Physics-Based Aggregate-Functions Approaches to Large Mom Problems
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Physics-Based Aggregate-Functions Approaches to Large Mom ProblemsAbstract
Aggregate functions approaches construct efficient MoM basis functions by suitably grouping standard (e.g. Rao-Wilton- Glisson) functions. The application domains, objectives and related means of achieving them can be significantly different. In this paper we review some recent advances in aggregatefunctions methods, putting them in a unifying perspective. We address matrix compression, multi-resolution sets, low- and high-frequency constructs. They can reduce the degrees of freedom of the problem so as to allow a direct, iteration-free solution, or can accelerate the convergence rate of iterative methods. We analyze compressive methods in more detail, providing general discussion and specific implementation examples.
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References
T. F. Eibert,“Iterative-solver convergence for loop
star and loop-tree decomposition in method of
moments solutions of the electricfield integral
equation”, IEEE Antennas Propagat. Mag., vol.
, no. 3, pp. 80, pp. 2509−2521, 2004.
S. Ooms and D. DeZutter, “A new iterative
diacoptics based multilevel moments method for
planar circuits”, IEEE Trans. Microw. Theory
Tech., vol. MTT-46, no. 3, pp. 280, pp.
−2521291, 1998.
J. Heinstad, “New approximation technique for
current distribution in microstrip array antennas”,
Electron. Lett ., vol. 29, no. 21, pp. 1809−1810,
E. Suter and J. Mosig, “A subdomain multilevel
approach for the MoM analysis of large planar
antennas”, Microw. Opt. Technol. Lett ., vol. 26,
no. 4, pp. 270−277, 2000.
V. V. S. Prakash and R. Mittra, “Characteristic
basis function method: a new technique for
efficient solution of method of moments matrix
equation”, Microw. Opt. Technol. Lett ., pp.
−100, 2003.
L. Matekovits, G. Vecchi, G. Dassano, and M.
Orefice, “Synthetic Function Analysis of Large
Printed Structures: the Solution Space Sampling
Approach”, Digest of 2001 IEEE AP-S Soc. Int’l
ACES JOURNAL, VOL. 24, NO. 2, APRIL 2009
Symp., pp. 568 −571, 8 −13, July 2001, Boston,
Massachusetts, USA.
L. Matekovits, V. A. Laza, and G. Vecchi,
“Analysis of Large Complex Structures with the
Synthetic Functions Approach”, IEEE Trans.
Antennas and Propagat., vol. 55, no. 9, pp.
−2521, 2007.
K. F. Sabet, J. C. Cheng, and L. P. B. Katehi,
“Efficient wavelet-based modelling of printed
circuit antenna arrays”, IEE Proc. Microwave
Antennas Propagat., vol. 146, no. 4, pp.
−304, 1999.
R. Loison, R. Gillard, J. Citerne, G. Piton and H.
Legay, “Optimised 2D multi-resolution method
of moment for printed antenna array modelling”,
IEE Proc. Microwave Antennas Propagat., vol.
, no. 1, pp. 1−8, 2001.
P. Pirinoli, G. Vecchi, and L. Matekovits,
“Multiresolution analysis of printed antennas and
circuits: a dual−isoscalar approach”, IEEE Trans.
Antennas Propagat., vol. 49, no. 6, pp. 858−874,
G. Schneider, G. Oberschmidt, and A. F. Jacob,
“Efficient Implementation of a Wavelet Based
Galerkin Scheme”, IEEE Trans. Antennas
Propagat., vol. 52, no. 9, pp. 2298−2304, 2004.
F. Vipiana, P. Pi rinoli, and G.Vecchi, “A
Multiresolution Method of Moments for
Triangular Meshes”, IEEE Trans. Antennas
Propagat., vol. 53, no. 7, pp. 2247−2258, 2005.
Z. Baharav, Y. Leviatan “Analysis Of Scattering
By Surfaces Using A Wavelet- Transformed
Triangular-Patch Model”, Microwave Opt. Tech.
Lett., vol. 21, no. 5, pp. 359−365, 1999.
W. C. Bandlow, G. Schneider, and A. F. Jacob,
“Vector-valued wavelets with triangular support
for method of moments applications”, IEEE
Trans. Antennas Propagat., vol. 53, no. 10, pp.
−3346, 2005.
F. Vipiana, G. Vecchi, and P. Pirinoli, “A Multi-
Resolution system of Rao-Wilton-Glisson
functions”, IEEE Trans. Antennas Propagat., vol.
, no. 3, pp. 924−930, 2007.
F. P. Andriulli, F.Vipiana, and G.Vecchi,
“Hierarchical bases for non-hierarchic 3D
triangular meshes”, IEEE Trans. Antennas
Propagat., vol. 56, no. 8, pp. 2288−2297, 2008.
