Electric and Magnetic Dual Meshes to Improve Moment Method Formulations
Keywords:
Electric and Magnetic Dual Meshes to Improve Moment Method FormulationsAbstract
A new Moment Method (MM) scheme to solve the Electric Field Integral Equation (EFIE) for some ill-conditioned problems is presented. The approach is an alternative to the Combined-Field Integral Equation (CFIE). The proposed formulation employs the Impedance Boundary Condition (IBC) to compute the scattering from conducting bodies uncoated or coated by dielectric materials. The scheme uses dual meshes to represent the currents: one mesh for the electric current and another mesh for the magnetic current. Each mesh is defined by a grid of quadrangles that can be conformed to arbitrarily curved surfaces. The quadrangle grids are interlocked; the corners of the quadrangles of one mesh are the centers of the quadrangles of the other mesh and vice versa. Several examples showing the potential of the approach to solve ill-conditioned problems are included.
Downloads
References
W. C. Chew, J. Jin, E. Michielssen, and J.
Song, Fast and Efficient Algorithms in
Computational Electromagnetics, Artech
House Inc. 2001.
J. R. Mautz and R. F. Harrington, “H-field, E-
field, and Combined-Field Solutions for
Conducting Bodies of Revolution,” AEU, vol
, pp. 157-164, 1978.
W. D. Wood Jr et al, “Convergence Properties
of the CFIE for several Conducting Scatterers,”
Proceedings of Applied Computational
Electromagnetics, Monterey, CA, pp 677-682,
March 2000.
R. A. Shore and A. D. Yaghjian, “Dual-Surface
electric Integral Equation,” Air Force
Research Laboratory Rep. AFRL-SN-HS-TR-
-013, 2001.
V. V. S. Prakash and R. Mittra, “Dual Surface
Combined Field Integral Equation for Three-
Dimensional Scattering,” Microwave and Opt.
Tech. letts., vol. 29, pp. 293-296, June 2001.
R. A. Shore and A. D. Yaghjian, “Dual-Surface
Integral Equation in Electromagnetic
Scattering,” IEEE Trans. Antennas and
Propag., vol. 53, pp. 1706-1709, May 2005.
J. M. Rius, E. Úbeda, and J. Parrón, “On The
Testing of the Magnetic Field Integral Equation
With RWG Basis Functions in Method of
Moments,” IEEE Trans. Antennas and
Propag., vol. 49, pp. 1550-1553, November
E. Ubeda and J. M. Rius, “Novel monopolar
MFIE MoM-discretization for the scattering
analysis of small objects,” IEEE Trans.
Antennas and Propag., vol. 54, pp. 50-57,
January 2005.
S. Lee and W. Gee, “How good is the
impedance boundary condition?,” IEEE Trans.
Antennas and Propag., vol. 35, pp. 1313- 1315,
November 1987.
T. B. A. Senior and J. L. Volakis,
“Approximate boundary conditions in
electromagnetics,” The Institution of Electrical
Engineers, 1995.
Y. Rahmat-Samii and D. J. Hoppe, “Impedance
Boundary Conditions in Electromagnetics,”
Hemisphere Pub., 1995.
O. Gutierrez, J. Bueno, I. Gonzalez, and F.
Catedra, “An Improvement of the Method of
Moments Combining EFIE and MFIE
Formulations for Coated Conducting Bodies,”
AP/S-URSI International Symposium,
Washington, July 2005.
A. W. Glisson and D. R. Wilton, “Simple and
Efficient Numerical Methods for Problems of
Electromagnetic Radiation and Scattering from
Surfaces,” IEEE Trans. Antennas and Propag.,
vol. 28, pp. 593-603, October 1997.
G. Farin, Curves and Surfaces for Computer
Aided Geometric Design: A practical Guide,
Academic Press.
L. Valle, F. Rivas, and M. F. Cátedra,
“Combining the Moment Method with
Geometrical Modelling by NURBS Surfaces
and Bezier Patches,” IEEE Trans. Antennas
and Propag., pp. 373-381, March 1994.
F. Rivas, L. Valle, and M. F. Cátedra, “A
moment method formulation for the analysis of
wire antennas attached to arbitrary conducting
bodies defined by parametric surfaces,” Journal
of Applied Computational Electromagnetics
Society Journal. pp. 32-39, July 1996.
M. F. Cátedra, F. Rivas, and L. Valle, “A
Moment Method Approach Using Frequency
Independent Parametric Meshes,” IEEE Trans.
Antennas and Propag., pp. 1567-1568, October
C. A. Klein and R. Mittra, “An Application of
the ‘Condition Number’ Concept to the
Solution of Scattering Problems in the Presence
of the Interior Resonances Frequencies,” IEEE
Trans. Antennas and Propag., vol. 23, pp.
-435, May 1975.
G. A. Deschamps and H. S. Cebayan, “Antenna
Synthesis and Solution of Inverse Problems by
Regularization Methods,” IEEE Trans.
Antennas and Propag., vol. 20, pp. 268-274,
May 1972.
M. H. Smith and A. F. Peterson, “Numerical
Solution of the CFIE Using Vector Bases and
Dual Interlocking Meshes,” IEEE Trans.
Antennas and Propag., vol. 53, pp. 3334-3339,
October 2005.
C. Balanis, Advanced Engineering
Electromagnetics, John Wiley&Sons, 1989,
New York.
G. L. G. Sleijpen and D. R. Fokkema,
“BICGSTAB(L) For Linear Equations
ACES JOURNAL, VOL. 22, NO. 3, NOVEMBER 2007
Involving Unsymmetric Matrices With
Complex Spectrum,” Electronic Transactions
On Numerical Analysis, vol. 1, pp. 11-32,
September 1993.
