The method of moments in electromagnetics

The Method of Moments in Electromagnetics

Volumn , Issue , 2007, Pages 1-273

  Gibson, Walton C ^a,b  

^a Tripoint Industries Inc   (United States)

^b NONE   (United States)

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[No Author keywords available]

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EID: 85056951655     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (125)

1. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method. Artech House, 3rd ed., 2005.
2. K. Kunz and R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. CRC Press, 1993.
3. J. Jin, The Finite Element Method in Electromagnetics. John Wiley and Sons, 1993.
4. J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics. IEEE Press, 1998.
5. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Amer., vol. 52, 116–130, February 1962.
6. R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for and edge in a perfectly conducting surface,” Proc. IEEE, vol. 62, 1448–1461, November 1974.
7. C. A. Balanis, Advanced Engineering Electromagnetics. John Wiley and Sons, 1989.
8. P. Ufimtsev, “Approximate computation of the diffraction of plane electromagnetic waves at certain metal bodies (i and ii),” Sov. Phys. Tech., vol. 27, 1708–1718, August 1957.
9. A. Michaeli, “Equivalent edge currents for arbitrary aspects of observation,” IEEE Trans. Antennas Propagat., vol. 23, 252–258, March 1984.
10. S. L. H. Ling and R. Chou, “Shooting and bouncing rays: Calculating the RCS of an arbitrarily shaped cavity,” IEEE Trans. Antennas Propagat., vol. 37, 194–205, February 1989.
11. S. L. H. Ling and R. Chou, “High-frequency RCS of open cavities with rectangular and circular cross sections,” IEEE Trans. Antennas Propagat., vol. 37, 648–652, May 1989.
12. C. A. Balanis, Advanced Engineering Electromagnetics. John Wiley and Sons, 1989.
13. W. C. Chew, Waves and Fields In Inhomogeneous Media. IEEE Press, 1995.
14. P. M. Morse and H. Feshbach, Methods of Theoretical Physics. McGraw-Hill, 1953.
15. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. National Bureau of Standards, 1966.
16. K. M. Mitzner, “Incremental length diffraction coefficients,” Tech. Rep. AFAL-TR-73-296, Northrop Corporation, Aircraft Division, April 1974.
17. A. Michaeli, “Equivalent edge currents for arbitrary aspects of observation,” IEEE Trans. Antennas Propagat., vol. 32, 252–257, March 1984.
18. N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics. Artech House, 1990.
19. J. M. Rius, E. Úbeda, and J. Parrón, “On the testing of the magnetic field integral equation with RWG basis functions in the method of moments,” IEEE Trans. Antennas Propagat., vol. 49, 1550–1553, November 2001.
20. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics. IEEE Press, 1998.
21. R. A. Shore and A. D. Yaghjian, “Dual-surface integral equations in electromagnetic scattering,” IEEE Trans. Antennas Propagat., vol. 53, 1706–1709, May 2005.
22. W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, 2001.
23. H. Dwight, Tables of Integrals and Other Mathematical Data. The Macmillan Company, 1961.
24. The Integrator. Wolfram Research, http://integrals.wolfram.com.
25. R. F. Harrington, Field Computation by Moment Methods. IEEE Press, 1993.
26. J. Jin, The Finite Element Method in Electromagnetics. John Wiley and Sons, 1993.
27. N. Morita, N. Kumagai, and J. R. Mautz, Integral Equation Methods for Electromagnetics. Artech House, 1990.
28. B. D. Popovich, “Polynomial approximation of current along thin symmetrical cylindrical dipoles,” Proc. IEE, vol. 117, 873–878, May 1970.
29. L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys., vol. 73, 325–348, 1987.
30. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation prob-lems,” Radio Sci., vol. 31, 1225–1251, 1996.
31. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes in C: The Art of Scientific Computing. Cambridge University Press, 1992.
32. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics. IEEE Press, 1998.
33. M. Hestenes and E. Steifel, “Methods of conjugate gradients for solving linear systems,” J. Res. Nat. Bur. Stand., vol. 49, 409–435, 1952.
34. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS, 1st ed., 1996.
