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Discretization of Maxwell’s Equations for Non-inertial Observers Using Space-Time Algebra

  • Mariusz Klimek
  • Stefan Kurz
  • Sebastian Schöps
  • Thomas Weiland
Article
  • 112 Downloads

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.

Keywords

Clifford’s geometric algebra Minkowski space-time Finite integration technique Whitney finite elements 

Mathematics Subject Classification

65M60 65M06 15A66 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Computational EngineeringTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Graduate School of Computational Engineering and Institut für Theorie Elektromagnetischer FelderTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Institut für Theorie Elektromagnetischer FelderTechnische Universität DarmstadtDarmstadtGermany

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