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Method of moments and the use of multipole expansion

Andersson, Tommy LU (1991) In Journal Electromagnetic Waves and Applications 5(11). p.1237-1257
Abstract
In electromagnetic boundary value problems integral equations involving the free space Green function for the Helmholtz equation often occur. Using the method of moments to numerically solve such an equation a matrix equation is obtained. The entries of the matrix are given as multidimensional integrals which in general have to be calculated numerically. This paper presents an efficient method to approximate the main Part of these integrals. The free space Green function is expanded in scalar spherical wave functions. The translation properties of these wave functions then imply that the matrix elements can be expressed as a series of multipole moments. The method is illustrated by an implementation in the static case and the computation... (More)
In electromagnetic boundary value problems integral equations involving the free space Green function for the Helmholtz equation often occur. Using the method of moments to numerically solve such an equation a matrix equation is obtained. The entries of the matrix are given as multidimensional integrals which in general have to be calculated numerically. This paper presents an efficient method to approximate the main Part of these integrals. The free space Green function is expanded in scalar spherical wave functions. The translation properties of these wave functions then imply that the matrix elements can be expressed as a series of multipole moments. The method is illustrated by an implementation in the static case and the computation of the capacitance of a square plate. Basis functions with the correct edge and corner behaviour are used. The calculations of the multipole moments are done analytically. Numerical results using the point-matching and Galerkin's method are presented. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal Electromagnetic Waves and Applications
volume
5
issue
11
pages
1237 - 1257
publisher
VSP BV
external identifiers
  • scopus:84941532831
ISSN
1569-3937
DOI
10.1163/156939391X00815
language
English
LU publication?
yes
id
86ffaabf-3211-49f1-916c-f035a72ca6e1 (old id 144396)
date added to LUP
2007-06-27 09:54:48
date last changed
2017-10-01 03:48:59
@article{86ffaabf-3211-49f1-916c-f035a72ca6e1,
  abstract     = {In electromagnetic boundary value problems integral equations involving the free space Green function for the Helmholtz equation often occur. Using the method of moments to numerically solve such an equation a matrix equation is obtained. The entries of the matrix are given as multidimensional integrals which in general have to be calculated numerically. This paper presents an efficient method to approximate the main Part of these integrals. The free space Green function is expanded in scalar spherical wave functions. The translation properties of these wave functions then imply that the matrix elements can be expressed as a series of multipole moments. The method is illustrated by an implementation in the static case and the computation of the capacitance of a square plate. Basis functions with the correct edge and corner behaviour are used. The calculations of the multipole moments are done analytically. Numerical results using the point-matching and Galerkin's method are presented.},
  author       = {Andersson, Tommy},
  issn         = {1569-3937},
  language     = {eng},
  number       = {11},
  pages        = {1237--1257},
  publisher    = {VSP BV},
  series       = {Journal Electromagnetic Waves and Applications},
  title        = {Method of moments and the use of multipole expansion},
  url          = {http://dx.doi.org/10.1163/156939391X00815},
  volume       = {5},
  year         = {1991},
}