A review of finite element open boundary techniques for static and quasi-static electromagnetic field problems

IEEE Transactions on Magnetics

Volumn 33, Issue 1 PART 2, 1997, Pages 663-676

  Chen, Qiushi ^a   Konrad, Adalbert ^b  

^a Brown Applied Technology Inc   (Canada)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; ELECTROSTATICS; FINITE ELEMENT METHOD; PROBLEM SOLVING;

FINITE ELEMENT OPEN BOUNDARY TECHNIQUES;

ELECTROMAGNETIC FIELDS;

EID: 0030677549     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/20.560095     Document Type: Article

References (159)

1. A. M. Winslow, "Magnetic field calculations in an irregular triangular mesh," Lawrence Radiation Lab., Livermore, ÇA, UCRL-7784-T, Rev. 1, 1965.
2. P. Bettess, "Finite element modelling of exterior electromagnetic problems," IEEE Trans. Magn., vol. 24, pp. 238-243, Jan. 1988. [3] C. R. I. Emson, "Methods for the solution of open-boundary electromagnetic-field problems," Proc. IEE, Pt. A, vol. 135, pp. 151158, Mar. 1988.
3. J. D. Lavers, "Electromagnetic field computation in power engineering," IEEE Trans. Magn., vol. 29, pp. 2347-2352, Nov. 1993. [5] Y. Saito, T. Takahashi, and S. Hayano, "Finite element solution of open boundary magnetic field problems," IEEE Trans. Magn., vol. 23, pp. 3569-3571, Sept. 1987.
4. _, "Finite element solution of unbounded magnetic field problem containing ferromagnetic materials," IEEE Trans. Magn., vol. 24, pp. 2946-2948, Nov. 1988.
5. W. D. Smith, "A non-reflecting plane boundary for wave propagation problems," J. Comp. Phys., vol. 15, pp. 493-503, 1974.
6. M. Ikeuchi, H. Sawami, and H. Niki, "Analysis of open-type dielectric waveguides by the finite-element iterative method," IEEE Trans. Microwave Theory Tech.,vo\. 29, pp. 234-239, Mar. 1981.
7. P. P. Silvester, D. A. Lowther, C. J. Carpenter, and E. A. Wyatt, "Exterior finite elements for two-dimensional field problems with open boundaries," Proc. IEE, vol. 124, pp. 1267-1270, Dec. 1977.
8. G. Dasgupta, "Computation of exterior potential fields by infinite substructuring," Comput. Methods Appl. Mech. Eng., vol. 46, pp. 295-305, 1984.
9. D. A. Lowther, C. B. Rajanathan, and P. P. Silvester, "A finite element technique for solving 2-D open boundary problems," IEEE Trans. Magn., vol. 14, pp. 467-469, Sept. 1978.
10. K. S. Chiang, "Finite element method for cutoff frequencies of weakly guiding fibres of arbitrary cross-section," Opt. Quantum Electron., vol. 16, no. 6, pp. 487-493, Nov. 1984.
11. _, "Finite-element analysis of optical fibres with iterative treatment of the infinite 2D space," Opt. Quantum Electron., vol. 17, no. 6, pp. 381-391, Nov. 1985.
12. J. R. Brauer, "Open boundary finite elements for axisymmetric magnetic and skin effect problems," J. Appl. Phys., vol. 53, no. 11, pp. 8366-8368, 1982.
13. C. F. R. L. Antunes, E. M. Freeman, D. A. Lowther, and P. P. Silvester, "A static ballooning technique for 2-D open boundary problems," J. Appl. Phys., vol. 53, no. 11, pp. 8360-8362, 1982.
14. C. F. R. L. Antunes, "Approximate ballooning techniques," IEEE Trans. Magn., vol. 19, pp. 2555-2557, Nov. 1983.
15. R. L. Ungless, "An infinite finite element," M.Sc. thesis, Univ. British Columbia, Canada, 1973.
16. P. Bettess and J. A. Bettess, "Infinite elements for static problems," Eng. Compulal., vol. 1, no. 1, pp. 4-16, Mar. 1984.
