On the solution of waveguide boundary value problems in the absence of the Lorentz calibration

The spectral method for the solution of boundary value electrodynamic problems without the use of the Lorentz calibration is proposed. The method involves autonomous decompositions of the electromagnetic field components, and the Galerkin procedure is applied directly to the Maxwell equations. The efficiency of the method is demonstrated for the example of a rectangular waveguide that is inhomogeneously filled.