F. Vipiana, P. Pirinoli, and G.Vecchi, “Spectral
properties of the EFIE-MoM matrix for dense
meshes with different types of bases”, IEEE
Trans. Antennas Propagat., vol. 55, no. 11, pp.
−3238, 2007.
C. Craeye, “A Fast Impedance and Pattern
Computation Scheme for Finite Antenna Arrays”,
IEEE Trans. Antennas Propagat., vol. 54, no. 10,
pp. 3030−3034, 2006.
P. De Vita, A. Freni, L.Matekovits, P. Pirinoli,
and G.Vecchi, “A combined AIM-SFX approach
for complex arrays”, Digest of 2007 IEEE APS
Soc. Int’l Symp., pp. 3452 −3455, Honolulu,
Hawaii, USA, 10−15 June 2007.
V. A. Laza, L. Matekovits, and G. Vecchi,
“Synthetic Function Expansion with multi-grid
approach”, Proceedings of The First European
Conference on Antennas and Propagation
(EuCAP 2006 ), ESA SP-626 CD Proceedings,
pp. 386.1, Nice, France, 6−10 November 2006.
F. C ́atedra, E. Garca, C. Delgado, F. S. de Adana,
and R. Mittra, “Development of an efficient
rigorous technique based on the combination of
CBFM and MLFMA to solve very large
electromagnetic problems”, Proc. Int’l Conf.
Electromagnetics in Ad vanced Applications,
Torino, Italy, Sep. 2007.
R. Maaskant, R. Mittra, and A. Tijhuis, “Fast
Solution of Multi-Scale Antenna Problems for
the Square Kilometre Array (SKA) Radio
Telescope using the Characteristic Basis Function
Method (CBFM) ”, Applied Computational
Electromagnetics Society Journal , vol. 24, no. 2,
O. M. Bucci, and G. Franceschetti, “On the
degrees of freedom of scattered fields”, IEEE
Trans. Antennas and Propagat., vol. 37, no. 7, pp.
−926, 1989.
F. Vico, G. Vecchi, M. Ferrando, ”A New
Sparsification And Compression Technique For
High Frequency Mom By Means Of Wavefront
Basis Functions”, Proceedings of The First
European Conference on Antennas and
Propagation EuCAP, 2007.
K. R. Aberegg and A. F. Peterson, “Application
of the Integral Equation-Asymptotic Phase
Method to two-dimensional scattering”, IEEE
Trans. Antennas Propagat., vol. 43, no. 5, pp.
−537, 1995.
D. Kwon, R. J. Burkholder, and P. H. Pathak,
“Efficient Method of Moments Formulation for
Large PEC Scattering Problems Using
Asymptotic Phasefront Extraction (APE)”, IEEE
Trans. Antennas Propagat., vol. 49, no. 4, pp.
−591, 2001.
S. N. Chandler-Wilder, S. Langdon, “A Galerking
Boundary Element Method for High Frequency
Scattering by Convex Polygons”, SIAM J.
Numer. Anal., vol. 45, no. 2, pp. 610−640, 2007.
K. Tap, R. J. Burkholder, P. H. Pathak, and M.
Albani, “Methods for Efficiently Computig the
MoM Impedance Matrix for APEx Type Basis
Functions”, IEEE AP-S Soc. Int’l Symp., pp.
−4122, Albuquerque, 2006.
MATEKOVITS, VECCHI, VICO: PHYSICS-BASED AGGREGATE-FUNCTION APPROACHES TO LARGE MOM PROBLEMS
R. J. Burkholder, and T. Lee, “Adaptive Sampling
for Fast Physical Optics Numerical Integration”,
IEEE Trans. Antennas and Propagat., vol. 53, no.
, pp. 1843−1845, 2005.
C. P. Davis and W. C. Chew, “Frequency-
Independent Scattering from a Flat Strip with
TEz -Polarize Fields”, IEEE Trans. Antennas
Propagat., vol. 56, no. 4, pp. 1008−1016, 2008.
S. Raffaelli, M. Johansson, and B. Johannisson,
“Cylindrical Array Antenna Demonstrator for
WCDMA Applications”, Proc. of ICEAA03,
Turin, Italy, 8−12 Sept. 2003.
G. Vecchi, P. Nepa, G. Manara, A. Serra, M.
Orefice, V. A. Laza, L. Matekovits, G. L.
Dassano, and V. Kysrytsya, “Wideband Stacked-
Patch Designs for Base Station Antenna”,
Wireless Reconfigurable Terminals and
Platforms (WiRTeP), pp. 241−245, Rome, Italy,
−12 April 2006.
G. Dassano, V. A. Laza, L. Matekovits, M.
Orefice, and G. Vecchi, “Numerical and
Experimental Characteri zation of a Wide- Band
Conformal Base Station Antenna”, Digest of
IEEE AP-S Soc. Int’l Symp., pp.3735−3738,
Albuquerque, New Mexico, 9−14 July 2006.


