Higher order hierarchical Legendre basis functions for electromagnetic modeling

This paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments (MoM). The basis is derived from orthogonal Legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most o...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2004-11, Vol.52 (11), p.2985-2995
Main Authors: Jorgensen, E., Volakis, J.L., Meincke, P., Breinbjerg, O.
Format: Article
Language:English
Subjects:
Acceleration
Antennas
Applied sciences
Basis functions
Continuity
Differential equations
Diffraction, scattering, reflection
Electromagnetic modeling
Exact sciences and technology
Hierarchical systems
high-order methods
Integral equations
Interpolation
Iterative methods
Mathematical analysis
Mathematical models
method of moments (MoM)
Moment methods
orthogonal functions
polynomial approximation
Polynomials
Radiocommunications
Radiowave propagation
Solvers
Studies
Telecommunications
Telecommunications and information theory
Wire
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:This paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments (MoM). The basis is derived from orthogonal Legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features. Expressions are presented for wire, surface, and volume elements but emphasis is given to the surface elements. In this case, the new hierarchical basis leads to a near-orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge. In addition, all higher order terms in the expansion have two vanishing moments. In contrast to existing formulations, these properties allow the use of very high-order basis functions without introducing ill-conditioning of the resulting MoM matrix. Numerical results confirm that the condition number of the MoM matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions. As a consequence of the excellent condition numbers, we demonstrate that even very high-order MoM systems, e.g., tenth order, can be solved efficiently with an iterative solver in relatively few iterations.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2004.835279