TY - BOOK AU - Haddar,Houssem AU - Hiptmair,Ralf AU - Monk,Peter AU - Rodríguez,Rodolfo AU - Bermúdez de Castro,Alfredo AU - Valli,A. ED - CIME School on "Computational Electromagnetism" TI - Computational electromagnetism: Cetraro, Italy 2014 T2 - Lecture notes in mathematics, SN - 9783319193069 AV - QC759.6 U1 - 537.01/51 23 PY - 2015/// CY - Cham PB - Springer KW - Electromagnetism KW - Mathematics KW - Congresses KW - Maxwell equations KW - General KW - Physical Sciences & Mathematics KW - Équations de Maxwell KW - Congrès KW - Optical physics KW - bicssc KW - Differential calculus & equations KW - Mathematical physics KW - Numerical analysis KW - Science KW - Electricity KW - bisacsh KW - Differential Equations KW - Mathematical Physics KW - Counting & Numeration KW - Matemáticas KW - embne KW - Física matemática KW - Análisis numérico KW - fast KW - Congress KW - proceedings (reports) KW - aat KW - Conference papers and proceedings KW - lcgft KW - Actes de congrès KW - rvmgf N1 - Includes bibliographical references; 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); 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 N2 - 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 UR - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/978-3-319-19306-9 ER -