A multiresolution method of moments for triangular meshes

This paper presents the construction, use, and properties of a multiresolution (wavelet) basis for the method of moments (MoM) analysis of metal antennas, scatterers, and microwave circuits discretized by triangular meshes. Several application examples show fast convergence of iterative solvers and...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2005-07, Vol.53 (7), p.2247-2258
Main Authors: Vipiana, F., Pirinoli, P., Vecchi, G.
Format: Article
Language:English
Subjects:
Antennas
Applied sciences
Byproducts
Construction
Convergence
Discrete wavelet transforms
Electric, optical and optoelectronic circuits
Electromagnetic scattering
Electronics
Exact sciences and technology
Mathematical analysis
Method of moments
method of moments (MoM)
Microwave antennas
Microwave circuits
Microwave theory and techniques
Moment methods
multilayer printed devices
multiresolution (MR)
numerical methods
Solvers
Sparse matrices
Theoretical study. Circuits analysis and design
Transmission line matrix methods
Vectors
Wavelet
Wavelet analysis
wavelets
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Summary:This paper presents the construction, use, and properties of a multiresolution (wavelet) basis for the method of moments (MoM) analysis of metal antennas, scatterers, and microwave circuits discretized by triangular meshes. Several application examples show fast convergence of iterative solvers and accurate solutions with highly sparse MoM matrices. The proposed basis is organized in hierarchical levels, and keeps the different scales of the problem directly into the basis functions representation; the current is divided into a solenoidal and a quasi-irrotational part, which allows mapping these two vector parts onto fully scalar quantities, where the wavelets are defined. As a byproduct, this paper also presents a way to construct hierarchical sets of Rao-Wilton-Glisson (RWG) functions on a family of meshes obtained by subsequent refinement, i.e., with the RWG of coarser meshes expressed as linear combinations of those of finer meshes.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2005.850710