Mathematical Foundations of Computational Electromagnetism. 1st ed. 2018

種類:

電子ブック

責任表示:

by Franck Assous, Patrick Ciarlet, Simon Labrunie

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Assous, Franck.
• Ciarlet, Patrick.
• Labrunie, Simon.
• SpringerLink (Online service)

シリーズ名:

Applied Mathematical Sciences ; 198

ISBN:

9783319708423 [3319708422]    

注記:

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 -- T
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

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