17. P. Bettess, "Infinite elements," Int. J. Num. Methods Eng., vol. 11, no. 1, pp. 53-64, 1977.
18. C. Yeh, K. Ha, S. B. Dong, and W. P. Brown, "Single-mode optical waveguides," Appl. Opt., vol. 18, no. 10, pp. 1490-1504, May 1979.
19. B. M. A. Rahman and J. B. Davies, "Finite element analysis of optical and microwave problems," IEEE Trans. Microwave Theory Tech., vol. 32, pp. 20-28, Jan. 1984.
20. M. J. McDougall and J. P. Webb, "Infinite elements for the analysis of open dielectric waveguides," IEEE Trans. Microwave Theory Tech., vol. 37, pp. 1724-1731, Nov. 1989.
21. M. S. Towers, A. McCowen, and J. A. R. Macnab, "Electromagnetic scattering from an arbitrary, inhomogeneous 2-D object-A finite element and infinite element solution," IEEE Trans. Antennas Propagat., vol. 41, pp. 770-777, June 1993.
22. G. Beer and J. L. Meek, "Infinite domain elements," Int. J. Num. Methods Eng., vol. 17, no. 1, pp. 43-52, 1981.
23. O. C. Zienkiewicz, C. R. I. Emson, and P. Bettess, "A novel boundary infinite element," Int. J. Num. Methods Eng., vol. 19, no. 3, pp. 393-404, 1983.
24. S. Pissanetzky, "Solution of three-dimensional, anisotropic, nonlinear problems of magnetostatics using two scalar potentials, finite and infinite multipolar elements and automatic mesh generation," IEEE Trans. Magn., vol. 18, pp. 346-350, Mar. 1982.
25. -M, "A simple infinite element," COMPEL, vol. 3, no. 2, pp. 107-114, 1984.
26. S. Gratkowski and M. Ziolkowski, "A three-dimensional infinite element for modeling open-boundary field problems," IEEE Trans. Magn., vol. 28, pp. 1675-1678, Mar. 1992.
27. H. Hurwitz, Jr., "Infinitesimal scaling-A new procedure for modeling exterior field problems," IEEE Trans. Magn., vol. 20, pp. 1918-1923, Sept. 1984.
28. C. Crowley, H. Hurwitz, Jr., M. V! K. Chad, J. D.'Angelo, and J. F. Berkery, "Power line insulation analysis and design using finite elements and infinitesimal scaling," IEEE Trans. Magn., vol. 21, Nov. 1985.
29. M. V. K. Chari, J. D'Angelo, C. Crowley, J. Roeth, and H. Hurwitz, "Solution of open boundary problems by differential and integral methods," IEEE Trans. Magn., vol. 22, pp. 1037-1039, Sept. 1986.
30. B. Nath and J. Jamshidi, "The w-plane finite element method for the solution of scalar field problems in two dimensions," Int. J. Num. Methods Eng., vol. 15, no. 3, pp. 361-379, 1980.
31. S. H. Wong and I. R. Ciric, "Method of conformai transformation for the finite-element solution of axisymmetric exterior-field problems," COMPEL, vol. 4, no. 2, pp. 123-135, 1985.
32. R. B. Wu and C. H. Chen, "A variational analysis of dielectric waveguides by the conformai mapping technique," IEEE Trans. Microwave Theory Tech., vol. 33, pp. 681-685, Aug. 1985.
33. D. Greenspan and E. Silverman, "The calculation of electrostatic capacity by means of a high-speed digital computer," Proc. IEEE (Corres.), vol. 53, p. 1636, Oct. 1965.
34. E. M. Freeman and D. A. Lowther, "A novel mapping technique for open finite element solutions to Poisson's equation," IEEE Trans. Magn., vol. 24, pp. 2934-2936, Nov. 1988.
35. D. A. Lowther, E. M. Freeman, and B. Forghani, "A sparse matrix open boundary method for finite element analysis," IEEE Trans. Magn., vol. 25, pp. 2810-2812, July 1989.
36. I. R. Ciric and S. H. Wong, "Inversion transformation for the finite-element solution of three-dimensional exterior-field problems," COMPEL, vol. 5, no. 2, pp. 109-119, 1986.
