  We employ Maxwell's equations formulated in Space-Time Algebra to perform
discretization of moving geometries directly in space-time. All the derivations
are carried out without any non-relativistic assumptions, thus the application
area of the scheme is not restricted to low velocities. The 4D mesh
construction is based on a 3D mesh stemming from a conventional 3D mesh
generator. The movement of the system is encoded in the 4D mesh geometry,
enabling an easy extension of well-known 3D approaches to the space-time
setting. As a research example, we study a manifestation of Sagnac's effect in
a rotating ring resonator. In case of constant rotation, the space-time
approach enhances the efficiency of the scheme, as the material matrices are
constant for every time step, without abandoning the relativistic framework.
