Maxwell’s Equations in Periodic Structures

Maxwell’s Equations in Periodic Structures
Author: Gang Bao
Publisher: Springer Nature
Total Pages: 361
Release: 2021-11-22
Genre: Mathematics
ISBN: 9811600619

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.

The Mathematical Theory of Time-Harmonic Maxwell's Equations

The Mathematical Theory of Time-Harmonic Maxwell's Equations
Author: Andreas Kirsch
Publisher: Springer
Total Pages: 347
Release: 2014-11-20
Genre: Mathematics
ISBN: 3319110861

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.

The Mathematical Analysis of Electrical and Optical Wave-Motion

The Mathematical Analysis of Electrical and Optical Wave-Motion
Author: H. Bateman
Publisher: Cambridge University Press
Total Pages: 171
Release: 2016-10-06
Genre: Science
ISBN: 1316626121

This textbook introduces developments of Maxwell's electromagnetic theory which are directly connected with the solution of the partial differential equation of wave-motion.

Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials

Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
Author: Jichun Li
Publisher: Springer Science & Business Media
Total Pages: 309
Release: 2012-12-15
Genre: Computers
ISBN: 3642337899

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.

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
Author: G. F. Roach
Publisher: Princeton University Press
Total Pages: 400
Release: 2012-03-04
Genre: Mathematics
ISBN: 1400842654

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.

Finite Element Methods for Maxwell's Equations

Finite Element Methods for Maxwell's Equations
Author: Peter Monk
Publisher: Clarendon Press
Total Pages: 468
Release: 2003-04-17
Genre: Mathematics
ISBN: 0191545228

Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.

Eddy Current Approximation of Maxwell Equations

Eddy Current Approximation of Maxwell Equations
Author: Ana Alonso Rodriguez
Publisher: Springer Science & Business Media
Total Pages: 355
Release: 2010-11-22
Genre: Mathematics
ISBN: 8847015065

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.

Electricity and Magnetism for Mathematicians

Electricity and Magnetism for Mathematicians
Author: Thomas A. Garrity
Publisher: Cambridge University Press
Total Pages: 297
Release: 2015-01-19
Genre: Mathematics
ISBN: 1107435161

Maxwell's equations have led to many important mathematical discoveries. This text introduces mathematics students to some of their wonders.

A Student's Guide to Maxwell's Equations

A Student's Guide to Maxwell's Equations
Author: Daniel Fleisch
Publisher: Cambridge University Press
Total Pages: 129
Release: 2008-01-10
Genre: Science
ISBN: 1139468472

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Symmetries of Maxwell’s Equations

Symmetries of Maxwell’s Equations
Author: W.I. Fushchich
Publisher: Springer Science & Business Media
Total Pages: 236
Release: 1987-07-31
Genre: Science
ISBN: 9789027723208

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.