Solution of the Helmholtz equation with the method of lines in cylindrical coordinates

This paper presents a method of lines algorithm to solve Helmholtz equations in cylindrical coordinates. Discretizing the angular space direction, only two space variables remain, the radial and the z-direction. For eigenvalue problems the Helmholtz equation becomes an ordinary differential equation which can be solved analytically in radial direction after an orthogonal transformation. An analytical form of the transformation matrix is derived. The method is then used for the analysis of a class of circular waveguide structures and cylindrical patch antennas.