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.

This conference was held in Santiago de Compostela, Spain, July 10-14, 2000. This volume contains papers presented at the conference covering a broad range of topics in theoretical and applied wave propagation in the general areas of acoustics, electromagnetism, and elasticity. Both direct and inverse problems are well represented. This volume, along with the three previous ones, presents a state-of-the-art primer for research in wave propagation. The conference is conducted by the Institut National de Recherche en Informatique et en Automatique with the cooperation of SIAM.

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.

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 problems can be approached either by analytical or numerical methods. This book presents the analytical methods for determining the eddy current density and associated loss in linear conducting media at low frequencies in the steady state. The methods are described and presented in such a manner that they can readily be used by engineers and researchers.

Front cover -- Titelseite -- Impressum -- Acknowledgments -- Contents -- Summary -- Introduction to Eddy Current Sensors and Modeling Techniques -- Statement of the Problem of Hot Wire Steel Inspection -- Numerical Modeling and Simulation of the Inspection Technique -- Modeling Tools -- MQSFIT -- Opera -- Faraday 6.1 -- Other Tools -- Governing Equations for Magnetoquasistatic Problem -- Maxwell's Equations for Macroscopic Non-moving Medium -- Transition and Boundary Conditions -- Transition Conditions -- Boundary Conditions -- Field Equations in the Frequency Domain -- Inhomogeneous Helmholtz Equations -- Inhomogeneous Helmholtz Equation for the Electric Field -- Inhomogeneous Helmholtz Equation for the Magnetic Field -- Electromagnetic Potentials of an Electrically Conducting Material -- Electromagnetic Potentials in Source-Free Case -- Derivation of the Potential Representation using Magnetic Vector Potential and Electric Scalar Potential -- Derivation of the Potential Representation using Magnetic Scalar Potential and Electric Vector Potential -- Electromagnetic Potentials in Case with Electric and Magnetic Sources -- Decoupling of Maxwell's Equations by Electromagnetic Potentials -- Expression of the Magnetic Vector Potential in the Frequency Domain -- Expression of the Electric Scalar Potential in the Frequency Domain -- Expression of the Electric Vector Potential in the Frequency Domain -- Expression of the Magnetic Scalar Potential in the Frequency Domain -- Summary of Electromagnetic Potentials in the Frequency Domain -- Magnetoquasistatic Field -- Magnetoquasistatic Field Equations with Magnetic Vector Potential -- Transition and Boundary Conditions for the Magnetic Vector Potential -- Field Equations for a Moving Conductor -- Finite Integration Technique (FIT) -- Discretization of the Electromagnetic Medium in Space.

This book covers the topic of eddy current nondestructive evaluation, the most commonly practiced method of electromagnetic nondestructive evaluation (NDE). It emphasizes a clear presentation of the concepts, laws and relationships of electricity and magnetism upon which eddy current inspection methods are founded. The chapters include material on signals obtained using many common eddy current probe types in various testing environments. Introductory mathematical and physical concepts in electromagnetism are introduced in sufficient detail and summarized in the Appendices for easy reference. Worked examples and simple calculations that can be done by hand are distributed throughout the text. These and more complex end-of-chapter examples and assignments are designed to impart a working knowledge of the connection between electromagnetic theory and the practical measurements described. The book is intended to equip readers with sufficient knowledge to optimize routine eddy current NDE inspections, or design new ones. It is useful for graduate engineers and scientists seeking a deeper understanding of electromagnetic methods of NDE than can be found in a guide for practitioners.

Presenting topics that have not previously been contained in a single volume, this book offers an up-to-date review of computational methods in electromagnetism, with a focus on recent results in the numerical simulation of real-life electromagnetic problems and on theoretical results that are useful in devising and analyzing approximation algorithms. Based on four courses delivered in Cetraro in June 2014, the material covered includes the spatial discretization of Maxwell’s equations in a bounded domain, the numerical approximation of the eddy current model in harmonic regime, the time domain integral equation method (with an emphasis on the electric-field integral equation) and an overview of qualitative methods for inverse electromagnetic scattering problems. Assuming some knowledge of the variational formulation of PDEs and of finite element/boundary element methods, the book is suitable for PhD students and researchers interested in numerical approximation of partial differential equations and scientific computing.

This book presents a comprehensive mathematical approach for solving stochastic magnetic field problems. It discusses variability in material properties and geometry, with an emphasis on the preservation of structural physical and mathematical properties. It especially addresses uncertainties in the computer simulation of magnetic fields originating from the manufacturing process. Uncertainties are quantified by approximating a stochastic reformulation of the governing partial differential equation, demonstrating how statistics of physical quantities of interest, such as Fourier harmonics in accelerator magnets, can be used to achieve robust designs. The book covers a number of key methods and results such as: a stochastic model of the geometry and material properties of magnetic devices based on measurement data; a detailed description of numerical algorithms based on sensitivities or on a higher-order collocation; an analysis of convergence and efficiency; and the application of the developed model and algorithms to uncertainty quantification in the complex magnet systems used in particle accelerators.