Abstract
We employ classical 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.
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Communicated by Bertfried Fauser
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Klimek, M., Kurz, S., Schöps, S. et al. Discretization of Maxwell’s Equations for Non-inertial Observers Using Space-Time Algebra. Adv. Appl. Clifford Algebras 28, 22 (2018). https://doi.org/10.1007/s00006-018-0841-3
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DOI: https://doi.org/10.1007/s00006-018-0841-3