Finite element time-domain body-of-revolution Maxwell solver based on discrete exterior calculus

Abstract

We present a finite-element time-domain (FETD) Maxwell solver for the analysis of body-of-revolution (BOR) geometries based on discrete exterior calculus (DEC) of differential forms and transformation optics (TO) concepts. We explore TO principles to map the original 3-D BOR problem to a 2-D one in the meridian ρz-plane based on a Cartesian coordinate system where the cylindrical metric is fully embedded into the constitutive properties of an effective inhomogeneous and anisotropic medium that fills the domain. The proposed solver uses a (TE φ , TM φ ) field decomposition and an appropriate set of DEC-based basis functions on an irregular grid discretizing the meridian plane. A symplectic time discretization based on a leap-frog scheme is applied to obtain the full-discrete marching-on-time algorithm. We validate the algorithm by comparing the numerical results against analytical solutions for resonant fields in cylindrical cavities and against pseudo-analytical solutions for fields radiated by cylindrically symmetric antennas in layered media. We also illustrate the application of the algorithm for a particlein-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.

Some Novel Full-Wave, Variational, and Perturbational Pseudo-Analytic Methods for Electromagnetic Propagation Modeling in Complex Geophysical Formations

“…As said before, due to the antenna geometry, only fields with azimuthal harmonic index n = 0 will be excited by the TX. Consider now that the formation 2 presents a non-symmetric invasion zone with a conductivity of σ = 0.5 S/m, extending over a cylindrical sector of 10-in in the radial direction and defined by the azimuthal angle α as depicted in We compare this case with the results presented in [21,63,64], and we have observed very good agreement. For α = 180 • , the problem is non-symmetrical, as presented in In order to obtain a deeper knowledge about the electric field behavior along the coil antennas (0 • < φ < 360 • ) and its relation with α, As said above, we use the azimuthal modes n = 0 and ±1, but it is worth noting that when the invasion is symmetric, we only need the harmonic n = 0 to calculate in a precise fashion the induced voltages at RX 1 and RX 2 .…”

“…The background medium has two vertical and three radial layers similar to that illustrated in Figure 4.10. This axis-symmetric configuration was considered before in [21,63,64] for modeling a LWD tool operating at 2 MHz. This tool consists of one TX and two RXs horizontal coil antennas.…”