Fast Iterative Solution of Integral Equations With Method of Moments and Matrix Decomposition Algorithm - Singular Value Decomposition

The multilevel matrix decomposition algorithm (MLMDA) was originally developed by Michielsen and Boag for 2D TMz scattering problems and later implemented in 3D by Rius et al. The 3D MLMDA was particularly efficient and accurate for piece-wise planar objects such as printed antennas. However, for ar...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2008-08, Vol.56 (8), p.2314-2324
Main Authors: Rius, J.M., Parron, J., Heldring, A., Tamayo, J.M., Ubeda, E.
Format: Article
Language:English
Subjects:
Algorithms
Approximation algorithms
Compressing
Computation
Decomposition
Errors
Fast integral equation methods
Integral equations
Iterative algorithms
Iterative methods
Mathematical analysis
Matrix decomposition
method of moments (MoM)
MLFMA
Moment methods
multilayer Green's function
Printed antennas
Scattering
Singular value decomposition
Studies
Three dimensional
Transmission line matrix methods
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Summary:The multilevel matrix decomposition algorithm (MLMDA) was originally developed by Michielsen and Boag for 2D TMz scattering problems and later implemented in 3D by Rius et al. The 3D MLMDA was particularly efficient and accurate for piece-wise planar objects such as printed antennas. However, for arbitrary 3D problems it was not as efficient as the multilevel fast multipole algorithm (MLFMA) and the matrix compression error was too large for practical applications. This paper will introduce some improvements in 3D MLMDA, like new placement of equivalent functions and SVD postcompression. The first is crucial to have a matrix compression error that converges to zero as the compressed matrix size increases. As a result, the new MDA-SVD algorithm is comparable with the MLFMA and the adaptive cross approximation (ACA) in terms of computation time and memory requirements. Remarkably, in high-accuracy computations the MDA-SVD approach obtains a matrix compression error one order of magnitude smaller than ACA or MLFMA in less computation time. Like the ACA, the MDA-SVD algorithm can be implemented on top of an existing MoM code with most commonly used Green's functions, but the MDA-SVD is much more efficient in the analysis of planar or piece-wise planar objects, like printed antennas.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2008.926762