Finite element scheme for 3D cavities without spurious modes

A numerically efficient finite-element formulation is presented for the analysis of inhomogeneously loaded three-dimensional cavities of arbitrary shape. The electromagnetic field is described either by the three components of a magnetic vector potential and by an electric scalar potential, or by the three components of an electric vector potential and by a magnetic scalar potential. The uniqueness of the potentials is ensured by the incorporation of the Coulomb gauge and by proper boundary conditions. Owing to the correct description of the electromagnetic field, no spurious modes appear. The Galerkin equations are formulated for the finite element method leading to a generalized eigenvalue problem with symmetric, sparse matrices. This is solved by means of the bisection method with the sparsity of the matrices fully utilized. Several 3-D cavity problems are solved to illustrate the method.