Mathematical Foundations of Computational Electromagnetism

• Κύριοι συγγραφείς: Assous, Franck (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Ciarlet, Patrick (http://id.loc.gov/vocabulary/relators/aut), Labrunie, Simon (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Applied Mathematical Sciences, 198
• Θέματα: Mathematical physics.; Optics.; Electrodynamics.; Engineering mathematics.; Functional analysis.; Plasma (Ionized gases).; Mathematical Applications in the Physical Sciences.; Classical Electrodynamics.; Engineering Mathematics.; Functional Analysis.; Theoretical, Mathematical and Computational Physics.; Plasma Physics.

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 equatio...

Πίνακας περιεχομένων:

• 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.