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Mathematical foundations of computat...

Assous, Franck.

Mathematical foundations of computational electromagnetism

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical foundations of computational electromagnetismby Franck Assous, Patrick Ciarlet, Simon Labrunie.
Author:	Assous, Franck.
other author:	Ciarlet, Patrick.
Published:	Cham :Springer International Publishing :2018.
Description:	ix, 458 p. :ill., digital ;25 cm.
Contained By:	Springer eBooks
Subject:	ElectromagnetismMathematics.
Online resource:	http://dx.doi.org/10.1007/978-3-319-70842-3
ISBN:	9783319708423$q(electronic bk.)

Mathematical foundations of computational electromagnetism
Assous, Franck.

Mathematical foundations of computational electromagnetism[electronic resource] /by Franck Assous, Patrick Ciarlet, Simon Labrunie. - Cham :Springer International Publishing :2018. - ix, 458 p. :ill., digital ;25 cm. - Applied mathematical sciences,v.1980066-5452 ;. - Applied mathematical sciences ;v.176..

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.

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.

ISBN: 9783319708423$q(electronic bk.)

Standard No.: 10.1007/978-3-319-70842-3doiSubjects--Topical Terms:

225080
Electromagnetism
--Mathematics.

LC Class. No.: QC760.4.M37 / A87 2018

Dewey Class. No.: 537.0151

Mathematical foundations of computational electromagnetism
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245 1 0 $a Mathematical foundations of computational electromagnetism $h [electronic resource] / $c by Franck Assous, Patrick Ciarlet, Simon Labrunie.
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505 0 $a 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.
520 $a 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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