Mathematical foundations of computational electromagnetism. ([2018])

• Record Type: Book
• Further Information: Note: Franck Assous, Patrick Ciarlet, Simon Labrunie.
• Authors: Assous, Franck; Ciarlet, Patrick; Labrunie, Simon
• 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.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource (ix, 458 pages), illustrations
• Subjects: 537.01/51; Mathematics; Electromagnetism -- Mathematics; Electromagnetism -- Data processing; Electromagnetism -- Mathematical models; SCIENCE / Physics / Electricity; SCIENCE / Physics / Electromagnetism; Functional analysis; Mathematical physics; Mathematics; Physics; Plasma (Ionized gases); Science -- Electricity; Technology & Engineering -- Engineering (General); Mathematics -- Functional Analysis; Science -- Mathematical Physics; Science -- Nuclear Physics; Optical physics; Maths for engineers; Functional analysis & transforms; Mathematical physics; Plasma physics; Engineering mathematics; Functional analysis; Mathematics -- Applied; Mathematical modelling; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783319708423; 3319708422
• Related ISBNs: 9783319708416; 3319708414
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.