35. T. K. Sarkar, K. R. Siarkiewicz, and R. F. Stratton, “Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems,” IEEE Trans. Antennas Propagat., vol. 29, 847–856, November 1981.
36. T. K. Sarkar, “The conjugate gradient method as applied to electromagnetic field problems,” IEEE Antennas Propagat. Soc. Newsletter, 5–14, August 1986.
37. A. F. Peterson and R. Mittra, “Convergence of the conjugate gradient method when applied to matrix equations representing electromagnetic scattering prob-lems,” IEEE Trans. Antennas Propagat., vol. 34, 1447–1454, December 1986.
38. A. F. Peterson, C. F. Smith, and R. Mittra, “Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm,” IEEE Trans. Antennas Propagat., vol. 36, 1177–1179, August 1988.
39. C. Lanczos, “Solution of systems of linear equations by minimized iterations,” J. Res. Nat. Bur. Standards, vol. 49, 33–53, 1952.
40. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Ei-jkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, 2nd ed., 1994.
41. P. Sonneveld, “Cgs, a fast lanczos-type solver for nonsymmetric linear sys-tems,” SIAM J. Sci. Statist. Comput., vol. 10, 36–52, 1989.
42. L. S. Blackford, J. Demmel, J. Dongarra, I. Duff, S. Hammarling, G. Henry, M. Heroux, L. Kaufman, A. Lumsdaine, A. Petitet, R. Pozo, K. Remington, and R. C. Whaley, “An updated set of Basic Linear Algebra Subprograms (BLAS),” ACM Transactions on Mathematical Software, vol. 28, 135–151, June 2002.
43. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide. Society for Industrial and Applied Mathematics, 3rd ed., 1999.
44. R. W. P. King, “The linear antenna–eighty years of progress,” Proc. IEEE, vol. 55, 2–26, January 1967.
45. W. Wang, “The exact kernel for cylindrical antenna,” IEEE Trans. Antennas Propagat., vol. 39, 434–435, April 1991.
46. D. R. Wilton and N. J. Champagne, “Evaluation and integration of the thin wire kernel,” IEEE Trans. Antennas Propagat., vol. 54, 1200–1206, April 2006.
47. E. Hallen, “Theoretical investigations into the transmitting and receiving qualities of antennae,” Nova Acta (Uppsala), vol. 11, 1–44, 1938.
48. H. C. Pocklington, “Electrical oscillations in wires,” Proc. Camb. Phil. Soc., vol. 9, 1897.
49. W. Stutzman and G. Thiele, Antenna Theory and Design. John Wiley and Sons, 1981.
50. C. A. Balanis, Advanced Engineering Electromagnetics. John Wiley and Sons, 1989.
51. S. J. Orfanidis, “Electromagnetic waves and antennas.” Electronic version: http://www.ece.rutgers.edu/orfanidi/ewa/.
52. H. Dwight, Tables of Integrals and Other Mathematical Data. The Macmillan Company, 1961.
53. The Integrator. Wolfram Research, http://integrals.wolfram.com.
54. The ARRL Antenna Book. The Amateur Radio Relay League, 17th ed., 1994.
55. W. Orr, Radio Handbook. Sams, 1992.
56. D. Wilton, S. Rao, A. Glisson, D. Schaubert, M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antennas Propagat., vol. 32, 276–281, March 1984.
57. C. A. Balanis, Advanced Engineering Electromagnetics. John Wiley and Sons, 1989.
58. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. National Bureau of Standards, 1966.
59. H. Dwight, Tables of Integrals and Other Mathematical Data. The Macmillan Company, 1961.
60. G. T. Ruck, ed., Radar Cross Section Handbook. Plenum Press, 1970.
61. R. Mautz and R. Harrington, “H-field, e-field and combined solutions for bodies of revolution,” Tech. Rep. Report RADC-TR-77-109, Rome Air Development Center, Griffiss AFB, NY, March 1977.
62. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. National Bureau of Standards, 1966.
63. K. Faison, “The electromagnetics code consortium,” IEEE Antennas Propagat. Magazine, vol. 30, 19–23, February 1990.
64. G. T. Ruck, ed., Radar Cross Section Handbook. Plenum Press, 1970.
65. B. R. Mahafza, Introduction to Radar Analysis. CRC Press, 1998.
66. A. C. Woo, H. T. G. Wang, M. J. Schuh, and M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propagat. Magazine, vol. 35, 84–89, February 1993.
67. A. Ausherman, A. Kozma, J. Waker, H. M. Jones, and E. C. Poggio, “De-velopments in radar imaging,” IEEE Trans. Aerospace Electron. Syst, vol. 20, 363–400, July 1984.
68. Rhinoceros 3D. Robert McNeel and Associates, http://www.rhino3d.com.
69. L. Piegl and W. Tiller, The NURBS Book. Springer, 1995.
