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Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorithms for solving the discretized equations, techniques for non-matching grid discretizations and techniques for heterogeneous approximations. This book serves as an introduction to this subject, with emphasis on matrix formulations. The topics studied include Schwarz, substructuring, Lagrange multiplier and least squares-control hybrid formulations, multilevel methods, non-self adjoint problems, parabolic equations, saddle point problems (Stokes, porous media and optimal control), non-matching grid discretizations, heterogeneous models, fictitious domain methods, variational inequalities, maximum norm theory, eigenvalue problems, optimization problems and the Helmholtz scattering problem. Selected convergence theory is included.
Domain Decomposition Methods - Algorithms and Theory
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Dissipative Systems Analysis and Control : Theory and Applications
Dissipative Systems Analysis and Control (second edition) presents a fully revised and expanded treatment of dissipative systems theory, constituting a self-contained, advanced introduction for graduate students, researchers and practising engineers. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional examples are also included. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. The theory is substantiated by experimental results and by reference to its application in illustrative physical cases (Lagrangian and Hamiltonian systems and passivity-based and adaptive controllers are covered thoroughly).
Dissipative Solitons : From Optics to Biology and Medicine
The dissipative soliton concept is a fundamental extension of the concept of solitons in conservative and integrable systems. It includes ideas from three major sources, namely standard soliton theory developed since the 1960s, nonlinear dynamics theory, and Prigogine's ideas of systems far from equilibrium. These three sources also correspond to the three component parts of this novel paradigm. This book explains the above principles in detail and gives the reader various examples from optics, biology and medicine. These include laser systems, optical transmission lines, cortical networks, models of muscle contraction, localized vegetation structures and waves in brain tissues.
Dissipative Solitons
This volume is devoted to the exciting topic of dissipative solitons, i.e. pulses or spatially localised waves in systems exhibiting gain and loss. Examples are laser systems, nonlinear resonators and optical transmission lines. The physical principles and mathematical concepts are explained in a clear and concise way, suitable for students and young researchers. The similarities and differences in the notion of a soliton between dissipative systems and Hamiltonian and integrable systems are discussed, and many examples are given. The contributions are written by the world's leading experts in the field, making it a unique exposition of this emerging topic.
Discrete-time Markov jump linear systems
Safety critical and high-integrity systems, such as industrial plants and economic systems, can be subject to abrupt changes - for instance, due to component or interconnection failure, sudden environment changes, etc. Combining probability and operator theory, Discrete-Time Markov Jump Linear Systems provides a unified and rigorous treatment of recent results for the control theory of discrete jump linear systems, which are used in these areas of application. The book is designed for experts in linear systems with Markov jump parameters, but is also of interest for specialists in stochastic control since it presents stochastic control problems for which an explicit solution is possible - making the book suitable for course use.
Discrete-Time High Order Neural Control : Trained with Kaiman Filtering
The objective of this work is to present recent advances in the theory of neural control for discrete-time nonlinear systems with multiple inputs and multiple outputs. The book presents solutions for the output trajectory tracking problem of unknown nonlinear systems based on four schemes.
Discrete Multivariate Analys : Theory and Practice
Thes book is a most welcome contribution to an interesting and lively subject." -- NatureOriginally published in 1974, this book is a reprint of a classic, still-valuable text.
Discrete Dynamical Systems
This book provides an introduction to discrete dynamical systems -- a framework of analysis commonly used in the fields of biology, demography, ecology, economics, engineering, finance, and physics.
Discontinuous Galerkin Methods for Viscous Incompressible Flow
Guido Kanschat reviews several discontinuous Galerkin schemes for elliptic and viscous flow problems. Setting out from Nitsche's method for weak boundary conditions, he studies the interior penalty and LDG methods. Combined with a stable advection discretization, they yield stable DG methods for linear flow problems of Stokes and Oseen type which are applied to the Navier-Stokes problem. The author not only presents the analytical techniques used to study these methods but also devotes a major discussion to the efficient numerical solution of discrete problems.
