Abstract
In this chapter, we present a technique for efficient derivation of the Method of Moments (MoM) matrix elements arising in radiation and scattering problems. The proposed method is designed to overcome some of the limits of the conventional MoM formulation, and it aims to provide a robust as well as efficient MoM-based approach. The chapter will begin by introducing a formulation based on the use of Dipole Moment (DM)-type of basis functions, and goes on to present the closed-form expressions for the fields radiated by the employed basis functions.
The main body of the chapter is dedicated to the introduction of an extension of the DM approach, based on the use of sinusoidal rooftop basis functions. A unique attribute of the formulation is that the fields of the DM-type basis functions representing the induced current can be generated directly, without having to go through the derivation of the vector and scalar potentials that are typically employed in the conventional MoM formulation. This particular feature eliminates the need to scale the potentials, and this, in turn, eliminates the low-frequency breakdown problem, which arises when discretizing the EFIE with the MoM. As a result, it is possible to use a uniform formulation over a much wider frequency range without having to resort to special basis functions, e.g., the loop-stars. Furthermore, the direct expression of the fields generated by the basis functions bypasses the conventional integration over the source bases rendering the process of filling the impedance matrix more efficient. Solution of both the Surface Integral Equation (SIE) and Volume Integral Equation (VIE) formulations are presented, and the problem of computing both the induced current distribution, and the fields scattered by conducting as well as dielectric structures, are detailed.
Some numerical examples, which demonstrate the seamless applicability of the method, even as we go to very low frequencies, are presented, and the numerical efficiency of the proposed technique is compared to that of the conventional MoM formulation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Harrington RF (1993) Field computation by moment methods. Oxford University Press, USA
Peterson AF, Ray SL, Mittra R (1998) Computational methods for electromagnetics. Wiley, NJ, USA
Rao SM, Wilton DR, Glisson AW (1982) Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans Antenn Propag 30(3):409–418
Zhao JS, Chew WC (2000) Integral equation solution of Maxwell’s equations from zero frequency to microwave frequencies. IEEE Trans Antenn Propag 48(10):1635–1645
Wilton DR, Glisson AW (1981) On improving the electric field integral equation at low frequencies. In: Proceedings of URSI radio science meeting digest, Los Angeles, June 1981, p 24
Mautz JR, Harrington RF (1984) An E-field solution for a conducting surface small or comparable to the wavelength. IEEE Trans Antenn Propag 32(4):330–339
Graglia RD (1993) On the numerical integration of the linear shape functions times the 3-D Green’s function or its gradient on a plane triangle. IEEE Trans Antenn Propag 41(10):1448–1455
Qian ZG, Chew WC (2008) A quantitative study on the low frequency breakdown of EFIE. Microwave Opt Tech Lett 50(5):1159–1162
Richmond JH (1966) A wire-grid model for scattering by conducting bodies. IEEE Trans Antenn Propag 14(6):782–786
Jordan EC, Balmain KG (1968) Electromagnetic waves and radiating systems. 2nd ed., Prentice-Hall, Englewood Cliffs, N.J
Richmond JH (1974) Computer program for thin-wire structures in a homogeneous conducting medium. Report NASA CR-2399
Richmond JH (1974) Radiation and scattering by thin-wire structures in a homogeneous conducting medium. IEEE Trans Antenn Propag 22(2):365
Wang NN, Richmond JH, Gilreath MC (1975) Sinusoidal reaction formulation for radiation and scattering from conducting surfaces. IEEE Trans Antenn Propag 23(3):376–382
Kwon SJ, Mittra R (2009) Impedance matrix generation by using the fast matrix generation technique. Microw Opt Technol Lett 51(1):204–213
Liu X, Cai W, Guo H, Yin H (2005) The application of the equivalent dipole-moment method to electromagnetic scattering of 3D objects. In: APMC Proceedings, Asia-Pacific, 2005
Pelletti C, Bianconi G, Mittra R, Monorchio A, Panayappan K (2012) Numerically efficient method of moments formulation valid over a wide frequency band including very low frequencies. IET Microw Antenn Propag 6(1):46–51
Leviatan Y, Boag A (1988) Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies-theory and numerical solution. IEEE Trans Antenn Propag 36(12):1722–1734
Harrington R (2001) Time-harmonic electromagnetic fields. IEEE Press, New Jersey
Lucente E, Monorchio A, Mittra R (2008) An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems. IEEE Trans Antenn Propag 56:999–1007
Chiang IT, Chew WC (2006) Thin dielectric sheet simulation by surface integral equation using modified RWG and pulse basis. IEEE Trans Antenn Propag 54(7):1927–1934
Naeem M (2011) Scattering and absorption analysis of radomes using the method of equivalent dipole moments. Ph.D. Thesis, Chalmers University of Technology, Gothenburg
Pelletti C, Mittra R, Bianconi G (2012) A macro basis-function-based technique for the analysis of thin penetrable scatterers over a wide frequency band. USNC/URSI, Chicago, July 2012
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Panayappan, K., Pelletti, C., Mittra, R. (2014). An Efficient Dipole-Moment-Based Method of Moments (MoM) Formulation. In: Mittra, R. (eds) Computational Electromagnetics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4382-7_6
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4382-7_6
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4381-0
Online ISBN: 978-1-4614-4382-7
eBook Packages: EngineeringEngineering (R0)