A Local Discontinuous Galerkin Method for Numerical Computation of Waveguide Eigenvalue Problems in Polar Coordinates

A numerical method for symmetric cylindrical and spherical waveguide eigenvalue problems is presented using local discontinuous Galerkin (LDG) method based on polar coordinates. The method has the merit of having high accuracy without geometrical triangulation errors on the curved boundaries of the solution domain. As an illustration, the formulation of the LDG schemes in both cylindrical polar coordinates and spherical polar coordinates are derived and several numerical examples are presented. Numerical results reported demonstrate that the proposed LDG method can be used readily to solve waveguide eigenvalue problems accurately.