A method of lines solution of a cylindrical problem via radial discretization

Author

Nelatury, Sudarshan Rao ; Sadiku, Matthew N O

Author_Institution

Dept. of Electr. & Comput. Eng., Villanova Univ., PA, USA

fYear

2001

fDate

2001

Firstpage

169

Lastpage

173

Abstract

The method of lines (MOL) is applied to solve for the electrostatic potential in a coaxial trough by discretizing in both the longitudinal and radial directions. The coupled equations are diagonalized by eigendecomposition with the aid of MATLAB software. The results agree quite well. An attempt is made to do the same exercise in the case of a cylindrical region without the inner conductor. While it is straight forward when we discretize along the longitudinal dimension, it is difficult to do the same along the radial dimension. We give an approximation to the first two terms of the P matrix. In the analytical solution truncating the infinite summation gives rise to the Gibb´s phenomenon in the form of ripples at the discontinuities. A smoothing window gives a potential that is free of overshoots at the discontinuities

Keywords

coaxial cables; eigenvalues and eigenfunctions; electric potential; electrostatics; method of lines; Gibb´s phenomenon; MATLAB; MOL; P matrix; analytical solution; coaxial trough; coupled equations; cylindrical problem; cylindrical region; discontinuities; eigendecomposition; electrostatic potential; infinite summation; inner conductor; longitudinal direction; method of lines solution; radial direction; radial discretization; ripples; smoothing window; Coaxial components; Conductors; Electrostatics; Geometry; Laplace equations; Matrices; Matrix converters; Matrix decomposition; Partial differential equations; Transmission line matrix methods;

fLanguage

English

Publisher

ieee

Conference_Titel

SoutheastCon 2001. Proceedings. IEEE

Conference_Location

Clemson, SC

Print_ISBN

0-7803-6748-0

Type

conf

DOI

10.1109/SECON.2001.923109

Filename

923109