The Mathematical Theory of Time-Harmonic Maxwell's Equations

The Mathematical Theory of Time-Harmonic Maxwell's Equations PDF

Author: Andreas Kirsch

Publisher: Springer

Published: 2014-11-20

Total Pages: 347

ISBN-13: 3319110861

DOWNLOAD EBOOK →

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.

Maxwell’s Equations

Maxwell’s Equations PDF

Author: Ulrich Langer

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-07-08

Total Pages: 444

ISBN-13: 3110543613

DOWNLOAD EBOOK →

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.

Eddy Current Approximation of Maxwell Equations

Eddy Current Approximation of Maxwell Equations PDF

Author: Ana Alonso Rodriguez

Publisher: Springer Science & Business Media

Published: 2010-11-22

Total Pages: 355

ISBN-13: 8847015065

DOWNLOAD EBOOK →

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.

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics PDF

Author: G. F. Roach

Publisher: Princeton University Press

Published: 2012-03-04

Total Pages: 400

ISBN-13: 1400842654

DOWNLOAD EBOOK →

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

Maxwell's Equations

Maxwell's Equations PDF

Author: Ulrich Langer

Publisher: de Gruyter

Published: 2019

Total Pages: 0

ISBN-13: 9783110542646

DOWNLOAD EBOOK →

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.

75 Years of Mathematics of Computation

75 Years of Mathematics of Computation PDF

Author: Susanne C. Brenner

Publisher: American Mathematical Soc.

Published: 2020-07-29

Total Pages: 364

ISBN-13: 1470451638

DOWNLOAD EBOOK →

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.

Maxwell Equation

Maxwell Equation PDF

Author: Hiroshi Isozaki

Publisher: World Scientific Publishing Company

Published: 2020-04-28

Total Pages: 0

ISBN-13: 9789811221392

DOWNLOAD EBOOK →

How can one determine the physical properties of the medium or the geometrical properties of the domain by observing electromagnetic waves? To answer this fundamental problem in mathematics and physics, this book leads the reader to the frontier of inverse scattering theory for electromagnetism. The first three chapters, written comprehensively, can be used as a textbook for undergraduate students. Beginning with elementary vector calculus, this book provides fundamental results for wave equations and Helmholtz equations, and summarizes the potential theory. It also explains the cohomology theory in an easy and straightforward way, which is an essential part of electromagnetism related to geometry. It then describes the scattering theory for the Maxwell equation by the time-dependent method and also by the stationary method in a concise, but almost self-contained manner. Based on these preliminary results, the book proceeds to the inverse problem for the Maxwell equation. The chapters for the potential theory and elementary cohomology theory are good introduction to graduate students. The results in the last chapter on the inverse scattering for the medium and the determination of Betti numbers are new, and will give a current scope for the inverse spectral problem on non-compact manifolds. It will be useful for young researchers who are interested in this field and trying to find new problems.

Integral Equation Methods in Scattering Theory

Integral Equation Methods in Scattering Theory PDF

Author: David Colton

Publisher: SIAM

Published: 2013-11-15

Total Pages: 286

ISBN-13: 1611973155

DOWNLOAD EBOOK →

This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.

Lanterna Rally - Theme by Grace Themes