2019/02/05 by Alysson Gold, Sami Tantawi, Gold, Alysson +1
Earth and Planetary Sciences · Engineering · Materials Science · #Computational Physics (physics.comp-ph) #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Geophysical and Geoelectrical Methods #Magnetic Properties and Applications
paper · pdf · doi:10.48550/arxiv.1902.01805
openalex publication_date 2019/02/05 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
Finite element representations of Maxwell's equations pose unusual challenges\ninherent to the variational representation of the `curl-curl' equation for the\nfields. We present a variational formulation based on classical field theory.\nBorrowing from QED, we modify the Lagrangian by adding an implicit gauge-fixing\nterm. Our formulation, in the language of differential geometry, shows that\nconventional edge elements should be replaced by the simpler nodal elements for\ntime-harmonic problems. We demonstrate how this formulation, adhering to the\ndeeper underlying symmetries of the four-dimensional covariant field\ndescription, provides a highly general, robust numerical framework.\n