70. J. Foley, A. van Dam, S. Feiner, and J. Hughes, Computer Graphics: Principles and Practice. Addison-Wesley, 1996.
71. D. Wilton, S. Rao, A. Glisson, D. Schaubert, M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antennas Propagat., vol. 32, 276– 281, March 1984.
72. S. Caorsi, D. Moreno, and F. Sidoti, “Theoretical and numerical treatment of surface integrals involving the free-space green’s function,” IEEE Trans. Antennas Propagat., vol. 41, 1296–1301, September 1993.
73. R. D. Graglia, “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. Antennas Propagat., vol. 41, 1448–1454, October 1993.
74. T. F. Eibert and V. Hansen, “On the calculation of potential integrals for linear source distributions on triangular domains,” IEEE Trans. Antennas Propagat., vol. 43, 1499–1502, December 1995.
75. J. Jin, The Finite Element Method in Electromagnetics. John Wiley and Sons, 1993.
76. S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propagat., vol. 30, 409–418, May 1982.
77. R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propagat., vol. 45, 329–342, March 1997.
78. M. G. Duffy, “Quadrature over a pyramide or cube of integrands with a singularity at a vertex,” SIAM J. Numer. Anal, vol. 19, 1260–1262, December 1982.
79. A. Tzoulis and T. Eibert, “Review of singular potential integrals for method of moments solutions of surface integral equations,” Advances in Radio Science, vol. 2, 97–99, 2004.
80. W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, 2001.
81. P. Ylä-Oijala and M. Taskinen, “Calculation of CFIE impedance matrix elements with RWG and n × RWG functions,” IEEE Trans. Antennas Propagat., vol. 51, 1837–1846, August 2003.
82. R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Micro. Opt. Tech. Lett., vol. 14, 9–14, January 1997.
83. O. Ergül and L. Gürel, “Investigation of the inaccuracy of the MFIE discretized with the RWG basis functions,” Proc. IEEE Antennas and Propagation Soc. Int. Symp., vol. 3, 3393–3396, 2004.
84. L. Gürel and O. Ergül, “Singularity of the magnetic-field integral equation and its extraction,” IEEE Antennas Wireless Propag. Lett, vol. 4, 229–232, 2005.
85. J. M. Rius, E. Úbeda, and J. Parrón, “On the testing of the magnetic field integral equation with RWG basis functions in the method of moments,” IEEE Trans. Antennas Propagat., vol. 49, 1550–1553, November 2001.
86. O. Ergül and L. Gürel, “Solid-angle factor in the magnetic-field integral equa-tion,” Microw. Opt. Technol. Lett., vol. 45, 452–456, June 2005.
87. O. Ergül and L. Gürel, “Improving the accuracy of the MFIE with the choice of basis functions,” Proc. IEEE Antennas and Propagation Soc. Int. Symp., vol. 3, 3389–2292, 2004.
88. O. Ergül and L. Gürel, “The use of curl-conforming basis functions for the magnetic-field integral equation,” IEEE Trans. Antennas Propagat., vol. 54, 1917–1926, July 2006.
89. E. Úbeda and J. M. Rius, “MFIE MoM-formulation with curl-conforming basis functions and accurate kernel integration in the analysis of perfectly conducting sharp-edged objects,” Microw. Opt. Technol. Lett., vol. 44, 354– 358, February 2005.
90. O. Ergül and L. Gürel, “Improving the accuracy of the magnetic field integral equation with the linear-linear basis function,” Radio Sci., vol. 41, 2006.
91. O. Ergül and L. Gürel, “Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations,” IEEE Trans. Antennas Propagat., vol. 55, 1103–1110, April 2007.
92. E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, LAPACK Users’ Guide. Society for Industrial and Applied Mathematics, 3rd ed., 1999.
93. A. C. Woo, H. T. G. Wang, M. J. Schuh, and M. L. Sanders, “Benchmark plate radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propagat. Magazine, vol. 34, 52–56, December 1992.
94. G. H. Brown and J. O. M. Woodward, “Experimentally determined radiation characteristics of conical and triangular antennas,” RCA Review, 425–452, 1952.
95. C. Leat, N. Shuley, and G. Stickley, “Triangular-patch model of bowtie antennas: validation against Brown and Woodward,” IEE Proc.-Microw. Antennas Propag., vol. 145, 465–470, December 1998.
96. W. L. Curtis, “Spiral antennas,” IRE Trans. Antennas Propagat., vol. 8, 298– 306, May 1960.
97. J. A. Kaiser, “The archimedean two-wire spiral antenna,” IRE Trans. Antennas Propagat., vol. 8, 312–323, May 1960.
