An Alternative Multiresolution Basis in EFIE for Analysis of Low-Frequency Problems
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An Alternative Multiresolution Basis in EFIE for Analysis of Low-Frequency ProblemsAbstract
An alternative multiresolution (MR) basis is presented for the method-of-moments (MoM) solution of the electric-field integral equation (EFIE) for the analysis of low-frequency problems. The proposed MR basis functions can be treated as an extension of the traditional looptree basis function to hierarchical functions. Similar to the loop-tree basis, the MR basis functions are linear combinations of standard Rao- Wilton-Glisson (RWG) functions. Therefore, the MR algorithm can be easily applied to MoM codes with RWG basis. Since the MR basis is immune from the so-called low-frequency breakdown, the MR basis is especially suitable for the analysis of low-frequency problems. Compared with the previous MR basis, the present MR basis is easier to construct and comprehend, and the basischanging matrix is sparser. Physical interpretation and comparison are given for the previous and present MR bases. Numerical results demonstrate that both the previous and present MR bases are efficient for 3D electromagnetic scattering problems at low frequencies.
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References
R. F. Harrington, Field Computations by
Moment Methods, MacMillan, New York,
S. M. Rao, D. R. Wilton, and A. W. Glisson,
‘‘Electromagnetic Scattering by Surfaces of
Arbitrary Shape,’’ IEEE Trans. Antennas
Propagat., vol. AP-30, pp. 409-418, May
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. Harrington, “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, A. Tabacco, and G. Vecchi,
“Solving the EFIE at Low Frequencies with a
Conditioning that Grows Only
Logarithmically with the Number of
Unknowns,” IEEE Trans. Antennas Propagat.,
vol. 58, no. 5, pp. 1614-1624, May 2010.
F. Vipiana, P. Pirinoli, and G. Vecchi, “A
Multiresolution Method of Moments for
Triangular Meshes,” IEEE Trans. Antennas
Propag., vol. 53, no. 7, pp. 2247-2258, Jul.
F. Vipiana, G. Vecchi, and P. Pirinoli. “A
Multiresolution System of Rao–Wilton–
Glisson Functions,” IEEE Trans. Antennas
Propagat., vol. 55, no. 3, pp. 924-930, Mar.
F. Andriulli, A. Tabacco, and G. Vecchi, “A
Multiresolution Approach to the Electric Field
Integral Equation in Antenna Problems,”
SIAM J. Sci. Comput., vol. 29, pp. 1-21, Jan.
R. S. Chen, J. J. Ding, D. Z. Ding, Z. H. Fan,
and D. X. Wang, “A Multiresolution
Curvilinear Rao-Wilton-Glisson Basis
Function for Fast Analysis of Electromagnetic
Scattering,” IEEE Trans. Antennas Propagat.,
vol. 57, no. 10, pp. 3179-3188, Oct., 2009.
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., Honolulu, HI, Jun.
, pp. 5612-5615.
DING, ZHU, CHEN, FAN, LEUNG: AN ALTERNATIVE MULTIRESOLUTION BASIS IN EFIE FOR LOW-FREQUENCY PROBLEMS
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. Vipiana, 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,
Feb. 2009, pp.126-146.
F. Vipiana, and G. Vecchi, “A Novel,
Symmetrical Solenoidal Basis for the MoM
Analysis of Closed Surfaces,” IEEE Trans.
Antennas Propagat., vol. 57, no. 4, pp. 1294-
, April 2009.
F. Vipiana, P. Pirinoli, and G. Vecchi,
“Regularization Effect of a Mutiresolution
Basis on the EFIE-MoM Matrix,” IEEE
Antennas and Propagation Society Int. Symp.
Digest, Washington, DC, Jul. 2005, vol. 3b,
pp. 192-195.
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.
J. J. Ding, J. Zhu, D. Z. Ding, and R. S. Chen,
“Application of Perturbed Multiresolution
Preconditioner Technique Combined with
MLFMA for Scattering Problem,” in Proc. Int.
Conf. on Microwave and Millimeter Wave
Technology, pp. 978-981, Apr. 2008.
H. Chen, D. Z. Ding, R. S. Chen, D. X. Wang,
and E. K. Yung, “Application of
Multiresolution Preconditioner Technique for
Scattering Problem in a Half Space,” in Proc.
Int. Conf. on Microwave and Millimeter Wave
Technology, pp. 975-977, Apr. 2008.
Y. Q. Hu, J. J. Ding, D. Z. Ding, and R. S.
Chen, “Analysis of Electromagnetic Scattering
from Dielectric Objects above a Lossy Half-
Space by Multiresolution Preconditioned
Multilevel Fast Multipole Algorithm,” IET
Microw. Antennas Propag., vol. 4, iss. 2, pp.
-239, Feb., 2010.
M. M. Li, J. J. Ding, D. Z. Ding, Z. H. Fan,
and R. S. Chen, “Multiresolution
Preconditioned Multilevel UV Method for
Analysis of Planar Layered Finite Frequency
Selective Surface,” Microwave and Optical
Technology Letters, vol. 52, no. 7, pp. 1530-
, July 2010.
F. Vipiana, M. A. Francavilla, and G. Vecchi,
“A Multi-Resolution Stabilization of the
Incomplete LU Preconditioner,” in Antennas
and Propagation Society International
Symposium, Charleston, SC, June 2009, pp. 1-
F. Vipiana, M. A. Francavilla, and G. Vecchi,
“EFIE Modeling of High-Definition
Multiscale Structures,” IEEE Trans. Antennas
Propagat., vol. 58, no. 7, pp. 2362-2374, July
F. Vipiana, G. Vecchi, and D. R. Wilton,
“Automatic Loop-Tree Scheme for Arbitrary
Conducting Wire-Surface Structures,” IEEE
Trans. Antennas Propagat., vol. 57, no. 11,
pp. 3564-3574, Nov. 2009.


