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Electromagnetism. --- Electrical engineering --- Electromagnétisme --- Génie électrique --- Mathematics --- Mathématiques --- Electromagnetism --- Electric engineering --- Mathematical models --- Mathematical models. --- Electromagnétisme --- Génie électrique --- Mathématiques --- Electric engineering - Mathematical models

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    Comprehensive treatment of edge finite element methods 
    Variational theory of Maxwell's equations 
    Error analysis of finite element methods 
    Background material in functional analysis and Sobolev space theory 
    Introduction to inverse problems 

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.


535.13 --- 535.13 Electromagnetic theory (Maxwell) --- Electromagnetic theory (Maxwell) --- finite element method --- computer-aided engineering --- CAE (computer aided engineering) --- Maxwell equations --- Electromagnétisme --- Equations de Maxwell --- Partitial differential equations: domain decomposition methods; elliptic equations; finite difference methods; finite element methods; finite volume methods; hyperbolic equations; inverse problems; iterative solution techniques; methods of lines; multigrid and multilevel methods; parabolic equations; special methods --- Maxwell equations. --- Electromagnétisme --- Electromagnetism --- Finite element method --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Mathematical models --- 519.63 --- 681.3*G18 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- Numerical solutions of differential equations --- Functional analysis --- eindige elementen --- Finite element method. --- Mathematical models. --- Méthode des éléments finis --- Modèles mathématiques --- Electromagnetism - Mathematical models --- Equations aux derivees partielles --- Equations de maxwell --- Methodes numeriques --- Elements finis