On the FEM Modal Approach for a Reverberation Chamber Analysis

Abstract

We review the difficulties of a modal approach when modeling a Reverberation Chamber (RC) by the Finite Element Method (FEM). The numerical challenge is due to the large scale problem involved by the over-dimensioned cavity. Moreover, the field singularity on the stirrer has to be captured by the FEM. First the following issues are discussed: existence of nullfrequency solutions, convergence rate for h and p adaption, and formulation type in E or H field. Then the modal analysis is compared to the classical harmonic one. A focus is put on the field singularity at the source point.

Wave chaos techniques to analyze a modeled reverberation chamber

“…This proof is based on a plane-wave, integral representation of the fields that is justified in the semiclassic limit where the wavelength is small comparing to RC dimensions. Because they are highly resonant structures, RCs can also be studied using modal expansion [2][3][4]. We will illustrate that both approaches are closely related to the so-called trace formula first established in the context of quantum mechanics [5,Chapter 7].…”

“…We chose the Jacobi-Davidson algorithm implemented in the open source program Pysparse [4] for its capability to compute a large number of consecutive modes. To find N eigenvalues of this high dimensional problem whose dimension is equal to the number of degrees of freedom (#DoF), the method is based on a projection onto a subspace whose dimension increases iteratively up to 2N .…”

Field Measurements Within a Large Resonant Cavity Based on the Perturbation Theory

“…For the analytical expression, unit amplitude is chosen for the electric field. For the computation of the cavity eigenmodes using the Finite Element Method, a modal approach is adopted [28]. In contrary to the harmonic approach, the excitation antenna and the generator power are not taken into account, and the eigenmodes obtained are of unit electromagnetic energy W 0 ; a normalization of the electric field is thus necessary while comparing However, the experimental determination of the effective field amplitude is possible.…”

Numerical simulation of a Reverberation Chamber with a stochastic collocation method

“…(2) and Hill's results concerning |E 0 | [9], it can be established that the conductivity σ which varies with frequency, follows a χ 4 6 distribution and its probability density function (pdf), its mean and its standard deviation being given by…”

“…The stirrer, usually in the form of a paddle wheel, varies the chamber's boundary conditions to provide a statistically uniform environment. For optimisation or better understanding of the behaviour of a RC, numerical modelling by frequential [3,4] or temporal methods [5][6][7][8] is meeting growing interest. If one observes suitable comparisons between theory and experimentation, these results nevertheless are obtained at high computing costs.…”