Spectral Properties of the EFIE-MoM Matrix for Dense Meshes With Different Types of Bases

The relationship between the properties of the basis functions employed to discretize the electric field integral equation (EFIE) and the eigenvalue spectrum of the resulting method of moments (MoM) matrix is studied. We concentrate on dense meshes, i.e., on complex geometries with large number of u...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2007-11, Vol.55 (11), p.3229-3238
Main Authors: Vipiana, F., Pirinoli, P., Vecchi, G.
Format: Article
Language:English
Subjects:
Antennas
Applied sciences
Basis functions
Eigenvalues
Eigenvalues and eigenfunctions
Exact sciences and technology
Fourier analysis
Frequency
Geometry
Green's function methods
Green's functions
Integral equations
Magnetic fields
Mathematical models
method of moments (MoM)
Microwave antennas
Microwave circuits
Moment methods
multiresolution (MR) techniques
Packaging
Preconditioning
Radiocommunications
Spectra
spectral domain analysis
Studies
Telecommunications
Telecommunications and information theory
wavelets
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The relationship between the properties of the basis functions employed to discretize the electric field integral equation (EFIE) and the eigenvalue spectrum of the resulting method of moments (MoM) matrix is studied. We concentrate on dense meshes, i.e., on complex geometries with large number of unknowns per wavelength, and/or disparate mesh cells sizes, and/or low frequency. These are typical occurrences in antennas, packaging and microwave circuits. We show that if the basis functions have separated Fourier spectra, the diagonal MoM matrix entries are close to the eigenvalues, and explain it in terms of the Fourier spectrum of the Green's function. For such a basis, diagonal preconditioning drastically reduces the condition number. This does not happen with sub-domain basis functions like the Rao-Wilton-Glisson (RWG), or with their linear combination into loop-tree or loop-star bases that are employed to solve low-frequency problems. Finally we analyze the properties of a multiresolution (MR) basis formed by linear combinations of RWG, but whose functions possess some degree of (Fourier) spectral resolution. We show that there is still correspondence between matrix diagonal, Green's function (Fourier) spectrum, and matrix eigenvalues. Diagonal preconditioning of the MR-MoM matrix causes the eigenvalues to cluster around 1, as it happens with the MoM matrix for the magnetic field integral equation. This strongly impacts on the EFIE matrix condition number and the speed of convergence of iterative solvers.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2007.908827