Mathematical foundations of computational electromagnetism /

Mathematical foundations of computational electromagnetism /

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Bibliographic Details
Author / Creator:Assous, Franck, author.
Imprint:Cham, Switzerland : Springer, [2018]
Description:1 online resource (ix, 458 pages) : illustrations
Language:English
Series:Applied Mathematical Sciences, 0066-5452 ; 198
Applied mathematical sciences (Springer-Verlag New York Inc.) ; 198.
Subject:
Electromagnetism -- Mathematics.
Electromagnetism -- Data processing.
Electromagnetism -- Mathematical models.
Electromagnetism -- Mathematics.
Electromagnetism -- Mathematical models.
Electromagnetism -- Data processing.
Functional analysis.
Mathematical physics.
Mathematics.
Physics.
Plasma (Ionized gases)
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11664185
Hidden Bibliographic Details
Other authors / contributors:Ciarlet, Patrick, author.
Labrunie, Simon, author.
ISBN:9783319708423
3319708422
3319708414
9783319708416
9783319708430
3319708430
9783030099978
3030099970
9783319708416
3319708414
Digital file characteristics:text file PDF
Notes:Includes bibliographical references and index.
Summary: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.
Other form:Printed edition: 9783319708416
Standard no.:10.1007/978-3-319-70842-3
9783319708416
10.1007/978-3-319-70
Table of Contents:
  • Foreword
  • Physical framework and models
  • Electromagnetic fields and Maxwell's equations
  • Stationary equations
  • Coupling with other models
  • Approximate models
  • Elements of mathematical classifications
  • Boundary conditions and radiation conditions
  • Energy matters
  • Bibliographical notes
  • Basic applied functional analysis
  • Function spaces for scalar fields
  • Vector fields: standard function spaces
  • Practical function spaces in the (t, x) variable
  • Complements of applied functional analysis
  • Vector fields: tangential trace revisited
  • Scalar and vector potentials: the analyst's and topologist's points of view
  • Extraction of scalar potentials and consequences
  • Extraction of vector potentials
  • Extraction of vector potentials
  • Vanishing normal trace
  • Extraction of vector potentials
  • Complements
  • Helmholtz decompositions
  • Abstract mathematical framework
  • Basic Results
  • Static problems
  • Time-dependent problems
  • Time-dependent problems: improved regularity results
  • Time-harmonic problems
  • Summing up
  • Analyses of exact problems: first-order models
  • Energy matters: uniqueness of the fields
  • Well-posedness
  • Analyses of approximate models
  • Electrostatic problem
  • Magnetostatic problem
  • Further comments around static problems
  • Other approximate models
  • Analyses of exact problems: second-order models
  • First-order to second-order equations
  • Well-posedness of the second-order Maxwell equations
  • Second-order to first-order equations
  • Other variational formulations
  • Compact imbeddings
  • Improved regularity for augmented and mixed augmented formulations
  • Analyses of time-harmonic problems
  • Compact imbeddings: complements
  • Free vibrations in a domain encased in a cavity
  • Sustained vibrations
  • Interface problem between a dielectric and a Lorentz material
  • Comments
  • Dimensionally reduced models: derivation and analyses
  • Two-and-a-half dimensional (2 1/2 2D) models
  • Two-dimensional (2D) models
  • Some results of functional analysis
  • Existence and uniqueness results (2D problems)
  • Analyses of coupled models
  • The Vlasov-Maxwell and Vlasov-Poisson systems
  • Magnetohydrodynamics
  • References
  • Index of function spaces
  • Basic Spaces
  • Electromagnetic spaces
  • Dimension reduction and weighted spaces
  • Spaces measuring time regularity
  • List of Figures
  • Index.

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