Finite Element Time-Domain Body-of-Revolution Maxwell Solver based on Discrete Exterior Calculus
This work provides a novel computational method for efficiently simulating electromagnetic problems with cylindrical symmetry, relevant to antenna design and high-power microwave devices.
The authors developed a finite-element time-domain Maxwell solver for body-of-revolution geometries using discrete exterior calculus and transformation optics, validated against analytical solutions for cylindrical cavities and antennas, and demonstrated in a particle-in-cell simulation of a backward-wave oscillator.
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 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/TM 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 particle-in-cell (PIC) simulation of beam-wave interactions inside a high-power backward-wave oscillator.