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The Mathematical Theory Of Time Harmonic Maxwells Equations
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Book Synopsis The Mathematical Theory of Time-Harmonic Maxwell's Equations by : Andreas Kirsch
Download or read book The Mathematical Theory of Time-Harmonic Maxwell's Equations written by Andreas Kirsch and published by Springer. This book was released on 2014-11-20 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Maxwell’s Equations by : Ulrich Langer
Download or read book Maxwell’s Equations written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects longer articles on the analysis and numerics of Maxwell’s equations. The topics include functional analytic and Hilbert space methods, compact embeddings, solution theories and asymptotics, electromagnetostatics, time-harmonic Maxwell’s equations, time-dependent Maxwell’s equations, eddy current approximations, scattering and radiation problems, inverse problems, finite element methods, boundary element methods, and isogeometric analysis.
Book Synopsis Maxwell's Equations by : Ulrich Langer
Download or read book Maxwell's Equations written by Ulrich Langer and published by de Gruyter. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects longer articles on the analysis and numerics of Maxwell's equations. The topics include functional analytic and Hilbert space methods, compact embeddings, solution theories and asymptotics, electromagnetostatics, time-harmonic Maxwell's equations, time-dependent Maxwell's equations, eddy current approximations, scattering and radiation problems, inverse problems, finite element methods, boundary element methods, and isogeometric analysis.
Book Synopsis 75 Years of Mathematics of Computation by : Susanne C. Brenner
Download or read book 75 Years of Mathematics of Computation written by Susanne C. Brenner and published by American Mathematical Soc.. This book was released on 2020-07-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.
Book Synopsis Maxwell’s Equations in Periodic Structures by : Gang Bao
Download or read book Maxwell’s Equations in Periodic Structures written by Gang Bao and published by Springer Nature. This book was released on 2021-11-22 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell’s equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.
Download or read book Maxwell's Equations written by Dirk Pauly and published by de Gruyter. This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Eddy Current Approximation of Maxwell Equations by : Ana Alonso Rodriguez
Download or read book Eddy Current Approximation of Maxwell Equations written by Ana Alonso Rodriguez and published by Springer Science & Business Media. This book was released on 2010-11-22 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. It takes into account all the most used formulations, placing the problem in a rigorous functional framework.
Book Synopsis Remote Sensing Image Processing Algorithms for Detecting Air Turbulence Patterns by : Maged Marghany
Download or read book Remote Sensing Image Processing Algorithms for Detecting Air Turbulence Patterns written by Maged Marghany and published by CRC Press. This book was released on 2024-11-22 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Injuries due to air turbulence has increased recently, therefore there is considerable concern and interest in understanding and detecting it more accurately. Presently hardly any research deals with air turbulence detection using remote sensing images. Most works use conventional optical remote sensing data with classical methods such as a library spectral signature, band ratio, and principal component analysis without designating new methods and technology. Very little research has attempted to implement optical and microwave remote sensing images for air turbulence detections. This book provides new image processing procedures for air turbulence detection using advanced remote sensing images and quantum image processing. Currently, there is a huge gap between research work in the field of air turbulence detection and advanced remote sensing technology. Most of the theories are not operated in terms of software modules. Most of the software packages in the field of remote sensing images cannot deal with advanced image processing techniques in air turbulence detections due to heavy mathematics work. In this view, this book fills a gap between advanced remote sensing technology and air turbulence detection. For instance, quantum image processing with a new generation of remote sensing technology such as RADARSAT-2 SAR images is also implemented to provide accurate air turbulence detections.
Book Synopsis Computational Partial Differential Equations Using MATLAB® by : Jichun Li
Download or read book Computational Partial Differential Equations Using MATLAB® written by Jichun Li and published by CRC Press. This book was released on 2019-09-26 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this popular text for an Numerical Analysis course, the authors introduce several major methods of solving various partial differential equations (PDEs) including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques including the classic finite difference method, finite element method, and state-of-the-art numercial methods.The text uniquely emphasizes both theoretical numerical analysis and practical implementation of the algorithms in MATLAB. This new edition includes a new chapter, Finite Value Method, the presentation has been tightened, new exercises and applications are included, and the text refers now to the latest release of MATLAB. Key Selling Points: A successful textbook for an undergraduate text on numerical analysis or methods taught in mathematics and computer engineering. This course is taught in every university throughout the world with an engineering department or school. Competitive advantage broader numerical methods (including finite difference, finite element, meshless method, and finite volume method), provides the MATLAB source code for most popular PDEs with detailed explanation about the implementation and theoretical analysis. No other existing textbook in the market offers a good combination of theoretical depth and practical source codes.
Book Synopsis An Introduction to the Mathematical Theory of Inverse Problems by : Andreas Kirsch
Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Nature. This book was released on 2021-02-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
Book Synopsis Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials by : Jichun Li
Download or read book Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials written by Jichun Li and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell’s equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.
Book Synopsis Adventures in Contemporary Electromagnetic Theory by : Tom G. Mackay
Download or read book Adventures in Contemporary Electromagnetic Theory written by Tom G. Mackay and published by Springer Nature. This book was released on 2023-07-31 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the most recent advances in electromagnetic theory, motivated and partly informed by developments in engineering science and nanotechnology. The collection of chapters provided in this edited book, authored by leading experts in the field, offers a bird’s eye view of recent progress in electromagnetic theory, spanning a wide range of topics of current interest, ranging from fundamental issues to applications.
Download or read book Wave Phenomena written by Willy Dörfler and published by Springer Nature. This book was released on 2023-03-30 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.
Book Synopsis Recent Trends in Operator Theory and Partial Differential Equations by : Vladimir Maz'ya
Download or read book Recent Trends in Operator Theory and Partial Differential Equations written by Vladimir Maz'ya and published by Birkhäuser. This book was released on 2017-02-23 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.
Book Synopsis Boundary Integral Equations by : George C. Hsiao
Download or read book Boundary Integral Equations written by George C. Hsiao and published by Springer Nature. This book was released on 2021-03-26 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
Book Synopsis Maxwell's Equations by : Paul G. Huray
Download or read book Maxwell's Equations written by Paul G. Huray and published by John Wiley & Sons. This book was released on 2011-11-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative view of Maxwell's Equations that takes theory to practice Maxwell's Equations is a practical guide to one of the most remarkable sets of equations ever devised. Professor Paul Huray presents techniques that show the reader how to obtain analytic solutions for Maxwell's equations for ideal materials and boundary conditions. These solutions are then used as a benchmark for solving real-world problems. Coverage includes: An historical overview of electromagnetic concepts before Maxwell and how we define fundamental units and universal constants today A review of vector analysis and vector operations of scalar, vector, and tensor products Electrostatic fields and the interaction of those fields with dielectric materials and good conductors A method for solving electrostatic problems through the use of Poisson's and Laplace's equations and Green's function Electrical resistance and power dissipation; superconductivity from an experimental perspective; and the equation of continuity An introduction to magnetism from the experimental inverse square of the Biot-Savart law so that Maxwell's magnetic flux equations can be deduced Maxwell's Equations serves as an ideal textbook for undergraduate students in junior/senior electromagnetics courses and graduate students, as well as a resource for electrical engineers.
Book Synopsis Inverse Scattering Theory and Transmission Eigenvalues by : Fioralba Cakoni
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2022-12-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
