Nodal-based finite-element modeling of Maxwell's equations

Weak forms are derived for Maxwell's equations which are suitable for implementation on conventional C⁰ elements with scalar bases. The governing equations are expressed in terms of general vector and scalar potentials for the electric field intensity vector. Gauge theory is invoked to close the system and dictates the continuity requirements for the potentials at material interfaces as well as the blend of boundary conditions at exterior boundaries. Two specific gauges are presented, both of which lead to Helmholtz weak forms which are parasite-free and enjoy simple, physically meaningful boundary conditions. A general and numerically efficient procedure for enforcing the jump discontinuities on the normal components of vector fields at dielectric interfaces and boundary conditions on curved surfaces is also given