A Classical Field Theory Formulation for the Numerical Solution of Time Harmonic Electromagnetic Fields

Abstract

Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the "curl-curl" equation for the fields. We present a variational formulation based on classical field theory. Borrowing from QED, we modify the Lagrangian by adding an implicit gauge-fixing term. Our formulation, in the language of differential geometry, shows that conventional edge elements should be replaced by the simpler nodal elements for time-harmonic problems. We demonstrate how this formulation, adhering to the deeper underlying symmetries of the four-dimensional covariant field description, provides a highly general, robust numerical frame-