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.
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