Efficient use of symmetry for finite element analysis of eigenvalue problems

Eigenvalue problems have an infinite spectrum of modal solutions with varying symmetry properties. Confusion often arises, especially for structures with a high degree of symmetry, as to the mesh size and boundary conditions required to solve the geometry most effectively. A systematic procedure for the use of symmetry in conjunction with the finite element method is described. Symmetry analysis allows the azimuthal symmetry of the modes, and their degeneracies to be predicted using representation theory of groups. The mesh size, boundary conditions and number of solutions required to calculate all the modes in the waveguide using finite element analysis can then be determined. The procedure is illustrated with some simple examples