Finite Element Methods For Maxwell's Equations is the first book to present the use of finite elements to analyse Maxwell's equations. This book is part of the Numerical Analysis and Scientific Computation Series.

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.

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.

We study the stability properties of, and the phase error present in, a nite element scheme for Maxwell's equations coupled with Debye or Lorentz polarization. In one dimension we consider a second order formulation for the electric eld with an ordinary di erential equation for the polarization added as an auxiliary constraint. The nite element method uses linear nite elements in space for the electric eld as well as the polarization, and a theta scheme for the time discretization. Numerical experiments suggest the method is unconditionally stable for both Debye and Lorentz models. We compare the stability and phase error properties of the method presented here with those of nite di erence methods that have been analyzed in the literature. We also conduct numerical simulations that verify the stability and dispersion properties of the scheme.

An analysis of the three-dimensional (3-D) finite element formulation of Maxwell's equations governing classical electromagnetic propagation in dielectrics is given including its analogy to Navier's equation. The weak form of the electric field equation is reviewed along with dispersion analysis and approximation equations. Radiation boundary conditions are also explored to include paraxial absorber, Sandier absorber, and other absorber comparisons. In addition, time domains vs. frequency domains are investigated with a listing of possible advantages and disadvantages. It was concluded that if large-scale calculations need to be done today, time-domain techniques provide the most practicable means; however, it is still premature to promote such solvers as production level tools for engineers.

This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.

Achieve optimal microwave system performance by mastering the principles and methods underlying today's powerful computational tools and commercial software in electromagnetics. This authoritative resource offers you clear and complete explanation of this essential electromagnetics knowledge, providing you with the analytical background you need to understand such key approaches as MoM (method of moments), FDTD (Finite Difference Time Domain) and FEM (Finite Element Method), and Green's functions. This comprehensive book includes all math necessary to master the material. Moreover, it features numerous solved problems that help ensure your understanding of key concepts throughout the book.

Describes most popular computational methods used to solve problems in electromagnetics Matlab code is included throughout, so that the reader can implement the various techniques discussed Exercises included