition, the book also presents applications from the automotive and circuit industries that show that descriptor systems provide challenging problems from the point of view of both theory and practice. The book contains nine papers and is organized into three parts: control, simulation, and model order reduction. It will serve as an ideal resource for applied mathematicians and engineers, in particular those from mechanics and electromagnetics, who work with coupled differential equations.
Book Synopsis Mathematical Analysis and Simulation of Field Models in Accelerator Circuits by : Idoia Cortes Garcia
Download or read book Mathematical Analysis and Simulation of Field Models in Accelerator Circuits written by Idoia Cortes Garcia and published by Springer Nature. This book was released on 2021-01-04 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Ordinary Differential Equations in Theory and Practice by : Robert Mattheij
Download or read book Ordinary Differential Equations in Theory and Practice written by Robert Mattheij and published by SIAM. This book was released on 1996-01-01 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role. Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained. Audience: the book is intended for use as a textbook for both undergraduate and graduate courses, and it can also serve as a reference for students and researchers alike.