37. E. M. Freeman and D. A. Lowther, "An open boundary technique for axisymmetric and three-dimensional magnetic and electric field problems," IEEE Trans. Magn., vol. 25, pp. 4135-4136, Sept. 1989.
38. J. F. Imhoflf, G. Meunier, and J. C. Sabonnadiere, "Finite element modeling of open boundary problems," IEEE Trans. Magn., vol. 26, pp. 588-591, Mar. 1990.
39. X. Brunotte, G. Meunier, and J. F. Imhoff, "Finite element modeling of unbounded problems using transformations: A rigorous, powerful and easy solution," IEEE Trans. Magn., vol. 28, pp. 1663-1666, Mar. 1992.
40. D. A. Lowther and E. M. Freeman, "Further aspects of the Kelvin transformation method for dealing with open boundaries," IEEE Trans. Magn., vol. 28, pp. 16667-1670, Mar. 1992.
41. D. L. Atherton, W. Czura, and D. A. Lowther, "Open-boundary finite-element calculations for remote-field eddy-current systems," IEEE Trans. Magn., vol. 26, pp. 2863-2865, Sept. 1990.
42. A. Stochniol, "A general transformation for open boundary finite element method for electromagnetic problems," IEEE Trans. Magn., vol. 28, pp. 1679-1681, Mar. 1992.
43. X. Brunotte, G. Meunier, and J. P. Bongiraud, "Ship magnetizations modelling by the finite element method," IEEE Trans. Magn., vol. 29, pp. 1970-1975, Mar. 1993.
44. I. A. Cermak and P. Silvester, "Solution of 2-dimensional field problems by boundary relaxation," Proc. IEE, vol. 115, no. 9, pp. 1341-1348, Sept. 1968.
45. C. D. Taylor, G. N. Elkhouri, and T. E. Wade, "On the parasitic capacitances of multilevel parallel metallization lines," IEEE Trans. Electron Devices, vol. 32, Nov. 1985.
46. G. Aiello, S. Alfonzeti, and S. Coco, "Charge iteration for N-dimensional unbounded electric field computations," IEEE Trans. Magn., vol. 28, pp. 1682-1685, Mar. 1992.
47. G. Aiello, S. Alfonzeti, S. Coco, and Salerno, "Axisymmetric unbounded electrical field computation by charge iteration," IEEE Trans. Magn., vol. 29, pp. 2043-2046, Mar. 1992.
48. Y. S. Sun, G. S. Zhang, and W. Chen, "A data base method for 3D open boundary computation," IEEE Trans. Magn., vol. 26, pp. 807-810, Mar. 1990.
49. W. Chen, G. S. Zhang, Y. S. Sun, M. J. Chen, and Y. Zhao, "The application of the data base method for 3-D open boundary field computation," IEEE Trans. Magn., vol. 29, pp. 1686-1689, Mar. 1992.
50. Z. Q. Zhou, Z. W. Jiang, Y. S. Sun, and L. Upda, "Application
51. of the sub-structure-frontal method for repeated solution of large sparse matrix equations to field problems," IEEE Trans. Magn., vol. 24, pp. 326-329, Jan. 1988.
52. B. H. McDonald and A. Wexler, "Finite element solution of unbounded field problems," IEEE Trans. Microwave Theory Tech., vol. 20, pp. 841-847, Dec. 1972.
53. B. H. McDonald and A. Wexler, "Mutually constrained partial differential and integral equation field formulations," in Finite Elements in Electrical and Magnetic Field Problems, M. V. K. Chari and P. P. Silvester, Eds. New York: Wiley, 1980, ch. 9, pp. 161-190.
54. C. H. Ahn, B. S. Jeong, and S. Y. Lee, "Efficient hybrid finite element-boundary element method for 3-dimensional open-boundary field problems," IEEE Trans. Magn., vol. 27, pp. 4069-4072, Sept. 1991.
55. Q. Chen, A. Konrad, and P. P. Biringer, "An integrodifferential finite element-Green's function method for the solution of unbounded eddy current problems," IEEE Trans. Magn., vol. 29, pp. 1874-1877, Mar. 1993.
