TY - CHAP

T1 - Dimensionally reduced models

T2 - Derivation and analyses

AU - Assous, Franck

AU - Ciarlet, Patrick

AU - Labrunie, Simon

N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85058244896&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-70842-3_9

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

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AN - SCOPUS:85058244896

T3 - Applied Mathematical Sciences (Switzerland)

SP - 347

EP - 392

BT - Applied Mathematical Sciences (Switzerland)

ER -