Finite Element Methods for Maxwell's Equations (Numerical Mathematics and Scientific Computation)

In light of increasing uses for direct numerical approximations of Maxwell's equations in science and engineering, this text provides mathematics graduate students and researchers with a theoretical foundation for finite element methods in computational electromagnetism. Monk (mathematical sciences, U. of Delaware) emphasizes finite element methods for scattering problems involving the solutions of Maxwell's equations on infinite domains. The book's main focus is on an error analysis of edge finite element methods that are well suited to Maxwell's equations. The book concludes with a short introduction to inverse problems in electromagnetism. 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. "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 in 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."--Jacket. This reference provides 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, and special attention is given to error analysis of edge FEM that are particularly well suited to Maxwell's equations Finite Element Methods For Maxwell's Equations is the first book to present the use of finite elements to analyze Maxwell's equations. This book is part of the Numerical Analysis and Scientific Computation Series.