# A Space-Time Approach for the Time-Domain Simulation in a Rotating Reference Frame

## TL;DR

This paper develops a space-time discretisation method for Maxwell's equations in rotating frames, enabling accurate simulation of phenomena like the Sagnac effect, and compares the stability of FIT and FEM approaches.

## Contribution

It introduces a direct space-time discretisation approach for Maxwell's equations in rotating frames, with a focus on stability and convergence analysis of FIT and FEM methods.

## Key findings

- The scheme accurately models the Sagnac effect in a rotating resonator.
- Comparison shows differences in stability between FIT and FEM approaches.
- The method avoids non-relativistic assumptions in simulations.

## Abstract

We approach the discretisation of Maxwell's equations directly in space-time without making any non-relativistic assumptions with the particular focus on simulations in rotating reference frames. As a research example we study Sagnac's effect in a rotating ring resonator. After the discretisation, we express the numerical scheme in a form resembling 3D FIT with leapfrog. We compare the stability and convergence properties of two 4D approaches, namely FIT and FEM, both using Whitney interpolation.