56. _, "A hybrid approach to the solution of open boundary eddy current problems under TM field excitation," IEEE Trans. Magn., vol. 29, pp. 2485-2487, Nov. 1993.
57. _, "A finite element-Green's function method for the solution of unbounded three dimensional eddy current problems," IEEE Trans. Magn., vol. 30, pp. 3048-3051, Sept. 1994.
58. M. V. K. Chari, "Electromagnetic field computation of open boundary problems by a semi-analytic approach," IEEE Trans. Magn., vol. 23, pp. 3566-3568, Nov. 1987.
59. M. V. K. Chari and G. Bedrosian, "Hybrid harmonic/finite element method for two-dimensional open boundary problems," IEEE Trans. Magn., vol. 23, pp. 3572-3574, Nov. 1987.
60. _, "A hybrid method for eddy current open-boundary field computation," J. Appl. Phys., vol. 63, no. 8, pp. 3019-3021, Apr. 1988.
61. J. F. Lee and Z. J. Cendes, "Transfmite elements: A highly efficient procedure for modeling open field problems," J. Appl. Phys., vol. 61, no. 8, pp. 3913-3915, Apr. 1987.
62. A. K. Gasiorski, "Application of finite-element method to calculation of the impedance of nonsymmetrically shaped bars conducting current," IEEE Trans. Electromagn. Compal., vol. 29, pp. 206-213, Aug. 1987.
63. _, "Finite-element method for power losses calculation in long rectangular conductors located in transverse harmonic magnetic field," IEEE Trans. Magn., vol. 24, pp. 2140-2145, July 1988.
64. K. K. Mei, "Unimoment method of solving antenna and scattering problems," IEEE Trans. Antennas Propagat., vol. 22, pp. 760-766, Nov. 1974.
65. S. K. ChangandK. K. Mei, "Application of the unimoment method to electromagnetic scattering of dielectric cylinders," IEEE Trans. Antennas Propagat., vol. 24, pp. 35-42, 1976.
66. T. Nakata, N. Takahashi, K. Fujiwara, M. Sakaguchi, "3-D open boundary magnetic field analysis using infinite element based on hybrid finite element method," IEEE Trans. Magn., vol. 26, pp. 368-370, Mar. 1990.
67. J. Sroka, H. Baggenstos, and R. Ballisti, "On the coupling of the generalized multipole technique with the finite element method," IEEE Trans. Magn., vol. 26, pp. 658-661, Mar. 1990.
68. C. Hafner and R. Ballisti, "Electromagnetic field calculations on PC's and workstations using the MMP method," IEEE Trans. Magn., vol. 25, pp. 2828-2830, Mar. 1989.
69. P. Silvester and M. S. Hsieh, "Finite-element solution of 2-dimensional exterior field problems," Proc. IEE, vol. 118, no. 12, pp. 1743-1747, 1971.
70. Z. J. Csendes, "A note on the finite-element solution of exteriorfield problems," IEEE Trans. Microwave Theory Tech., vol. 24, pp. 468-473, July 1976.
71. Z. Ren, F. Bouillault, A. Razek, and J. C. Vérité, "Comparison of different boundary integral formulations when coupled with finite elements in three dimensions," Proc. IEE, Pt. A, vol. 135, no. 8, pp. 501-507, 1988.
72. S. J. Salon and J. M. Schneider, "A hybrid finite element boundary integral formulation of Poisson's equation," IEEE Trans. Magn., vol. 17, pp. 2574-2576, Nov. 1981.
73. _, S. J. Salon and J. M. Schneider, "A hybrid finite element boundary integral formulation of the eddy current problem," IEEE Trans. Magn., vol. 18, pp. 461-466, Mar. 1982.
74. S. J. Salon and J. P. Peng, "A hybrid finite element-boundary element
75. formulation of Poisson's equation for axisymmetric vector potential problems," J. Appl. Phys., vol. 53, no. 11, pp. 8420-8422, Nov. 1982.
76. J. P. Peng and S. J. Salon, "Hybrid finite element-boundary solution using half-space Green's functions," J. Appl. Phys., vol. 55, no. 6, pp. 2198-2200, Mar. 1984.
