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

Author

Xiao, S. ; Vahldieck, R.

Author_Institution

Lab. for Lightwave Electron., Microwave & Commun., Victoria Univ., BC, Canada

Volume

3

fYear

1994

fDate

20-24 June 1994

Firstpage

2104

Abstract

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.

Keywords

Helmholtz equations; antenna theory; boundary-value problems; circular waveguides; differential equations; eigenvalues and eigenfunctions; matrix algebra; microstrip antennas; waveguide theory; Helmholtz equation solution; angular space direction; circular waveguide structures; cylindrical coordinates; cylindrical patch antennas; differential equation; eigenvalue problems; method of lines algorithm; orthogonal transformation; radial direction; space variables; transformation matrix; z-direction; Boundary conditions; Differential equations; Eigenvalues and eigenfunctions; Electromagnetic waveguides; Laboratories; Microwave communication; Microwave theory and techniques; Patch antennas; Symmetric matrices; Transmission line matrix methods;

fLanguage

English

Publisher

ieee

Conference_Titel

Antennas and Propagation Society International Symposium, 1994. AP-S. Digest

Conference_Location

Seattle, WA, USA

Print_ISBN

0-7803-2009-3

Type

conf

DOI

10.1109/APS.1994.408070

Filename

408070