Applied Mathematical Sciences

Mathematical Foundations of Computational Electromagnetism

Authors: Assous, Franck, Ciarlet, Patrick, Labrunie, Simon

  • Presents extensive treatment of the time-dependent equations
  • Includes the foundations of the analysis of the numerical schemes and computational methods
  • Uses only the “classical” formulation of electromagnetism (i.e. gradient, divergence and curl operators) avoiding the “intrinsic” formulations based on differential geometry
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eBook 91,62 €
price for France (gross)
  • ISBN 978-3-319-70842-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 116,04 €
price for France (gross)
  • ISBN 978-3-319-70841-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations.

The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.

Table of contents (10 chapters)

  • Physical Framework and Models

    Assous, Franck (et al.)

    Pages 1-71

  • Basic Applied Functional Analysis

    Assous, Franck (et al.)

    Pages 73-105

  • Complements of Applied Functional Analysis

    Assous, Franck (et al.)

    Pages 107-145

  • Abstract Mathematical Framework

    Assous, Franck (et al.)

    Pages 147-190

  • Analyses of Exact Problems: First-Order Models

    Assous, Franck (et al.)

    Pages 191-221

Buy this book

eBook 91,62 €
price for France (gross)
  • ISBN 978-3-319-70842-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 116,04 €
price for France (gross)
  • ISBN 978-3-319-70841-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Foundations of Computational Electromagnetism
Authors
Series Title
Applied Mathematical Sciences
Series Volume
198
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-70842-3
DOI
10.1007/978-3-319-70842-3
Hardcover ISBN
978-3-319-70841-6
Series ISSN
0066-5452
Edition Number
1
Number of Pages
IX, 458
Number of Illustrations and Tables
7 b/w illustrations
Topics