3.2018 - Numerical simulation of the 3D Faraday cage effect
Master Thesis proposal
A faraday cage is a an open structure made of a regular mesh of thin wires (see Figure 1) that blocks the electromagnetic waves: as a result, any object located into the cage is protected from the electromagnetic waves. This phenomenon has been observed by M. Faraday in 1836.
Figure 1: the Faraday cage in the Palais de la découverte, Paris (Picture from wikipedia)
Mathematically, this phenomenon has been explained in [1]-[2] using techniques of asymptotic anal-ysis (assuming for instance that the number of wires goes to infinity) in simplified two dimensional configurations. For the full-three dimensional problem (which requires to solve the time-harmonic Maxwell equations), we recently proved that the asymptotic behaviour of the faraday cage strongly depends on the structure of the cage. In a nutshell, if the cage consists of small disconnected equi-spaced obstacles, it does not block the electromagnetic fields while if it is made of a set of equi-spaced parallel wires, it blocks only one component of the electromagnetic fields. Finally, if it is made of a mesh of wires (as in Figure 1), then the electromagnetic waves are blocked and the Faraday Cage effet holds.
The objective of this Master Thesis is to illustrate the previous results by doing numerical simulations in parallel using the finite element software Freefem++ [3] associated with the domain decomposition librairy hpddm. A particular interest in parallel computing and numerical analysis is required. In a second part, which can be more theoretically oriented, the student shall develop homogenized models
in order to simulate more efficiently the phenomenon. Depending on the interest of the student, this internship might lead to a PhD thesis.
References
[1] Rauch, Jeffrey and Taylor Michael. Potential and scattering Theory on Widly Perturbed Domains, Journal of Functional Analysis, 18, 27-59 (1975)
[2] D. P. Hewett, I. J. Hewitt, Homogenized boundary conditions and resonance effects in Faraday cages, Proc. Roy. Soc. A, 472, 2189, 2016
- [3] Hecht, F. New development in FreeFem++. J. Numer. Math. 20 (2012), no. 3-4, 251265. 65Y15
