Dimensionally reduced models: Derivation and analyses

Franck Assous, Patrick Ciarlet, Simon Labrunie

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


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 languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages46
StatePublished - 2018

Publication series

NameApplied Mathematical Sciences (Switzerland)
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X


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