Diophantine Approximation : Festschrift for Wolfgang Schmidt
This volume contains 22 research and survey papers on recent developments in the field of diophantine approximation. The first article by Hans Peter Schlickewei is devoted to the scientific work of Wolfgang Schmidt. Further contributions deal with the subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavor. In particular, estimates for the number of solutions of diophantine equations as well as results concerning congruences and polynomials are established. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and to discrepancy theory.
Digital synthesizers and transmitters for software radio
By programming the digital synthesizers and transmitters, adaptive channel bandwidths, modulation formats, frequency hopping and data rates are easily achieved. Techniques such as digital predistortion for power amplifier linearization, digital compensation methods for analog I/Q modulator nonlinearities and digital power control and ramping are presented in this book
Digital Simulation in Electrochemistry
The book shows how to numerically solve the parabolic partial differential equations (pdes) encountered in electroanalytical chemistry. It does this in a didactic manner, by first introducing the basic equations to be solved and some model systems as text cases, for which solutions exist. Then it treats basic numerical approximation for derivatives and techniques for the numerical solution of ordinary differential equations, from which the more complicated methods for pdes can be derived. The major implicit methods are described in detail, and the handling of homogeneous chemical reactions, including coupled and nonlinear cases, is detailed. More advanced techniques are presented briefly, as well as some commercially available program packages.
Digital self-tuning controllers : Algorithms, implementation and applications
Digital Self-tuning Controllers presents you with a complete course in self-tuning control, beginning with a survey of adaptive control and the formulation of adaptive control problems. Modelling and identification are dealt with before passing on to algebraic design methods and particular PID and linear-quadratic forms of self-tuning control. Finally, laboratory verification and experimentation will show you how to ground your theoretical knowledge in real plant control.
Digital Enterprise Technology : Perspectives and Future Challenges
Digital engineering methods and systems are vitally important for performing key technical and business functions of global enterprises in a distributed and collaborative manner. The product design and engineering systems are gradually being developed to include a variety of tools for DfX, as well as incorporate aspects of digital manufacturing.The chapters presented in this book are contributed by world class leaders in the field. This volume includes relevant examples of current state-of-art in the development and use of systems and methods for the digital modelling of global development and realization processes in the context of life cycle management.
Digital Control Systems : Design, Identification and Implementation
Digital Control Systems demonstrates in detail how to design and implement high-performance model-based controllers combining system identification and control design techniques extensively tested in industrial milieux. The effective use of these techniques is illustrated in the context of various systems including: d.c. motors, flexible transmissions, air heaters, distillation columns and hot-dip galvanizing. Topics covered include: • essentials of computer-based control systems; • controller design methods (robust pole placement, long-range-predictive control, state space, digital PID, etc.); • system identification techniques; • practical aspects of system identification and digital control.
Digital Communications Using Chaos and Nonlinear Dynamics
This book introduces readers to a new and exciting cross-disciplinary field of digital communications with chaos. This field was born around 15 years ago, when it was first demonstrated that nonlinear systems which produce complex non-periodic noise-like chaotic signals, can be synchronized and modulated to carry useful information. Thus, chaotic signals can be used instead of pseudo-random digital sequences for spread-spectrum and private communication applications. This deceptively simple idea spun hundreds of research papers, and many novel communication schemes based on chaotic signals have been proposed. However, only very recently researchers have begun to make a transition from academic studies toward practical implementation issues, and many "promising" schemes had to be discarded or re-formulated. This book describes the state of the art (both theoretical and experimental) of this novel field.
Differential Models : An Introduction with Mathcad
Differential equations are often used in mathematical models for technological processes or devices. However, the design of a differential mathematical model is crucial and difficult in engineering.
Differential Analysis on Complex Manifolds
In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.
Difference Equations : From Rabbits to Chaos
Difference equations are models of the world around us. From clocks to computers to chromosomes, processing discrete objects in discrete steps is a common theme. Difference equations arise naturally from such discrete descriptions and allow us to pose and answer such questions as: How much? How many? How long? Difference equations are a necessary part of the mathematical repertoire of all modern scientists and engineers.The book cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron—Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly.