77. S. J. Salon, "The hybrid finite element-boundary element method in electromagnetics," IEEE Trans. Magn., vol. 21, pp. 1829-1834, Sept. 1985.
78. I. D. Mayergoyz and T. Doong, "Hybrid boundary-volume Galerkin's method for nonlinear magnetostatic problems, " J. Appl. Phys., vol. 57, no. 18, pp. 3838-3840, Apr. 1985.
79. G. Meunier, J. L. Coulomb, S. Salon, and L. Krähenbül, "Hybrid finite element-boundary element solutions for three-dimensional scalar potential problems," IEEE Trans. Magn., vol. 22, pp. 1040-1042, Sept. 1986.
80. F. Bouillault and A. Razek, "Hybrid numerical methods for movement consideration in electromagnetic systems," IEEE Trans. Magn., vol. 24, pp. 250-261, Jan. 1988.
81. S. J. Salon and J. D.'Angelo, "Application of the finite elementboundary element method in electromagnetics," IEEE Trans. Magn., vol. 24, pp. 80-85, Jan. 1988.
82. J. D'Angerlo, I. Mayergoyz, and M. Palmo, "Hybrid finite element/boundary element analysis for axisymmetric magnetostatic fields," IEEE Trans. Magn., vol. 24, pp. 2506-2508, Nov. 1988.
83. K. R. Shao and J. D. Lavers, "A new hybrid method using hinged finite element formulations for the skin depth effect eddy current problems," IEEE Trans. Magn., vol. 26, pp. 2765-2767, Mar. 1990.
84. _, "A skin depth-independent finite element method for eddy current problems," IEEE Trans. Magn., vol. 26, pp. 1248-1250, Sept. 1986.
85. A. Bossavit and J. C. Vérité, "A mixed FEM-BIEM method to solve 3-D eddy-current problems," IEEE Trans. Magn., vol. 18, pp. 431-435, Mar. 1982.
86. Z. Ren, F. Bouillault, A. Razek, A. Bossavit, and J. C. Verile, "A new hybrid model using electric field formulation for 3-D eddy current problems," IEEE Trans. Magn., vol. 26, pp. 470-473, Mar. 1990.
87. Z. Ren, C. Li, and A. Razek, "Hybrid FEM-BIM formulation using electric and magnetic variables," IEEE Trans. Magn., vol. 28, pp. 1647-1650, Mar. 1992.
88. F. Matsuoka and A. Kameari, "Calculation of three-dimensional eddy current by FEM-BEM coupling method," IEEE Trans. Magn., vol. 24, pp. 182-185, Jan. 1988.
89. T. Onuki, "Hybrid finite element and boundary element method applied to electromagnetic problems," IEEE Trans, Magn., vol. 26, pp. 582-587, Mar. 1990.
90. T. Onuki and S. Wakao, "Novel boundary element formulation in hybrid FE-BE method for electromagnetic field computations," IEEE Trans. Magn., vol. 28, pp. 1162-1165, Mar. 1992.
91. F. Bouillault, Z. Ren, and A. Razek, "Calculation of 3D eddy current problems by a hybrid T-Q method," IEEE Trans. Magn., vol. 26, pp. 478-481, Mar. 1990.
92. F. Bouillault, "T-Ü formulation by hybrid FEM-BIM and its gauges for 3D electromagnetic calculations," IEEE Trans. Magn., vol. 28, pp. 1208-1211, Mar. 1992.
93. S. Wakao and T. Onuki, "Electromagnetic field computations by the hybrid FE-BE method using edge elements," IEEE Trans. Magn., vol. 29, pp. 1487-1490, Mar. 1993.
94. J. Ruan, X. Chen, K. Zhou, and Z. Ren, "3D transient eddy current calculation by the hybrid FE-BE method using magnetic field intensity H," IEEE Trans. Magn., vol. 31, pp 1408-1411, May 1995.
95. I. D. Mayergoyz, M. V. K. Chari, and A. Konrad, "Boundary Galerkin's method for three-dimensional finite element electromagnetic field computation," IEEE Trans. Magn.,.vol. 19, pp. 2333-2336, Nov. 1983.
