Dimensionally reduced models: Derivation and analyses

Franck Assous; Patrick Ciarlet; Simon Labrunie

doi:10.1007/978-3-319-70842-3_9

Dimensionally reduced models: Derivation and analyses

Franck Assous
, Patrick Ciarlet
, Simon Labrunie

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In this chapter, we consider some special situations in which the three-dimensional (3D) Maxwell equations can be reformulated as two-dimensional (2D) models. More precisely, the computational domain boils down to a subset of ℝ², with respect to a suitable system of coordinates (cylindrical, spherical, cartesian). Nevertheless, the electric and magnetic fields, and other vector quantities, still belong to ℝ³. Under suitable symmetry assumptions, one gets a single set of 2D equations or, equivalently, a single 2D variational formulation. In the general case, the electromagnetic field would be the solution to an infinite set of 2D equations, or variational formulations, obtained by Fourier analysis.

Original language	English
Title of host publication	Applied Mathematical Sciences (Switzerland)
Publisher	Springer
Pages	347-392
Number of pages	46
DOIs	https://doi.org/10.1007/978-3-319-70842-3_9
State	Published - 2018
Externally published	Yes

Publication series

Name	Applied Mathematical Sciences (Switzerland)
Volume	198
ISSN (Print)	0066-5452
ISSN (Electronic)	2196-968X

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© Springer International Publishing AG, part of Springer Nature 2018.

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10.1007/978-3-319-70842-3_9

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Dimensionally reduced models: Derivation and analyses

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