Harmonic Wave Systems Partial Differential Equations Of The Helmholtz Decomposition
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Harmonic Wave Systems Partial Differential Equations Of The Helmholtz Decomposition
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Author : Victor A. Miroshnikov
language : en
Publisher: Scientific Research Publishing, Inc. USA
Release Date : 2017-12-15
Harmonic Wave Systems Partial Differential Equations Of The Helmholtz Decomposition written by Victor A. Miroshnikov and has been published by Scientific Research Publishing, Inc. USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Science categories.
Harmonic Wave Systems is the first textbook about the computational method of Decomposition in Invariant Structures (DIS) that generalizes the analytical methods of separation of variables, undetermined coefficients, asymptotic expansions, and series expansions. In recent years, there has been a boom in publications on propagation of nonlinear waves described by a fascinating list of partial differential equations (PDEs). The vast majority of wave problems are reducible to one-dimensional ones in propagation variables. However, a list of publications with two- and three-dimensional applications of the DIS method is brief. The book offers a comprehensive and rigorous treatment of the DIS method in two and three dimensions using the PDE approach to the Helmholtz decomposition that provides the most general background for mathematical modelling of harmonic waves in fluid dynamics, electrodynamics, heat transfer, and other numerous areas of science and engineering, which are dealing with propagation and interaction of N internal waves.
Harmonic Wave Systems Partial Differential Equations Of The Helmholtz Decomposition
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Author : A. Miroshnikov Victor
language : en
Publisher:
Release Date : 2017-12
Harmonic Wave Systems Partial Differential Equations Of The Helmholtz Decomposition written by A. Miroshnikov Victor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12 with categories.
The Mathematical Theory Of Time Harmonic Maxwell S Equations
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Author : Andreas Kirsch
language : en
Publisher: Springer
Release Date : 2014-11-20
The Mathematical Theory Of Time Harmonic Maxwell S Equations written by Andreas Kirsch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-20 with Mathematics categories.
This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations. The book arose from lectures taught by the authors over many years and can be helpful in designing graduate courses for mathematically orientated students on electromagnetic wave propagation problems. The students should have some knowledge on vector analysis (curves, surfaces, divergence theorem) and functional analysis (normed spaces, Hilbert spaces, linear and bounded operators, dual space). Written in an accessible manner, topics are first approached with simpler scale Helmholtz Equations before turning to Maxwell Equations. There are examples and exercises throughout the book. It will be useful for graduate students and researchers in applied mathematics and engineers working in the theoretical approach to electromagnetic wave propagation.
Control Of Nonlinear Distributed Parameter Systems
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Author : Goong Chen
language : en
Publisher: CRC Press
Release Date : 2001-03-14
Control Of Nonlinear Distributed Parameter Systems written by Goong Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-14 with Mathematics categories.
An examination of progress in mathematical control theory applications. It provides analyses of the influence and relationship of nonlinear partial differential equations to control systems and contains state-of-the-art reviews, including presentations from a conference co-sponsored by the National Science Foundation, the Institute of Mathematics and its Applications, the University of Minnesota, and Texas A&M University.
Partial Differential Equations
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Author : J. Necas
language : en
Publisher: Routledge
Release Date : 2018-05-04
Partial Differential Equations written by J. Necas and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.
Waves And Distributions
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Author : Jonsson Thordur
language : en
Publisher: World Scientific
Release Date : 1995-05-09
Waves And Distributions written by Jonsson Thordur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05-09 with Science categories.
This book begins with an introduction on continuum mechanics and a derivation of the linear partial differential equations for sound waves in fluids and elastic waves in solids. There is a brief chapter on the wave equations of electrodynamics. This is followed by a description of plane wave solutions and a discussion of concepts like reflection, refraction, polarization and the role of boundary conditions.The second part of the book deals with the theory and applications of distributions and Fourier transforms. Furthermore, dispersion, the method of stationary phase, Kramers-Kronig relations and various examples including surface waves on liquids are discussed.This text is unique because it emphasizes the use of distributions to analyze the solutions of the wave equation. The treatment of continuum mechanics is self-contained, as well as the discussion on distributions and Fourier transforms. In addition, many classical methods of theoretical physics are thoroughly discussed, e.g. the use of Green functions and multipole expansions.
Domain Decomposition Methods 10
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Author : Jan Mandel
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Domain Decomposition Methods 10 written by Jan Mandel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This volume contains the proceedings of the Tenth International Conference on Domain Decomposition Methods, which focused on the latest developments in realistic applications in structural mechanics, structural dynamics, computational fluid dynamics, and heat transfer. The proceedings of these conferences have become standard references in the field and contain seminal papers as well as the latest theoretical results and reports on practical applications.This volume is divided into four parts: the first part contains invited papers (some of which survey developments over the past decade), and the other parts gather material from minisymposia and contributed presentations under three headings: Algorithms, Theory, and Applications. The electronic version is available at no additional charge to purchasers of the print volume. Access instructions are provided in the book. There is also the option to purchase only the electronic version.
An Introduction To Domain Decomposition Methods
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Author : Victorita Dolean
language : en
Publisher: SIAM
Release Date : 2015-12-08
An Introduction To Domain Decomposition Methods written by Victorita Dolean and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Science categories.
The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.?
Wave Propagation In Solids And Fluids
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Author : Julian L. Davis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Wave Propagation In Solids And Fluids written by Julian L. Davis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids. Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of mass, momentum, and energy, which will be described in various sections of the book in their proper physical setting. These conservation laws are expressed either in the Lagrangian or the Eulerian representation depending on whether the boundaries are relatively fixed or moving. In any case, these laws of physics allow us to derive the "field equations" which are expressed as systems of partial differential equations. For wave propagation phenomena these equations are said to be "hyperbolic" and, in general, nonlinear in the sense of being "quasi linear" . We therefore attempt to determine the properties of a system of "quasi linear hyperbolic" partial differential equations which will allow us to calculate the displacement, velocity fields, etc.
Lectures On Non Linear Wave Equations
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Author : Christopher Donald Sogge
language : en
Publisher:
Release Date : 2008
Lectures On Non Linear Wave Equations written by Christopher Donald Sogge and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Nonlinear wave equations categories.
Presents an account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. This book examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced.