## 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 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 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.

Original language | English |
---|---|

Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 347-392 |

Number of pages | 46 |

DOIs | |

State | Published - 2018 |

Externally published | Yes |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
---|---|

Volume | 198 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Bibliographical note

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