96. R. Mathon, "On the approximation of elliptic boundary value problems by fundamental solutions," Ph.D. thesis, Univ. Toronto, Toronto, Canada, 1972.
97. M. T. Ahmed, J. D. Lavers, and P. E. Burke, "Skin and proximity effect calculation using the method of fundamental solutions (MFS)," IEEE Trans. Magn., vol. 24, pp. 2667-2669, Nov. 1988.
98. _, "An evaluation of the direct boundary element method and the method of fundamental solutions," IEEE Trans. Magn., vol. 25, pp. 3001-3006, July 1989.
99. _, "Constrained indirect BEM for eddy current calculations in
100. multiple conductor TM induction problems," IEEE Trans. Magn., vol. 25, pp. 3946-3948, Sept. 1989.
101. J. Wang and J. D. Lavers, "The method of fundamental solutions with a minimum order formulation applied to 3D eddy current problems," IEEE Trans. Magn., vol. 29, pp. 1359-1362, Mar. 1993.
102. A. Konrad, "The numerical solution of steady-state skin effect problems-An integrodifferential approach," IEEE Trans. Magn., vol. 17, pp. 1148-1152, Jan. 1981.
103. Q. Chen, A. Konrad, and P. P. Biringer, "Sensitivity analysis of the integrodifferential finite element-Green's function method," in Proc. 9th Annu. Rev. Progress Appl. Computat. Electromagn., Monterey, CA, Mar. 1993, pp. 720-726.
104. C. H. Wilcox, "An expansion theorem for electromagnetic fields," Commun. Pure Appl. Math., vol. IX, pp. 115-134, 1956.
105. B. Engquist and A. Majda, "Radiation boundary conditions for the numerical simulation of waves," Math. Comp., vol. 31, no. 139, pp. 629-651, July 1977.
106. A. Bayliss, M. Gunzburger, and E. Turkei, "Boundary conditions for the numerical solution of elliptic equations in exterior regions," S1AMJ. Appl. Math., vol. 42, no. 2, pp. 430-451, Apr. 1982.
107. E. L. Lindman, "Free-space" boundary conditions for the time dependent wave equation," J. Comput. Phys., vol. 18, pp. 66-78, 1975.
108. R. L. Higdon, "Absorbing boundary conditions for difference approximations to the multidimensional wave equation," Math. Cornput., vol. 47, no. 176, pp. 437-459, 1986.
109. _, "Numerical absorbing boundary conditions for the wave equation," Math. Comput., vol. 49, pp. 65-90, 1987.
110. G. A. Kriegsmann, A. Taflove, and K. R. Umashankar, "A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach," IEEE Trans. Antennas Propagat., vol. 35, pp. 152-161, Feb. 1987.
111. T. G. Moore, J. G. Blaschak, A. Taflove, and G. A. Kriegsmann, "Theory and application of radiation boundary operators," IEEE Trans. Antennas Propagat., vol. 36, pp. 1797-1812, Dec. 1988.
112. R. Mittra, O. Ramahi, A. Khebir, R. Gordon, and A. Kouki, "A review of absorbing boundary conditions for two- and three-dimensional electromagnetic scattering problems," IEEE Trans. Magn., vol. 25, pp. 3034-3039, July 1989.
113. F. R. Cooray and G. I. Costache, "An overview of the absorbing boundary conditions," J. Electromagnetic Waves Appl., vol. 5, no. 10, pp. 1041-1054, 1991.
114. J. D'Angelo and I. D. Mayergoyz, "On the use of the local absorbing boundary conditions for RF scattering problems," IEEE Trans. Magn., vol. 25, pp. 3040-3042, July 1989.
115. J. L. Yao-Bi, L. Nicolas, and A. Nicolas, "2D electromagnetic scattering by simple shapes: A quantification of the error due to open boundary," IEEE Trans. Magn., vol. 29, pp. 1830-1834, Mar. 1993.
116. M. Feliziani, "Numerical solutions of low-frequency scattering problems," IEEE Trans. Magn., vol. 28, pp. 1224-1227, Mar. 1992.
