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Conference CIME School on "Computational Electromagnetism" (2014 : Cetraro, Italy)
Title Computational electromagnetism : Cetraro, Italy 2014 / Houssem Haddar, Ralf Hiptmair, Peter Monk, Rodolfo Rodriguez ; Alfredo Bermudez de Castro, Alberto Valli, editors.
Imprint Cham : Springer, 2015.

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Conference CIME School on "Computational Electromagnetism" (2014 : Cetraro, Italy)
Series Lecture notes in mathematics, 0075-8434 ; 2148.
Lecture notes in mathematics (Springer-Verlag) ; 2148. 0075-8434.
Subject Electromagnetism -- Mathematics -- Congresses.
Maxwell equations -- Congresses.
Alt Name Haddar, Houssem,
Hiptmair, Ralf,
Monk, Peter, 1956-
Rodríguez, Rodolfo, 1954-
Bermúdez de Castro, Alfredo, 1950-
Valli, A. (Alberto), 1953-
Description 1 online resource (vii, 240 pages) : illustrations (some color).
polychrome rdacc
Bibliography Note Includes bibliographical references.
Note Online resource; title from PDF title page (SpringerLink, viewed July 30, 2015).
Summary 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.
Contents Intro; Preface; Contents; Maxwell's Equations: Continuous and Discrete; 1 Introduction; 2 Maxwell's Equations; Bibliographical Notes; 2.1 Fields; 2.1.1 The Electric Field; 2.1.2 The Magnetic Induction; 2.2 Differential and Integral Forms; 2.2.1 Fundamental Concepts; 2.2.2 Euclidean Vector Proxies in 3D; 2.2.3 Transformation of Forms; 2.3 Topological Electrodynamic Laws; 2.3.1 Circulation and Flux Laws; 2.3.2 Exterior Derivative; 2.3.3 Potentials; 2.4 Energies and Material Laws; 2.4.1 The Exterior Product; 2.4.2 Field Energies; 2.4.3 Material Laws; 2.4.4 Energy Balance (Poynting's Theorem)
5.2 The A, V-A-ψ Potential Formulation5.3 Variational Formulation: Existence and Uniqueness of Solution; 5.4 Numerical Approximation; References; Time Domain Integral Equation Methods in Computational Electromagnetism; 1 Introduction to Electromagnetic Scattering Theory; 2 Notation and Basic Results; 3 Analysis of the EFIE; 3.1 The Laplace Domain EFIE; 3.2 Convolutions Involving Operators; 3.3 The Time Domain EFIE; 4 Spatial and Temporal Discretization; 4.1 Spatial Finite Element Spaces; 4.1.1 Lowest Order Elements on Flat Patches; 4.1.2 Basis Functions on Curvilinear Patches
2.5 Maxwell's Equations: Variational Approach2.5.1 a-Based Variational Formulation; 2.5.2 h-Based Variational Formulation; 2.5.3 Boundary Conditions; 3 Co-chains and Whitney Forms; Bibliographical Notes; 3.1 Meshes; 3.2 Co-chains; 3.2.1 Definition; 3.2.2 Co-chain Calculus; 3.3 Discrete Electrodynamic Laws; 3.4 Whitney Forms; 3.4.1 Whitney Map; 3.4.2 Local Construction of Simplicial Whitney Forms; 3.4.3 Local Commuting Diagram Property; 3.4.4 Global Whitney Forms; 3.4.5 Affine Equivalence; 3.4.6 General Discrete Differential Forms; 3.5 Commuting Projections; 3.5.1 Nodal Interpolation
4.7.3 Discrete Maxwell Cavity ProblemReferences; Numerical Approximation of Maxwell Equations in Low-Frequency Regime; 1 Introduction; 2 Eddy Currents and Eddy Current Model; 2.1 Maxwell System in Harmonic Regime; 2.2 Eddy Current Model; 3 Eddy Current Problem with Input Current Intensities as Boundary Data; 3.1 A Magnetic Field Formulation; 3.2 Introducing a Magnetic Potential; 3.3 Discretization; 3.4 Numerical Experiments; 4 A Mixed Formulation; 4.1 Eddy Current Problems Involving Inner Source Currents; 5 A Potential Formulation; 5.1 Eddy Current Problem
ISBN 9783319193069 (electronic bk.)
3319193066 (electronic bk.)
ISBN/ISSN 10.1007/978-3-319-19306-9
OCLC # 915137507

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