98. L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys., vol. 73, 325–348, 1987.
99. R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” IEEE Antennas Propagat. Magazine, vol. 35, 7–12, June 1993.
100. W. C. Chew, J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, 2001.
101. J. Stratton, Electromagnetic Theory. McGraw-Hill, 1941.
102. J. M. Song and W. C. Chew, “Error analysis for the truncation of multipole expansion of vector green’s functions,” IEEE Microwave Wireless Components Lett., vol. 11, no. 7, 311–313, 2001.
103. O. M. Bucci, C. Gennarelli, and C. Savarese, “Optimal interpolation of radiated fields over a sphere,” IEEE Trans. Antennas Propagat., vol. 39, 1633–1643, November 1991.
104. P. Havé, “A parallel implementation of the fast multipole method for maxwell’s equations,” 2002.
105. E. Darve, “The fast multipole method: Numerical implementation,” J. Comput. Phys., vol. 160, 195–240, 2000.
106. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS, 1st ed., 1996.
107. J. Foley, A. van Dam, S. Feiner, and J. Hughes, Computer Graphics: Principles and Practice. Addison-Wesley, 1996.
108. R. Jakob-Chien and B. Alpert, “A fast spherical filter with uniform resolution,” J. Comput. Phys., vol. 136, 580–584, 1997.
109. J. Sarvas, “Performing interpolation and anterpolation entirely by fast fourier transform in the 3-d multilevel fast multipole algorithm,” SIAM J. Numer. Anal., vol. 41, no. 6, 2180–2196, 2003.
110. S. Koc, J. M. Song, and W. C. Chew, “Error analysis for the numerical evaluation of the diagonal forms of the spherical addition theorem,” SIAM J. Numer. Anal., vol. 36, no. 3, 906–921, 1999.
111. M. Nilsson, “A parallel shared memory implementation of the fast multipole method for electromagnetics,” Tech. Rep. Technical Report 2003-049, Department of Information Technology, Scientific Computing, Uppsala University, October 2003.
112. B. Hariharan, S. Aluru, and B. Shanker, “A scalable parallel fast multipole method for analysis of scattering from perfect electrically conducting surfaces,” in Supercomputing ’02: Proceedings of the 2002 ACM/IEEE conference on Supercomputing, 1–17, IEEE Computer Society Press, 2002.
113. K. Donepudi, J. Jin, S. Velamparambil, J. Song, and W. Chew, “A higher-order parallelized multilevel fast multipole algorithm for 3-d scattering,” IEEE Trans. Antennas Propagat., vol. 49, 1069–1078, July 2001.
114. S. Velamparambil and W. C. Chew, “Parallelization of multilevel fast multipole algorithm on distributed memory computers,” Tech. Rep. 13-01, Center for Computational Electromagnetics, University of Illinois at Urbana–Champaign, 2001.
115. S. Velamparambil and W. C. Chew, “Analysis and performance of a distributed memory multilevel fast multipole algorithm,” IEEE Trans. Antennas Propagat., vol. 53, 2719–2727, August 2005.
116. S. Velamparambil, W. C. Chew, and J. Song, “10 million unknowns: Is it that big?,” IEEE Antennas Propagat. Mag., vol. 45, no. 2, 43–58, 2003.
117. J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propagat., vol. 45, 1488–1493, October 1997.
118. A. C. Woo, H. T. G. Wang, M. J. Schuh, and M. L. Sanders, “Benchmark radar targets for the validation of computational electromagnetics programs,” IEEE Antennas Propagat. Magazine, vol. 35, 84–89, February 1993.
119. G. Thomas and R. Finney, Calculus and Analytic Geometry. Addison-Wesley, 1992.
120. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics. IEEE Press, 1998.
121. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical recipes in C: The Art of Scientific Computing. Cambridge University Press, 1992.
122. W. B. Gordon, “Far-field approximations to the kirchoff-helmholtz representations of scattered fields,” IEEE Trans. Antennas Propagat., vol. 23, 590–592, July 1975.
123. W. B. Gordon, “High frequency approximations to the physical optics scattering integral,” IEEE Trans. Antennas Propagat., vol. 42, 427–432, March 1994.
124. S. Lee and R. Mittra, “Fourier transform of a polygonal shape function and its application in electromagnetics,” IEEE Trans. Antennas Propagat., vol. 31, 99–103, January 1983.
125. D. Dunavant, “High degree efficient symmetrical gaussian quadrature rules for the triangle,” Internat. J. Numer. Methods Engrg., vol. 21, 1129–1148, 1985.