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" Mathematical foundations of computational electromagnetism / "
Franck Assous, Patrick Ciarlet, Simon Labrunie.
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BL
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| Record Number
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864210
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| Main Entry
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Assous, Franck
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| Title & Author
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Mathematical foundations of computational electromagnetism /\ Franck Assous, Patrick Ciarlet, Simon Labrunie.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2018]
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| Series Statement
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Applied Mathematical Sciences,; 198
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1 online resource (ix, 458 pages) :: illustrations
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| ISBN
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3030099970
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: 3319708414
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: 3319708422
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: 3319708430
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: 9783030099978
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: 9783319708416
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: 9783319708423
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: 9783319708430
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3319708414
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9783319708416
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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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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| Abstract
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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.
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Electromagnetism-- Data processing.
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Electromagnetism-- Mathematical models.
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Electromagnetism-- Mathematics.
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Functional analysis transforms.
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Functional analysis.
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Mathematical modelling.
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Mathematical physics.
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Mathematical physics.
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Mathematics.
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Maths for engineers.
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Optical physics.
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Physics.
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Plasma (Ionized gases)
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Plasma physics.
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SCIENCE-- Physics-- Electricity.
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SCIENCE-- Physics-- Electromagnetism.
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| Dewey Classification
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537.01/51
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| LC Classification
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QC760.4.M37A87 2018
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| Added Entry
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Ciarlet, Patrick
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Labrunie, Simon
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