Mathematical foundations of computational electromagnetism /
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| Author / Creator: | Assous, Franck, author. |
|---|---|
| Imprint: | Cham, Switzerland : Springer, [2018] |
| Description: | 1 online resource (ix, 458 pages) : illustrations |
| Language: | English |
| Series: | Applied Mathematical Sciences, 0066-5452 ; 198 Applied mathematical sciences (Springer-Verlag New York Inc.) ; 198. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11664185 |
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| 100 | 1 | |a Assous, Franck, |e author. | |
| 245 | 1 | 0 | |a Mathematical foundations of computational electromagnetism / |c Franck Assous, Patrick Ciarlet, Simon Labrunie. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2018] | |
| 300 | |a 1 online resource (ix, 458 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Applied Mathematical Sciences, |x 0066-5452 ; |v 198 | |
| 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. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 650 | 0 | |a Electromagnetism |x Mathematics. |0 http://id.loc.gov/authorities/subjects/sh2008119286 | |
| 650 | 0 | |a Electromagnetism |x Data processing. | |
| 650 | 0 | |a Electromagnetism |x Mathematical models. | |
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| 650 | 7 | |a Maths for engineers. |2 bicssc | |
| 650 | 7 | |a Functional analysis & transforms. |2 bicssc | |
| 650 | 7 | |a Mathematical physics. |2 bicssc | |
| 650 | 7 | |a Plasma physics. |2 bicssc | |
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| 650 | 7 | |a Electromagnetism |x Mathematical models. |2 fast |0 (OCoLC)fst00906599 | |
| 650 | 7 | |a Electromagnetism |x Data processing. |2 fast |0 (OCoLC)fst00906593 | |
| 650 | 7 | |a Functional analysis. |2 fast |0 (OCoLC)fst00936061 | |
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| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Ciarlet, Patrick, |e author. | |
| 700 | 1 | |a Labrunie, Simon, |e author. | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319708416 |w (OCoLC)1006451882 |
| 830 | 0 | |a Applied mathematical sciences (Springer-Verlag New York Inc.) ; |v 198. |x 0066-5452 |0 http://id.loc.gov/authorities/names/n42002591 | |
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| 928 | |t Library of Congress classification |a QC760.4.M37 A87 2018 |l Online |c UC-FullText |u https://link.springer.com/10.1007/978-3-319-70842-3 |z Springer Nature |g ebooks |i 12554725 | ||