Finite-difference solution of inhomogeneous modes using a fast direct solver routine

Author

Davies, J.B. ; Fernandez, F.A. ; Fang, Y.

Author_Institution

Dept. of Electron. & Electr. Eng., Univ. Coll., London, UK

Volume

27

Issue

5

fYear

1991

fDate

9/1/1991 12:00:00 AM

Firstpage

4028

Lastpage

4031

Abstract

A computer program, based on a fast direct solver, to solve for the dominant mode in a waveguide of arbitrary refractive index profile within a rectangular box is discussed. The two-dimensional field problem is reduced to a conventional eigenvalue problem in terms of the transverse magnetic field components. The two coupled scalar equations are solved using the FISHPAK software package, which solves a scalar Helmholtz problem using finite differences with an M by N mesh in time proportional to MNlog₂N. This fast solver is within two iteration loops. The outer is a Rayleigh quotient iteration, and the inner solves the two coupled equations. Results emerge typically in between 2 and 30 total calls of FISHPAK.

Keywords

difference equations; electrical engineering computing; iterative methods; software packages; waveguide theory; FISHPAK software package; Rayleigh quotient iteration; computer program; coupled scalar equations; dominant mode; eigenvalue problem; fast direct solver routine; finite difference solution; finite differences; inhomogeneous modes; rectangular box; refractive index profile; scalar Helmholtz problem; transverse magnetic field components; two-dimensional field problem; Difference equations; Differential equations; Eigenvalues and eigenfunctions; Finite difference methods; Magnetic fields; Maxwell equations; Partial differential equations; Permittivity; Rectangular waveguides; Software packages;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/20.104985

Filename

104985