Finite Element Time-Domain Body-of-Revolution Maxwell Solver based on Discrete Exterior Calculus

TL;DR

This paper introduces a finite-element time-domain Maxwell solver for body-of-revolution geometries using discrete exterior calculus and transformation optics, enabling efficient analysis of cylindrical structures with complex media.

Contribution

It develops a novel FETD Maxwell solver based on DEC and TO principles, transforming 3D BOR problems into 2D, with validation against analytical solutions and application to PIC simulations.

Findings

Accurately models resonant fields in cylindrical cavities.

Effectively simulates fields radiated by cylindrically symmetric antennas.

Demonstrates applicability to high-power beam-wave interaction simulations.

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 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.