A Redundant Loop Basis for Closed Structures with Application to MR Basis
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A Redundant Loop Basis for Closed Structures with Application to MR BasisAbstract
A redundant loop basis is proposed and applied as the solenoidal part of the recently developed multiresolution (MR) basis for closed surfaces at low frequencies. By keeping all loop basis functions, the “symmetry” of the MR solenoidal basis can be maintained for closed surfaces. As a consequence, the convergence of iterative solvers for the expanded MR basis can be effectively improved by using the redundant loop basis without disturbing the accuracy of results. Since the expanded MR basis functions are linear combinations of standard Rao-Wilton-Glisson (RWG) functions, it can be applied to the existing MoM codes easily. The positive behavior of redundant loop basis on MR basis for closed surfaces is analyzed and discussed in detail in this paper. Numerical results demonstrate that the expanded MR basis performs better than the original MR basis and has significant advantages over the traditional loop-tree basis for 3D electromagnetic scattering of closed structures in the low frequency range.
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References
R. F. Harrington, Field Computations by
Moment Methods, MacMillan, New York,
S. Rao, D. Wilton, and A. Glisson,
“Electromagnetic Scattering by Surfaces of
Arbitrary Shape,” IEEE Trans. Antennas
Propagat., vol. 30, pp. 409–418, May 1982.
D. R. Wilton and A. W. Glisson, “On
Improving the Electric Field Integral Equation
at Low Frequencies,” in Proc. URSI Radio
Science Meeting Dig., Los Angeles, CA, p. 24,
June 1981.
J. Mautz and R. F. Hanington, “An E-Field
Solution for a Conducting Surface Small or
Comparable to the Wavelength,” IEEE Trans.
Antennas Propagat., vol. AP-32, no. 4, pp.
-339, April 1984.
M. Burton and S. Kashyap, “A Study of a
Recent Moment-Method Algorithm that is
Accurate to Very Low Frequencies,” Applied
Computational Electromagnetic Society
(ACES) Journal, vol. 10, no. 3, pp. 58–68,
Nov. 1995.
W. L. Wu, A. Glisson, and D. Kajfez, “A
Study of Two Numerical Solution Procedures
for the Electric Field Integral Equation at Low
Frequency,” Applied Computational
Electromagnetic Society (ACES) Journal, vol.
, no. 3, pp. 69–80, Nov. 1995.
G. Vecchi, “Loop-Star Decomposition of
Basis Functions in the Discretization of the
EFIE,” IEEE Trans. Antennas Propagat., vol.
, no. 2, pp. 339–346, Feb. 1999.
J. S. Zhao and W. C. Chew, “Integral Equation
Solution of Maxwell’s Equations from Zero
Frequency to Microwave Frequency,” IEEE
Trans. Antennas Propagat., vol. 48, pp. 1635–
, Oct. 2000.
J. F. Lee, R. Lee, and R. J. Burkholder, “Loop
Star Basis Functions and a Robust
Precodnitioner for EFIE Scattering Problems,”
IEEE Trans. Antennas Propagat., vol. 51, pp.
–1863, Aug. 2003.
T. F. Eibert, “Iterative-Solver Convergence for
Loop-Star and Loop-Tree Decomposition in
Method-of-Moments Solutions of the Electric-
Field Integral Equation,” IEEE Antennas
Propag. Mag., vol. 46, pp. 80–85, Jun. 2004.
F. P. Andriulli, F. Vipiana, and G. Vecchi,
“Enhanced Multiresolution Basis for the MoM
Analysis of 3D Structures,” in Proc. IEEE Int.
Symp. Antennas Propagat., pp. 5612–5615,
Honolulu, HI, Jun. 2007.
F. P. Andriulli, F. Vipiana, and G. Vecchi,
“Hierarchical Bases for Non-Hierarchic 3-D
Triangular Meshes,” IEEE Trans. Antennas
Propagat., vol. 56, pp. 2288–2297, Aug. 2008.
F. V ipiana, F. P. Andriulli, and G. Vecchi,
“Two-Tier Non-Simplex Grid Hierarchic
Basis for General 3D Meshes,” Waves in
Random and Complex Media, vol. 19, no. 1,
pp. 126–146, Feb. 2009.
F. Vipiana, and G. Vecchi, “A Novel,
Symmetrical Solenoidal Basis for the MoM
ACES JOURNAL, VOL. 26, NO. 3, MARCH 2011
Analysis of Closed Surfaces,” IEEE Trans.
Antennas Propagat., vol. 57, no. 4, pp. 1294-
, April 2009.
J. J. Ding, R. S. Chen, J. Zhu, Z. H. Fan, and
D. Z. Ding, “A Multiresolution Basis for
Analysis of Scattering Problems,” in 2010
International Conference on Microwave and
Millimeter Wave Technology, Chengdu, pp.
-609, May 2010.
J. J. Ding, J. Zhu, R. S. Chen, Z. H. Fan, and
K. W. Leung, “An Alternative Multiresolution
Basis in EFIE for Analysis of Low-Frequency
Problems,” Applied Computational
Electromagnetic Society (ACES) Journal, vol.
, no. 1, pp. 26-36, Jan. 2011.
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.
, no. 11, pp. 3229–3238, Nov. 2007.
M. K. Li and W. C. Chew, “Applying
Divergence-Free Condition in Solving the
Volume Integral Equation,” Progress In
Electromagnetics Research, PIER 57, pp. 311-
, 2006.
I. C. F. Ipsen and C. D. Meyer, “The Idea
Behind Krylov Methods,” Amer. Math.
Monthly, vol. 105, no. 10, pp. 889–899, Dec.
