Finite element solutions to 3D waveguide problems using the magnetic vector potential

The authors use a formulation based on the Lorentz gauge, which is extended to solve `high´ frequency cavity and waveguide problems. The magnetic vector potential is used throughout space, along with the electric scalar potential. However, the Lorentz gauge can be used to decouple these equations, leading to a more efficient solution algorithm. Since the equations are properly gauged, there are no `spurious´ modes arising (in particular in an eigenvalue solution to cavity problems). Unlike field variables (E or H) the magnetic vector potential is continuous between materials of differing permeability, permittivity and conductivity. It is therefore ideally suited to problems involving waveguide discontinuities and to waveguides with permeable and lossy dielectric loads