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 \(\mathbb {R}^2\), with respect to a suitable system of coordinates (cylindrical, spherical, cartesian). Nevertheless, the electric and magnetic fields, and other vector quantities, still belong to \(\mathbb {R}^3\). 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.
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