117. _, "Characteristic boundary conditions for the solution of open boundary problems," IEEE Trans. Magn., vol. 29, pp. 1816-1819, Mar. 1993.
118. G. Mur, "A finite-element method for the computation of three-dimensional electromagnetic fields in strongly inhomogeneous media,' ' in Proc. Beijing Int. Symp. Electromagnetic Fields Elec. Eng., Beijing, P. R. China, Oct. 1988, pp. 273-276.
119. _, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromangetic-field equations," IEEE Trans. Electromagn. Compat., vol. 23, pp. 377-382, Nov. 1981.
120. J. P. Webb, "Absorbing boundary conditions for the finite-element analysis of planar devices," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1328-1332, Sept. 1990.
121. T. K. Sarkar, M. Manela, V. Narayanan, and A. R. Djordjevic, "Finite difference frequency-domain treatment of open transmission structures," IEEE Trans. Microwave Theory Techn., vol. 28, pp. 1609-1616, Nov. 1990.
122. O. M. Ramahi and R. Mittra, "Finite element solution for a class of unbounded geometries," IEEE Trans. Antennas Propagat., vol. 39, pp. 244-250, Feb. 1991.
123. K. Mclnturff and P. S. Simon, "Closed-form expressions for coefficients used in FD-TD high-order boundary conditions," IEEE Microwave Guided Wave Lett., vol. 3, pp. 222-223, July 1993.
124. L. W. Pearson, R. A. Whitaker, and L. J. Bahrmasel, "An exact radiation boundary condition for the finite-element solution of electromagnetic scattering on an open domain," IEEE Trans. Magn., vol. 25, pp. 3046-3048, July 1989.
125. O. M. Ramahi and R. Mittra, "Numerically derived absorbing boundary conditions for the solution of open region scattering problems," IEEE Trans. Antennas Propagat., vol. 39, pp. 350-353, Mar. 1991.
126. G. Mur, "The finite-element modeling of three-dimensional electromagnetic fields using edge and nodal elements," IEEE Trans. Antennas Propagat., vol. 41, pp. 948-953, July 1993.
127. Q. Chen, A. Konrad, and P. P. Biringer, "Computation of static and quasistatic electromagnetic fields using asymptotic boundary conditions," Appl. Computat. Electromagn. Soc. J., vol. 9, no. 2, pp. 37-42, July 1994.
128. A. F. Peterson, "Absorbing boundary conditions for the vector wave equation," IEEE Microwave Opt. Technol. Lett., vol. 1, pp. 62-64, Apr. 1988.
129. J. P. Webb and V. N. Kanellopoulos, "Absorbing boundary conditions for the finite element solution of the vector wave equation," IEEE Microwave Opt. Technol. Lett., vol. 2, pp. 370-372, Oct. 1989.
130. V. N. Kanellopoulos and J. P. Webb, "A numerical study of vector absorbing boundary conditions for the finite-element solution of Maxwell's equations," IEEE Microwave Opt. Technol. Lett., vol. 1, pp. 325-327, Nov. 1991.
131. J. R. Brauer, B. S. Brown, and M. M. Jenich, "ABC finite elements for open boundary electromagnetic problems from DC to GHZ," in Proc. 9th Annu. Rev. Progress Appl. Computat. Electromagn., Monterey, CA, Mar. 1993, pp. 830-837.
132. A. Khebir, J. D'Angelo, and J. Joseph, "A new finite element formulation of RF scattering by complex bodies of revolution," IEEE Trans. Antennas Propagat., vol. 41, pp. 534-541, May 1993.
133. C. F. Bryant, E. Deeley, C. R. I. Emson, J. Simkin, C. W. Trowbridge, and X. Zhou, "Solving EMC problems using a finite element package," IEEE Trans. Magn., vol. 30, pp. 3016-3019, Nov. 1994.
134. J. L. Yao-Bi, L. Nicolas, and A. Nicolas, "H(curl) elements on hexahedral and vector A.B.C.'s for unbounded microwave problems," IEEE Trans. Magn., vol. 31, pp. 1538-1541, May 1995.
135. J. Wang and R. Mittra, "Finite element analysis of MMIC structures and electronic packages using absorbing boundary conditions," IEEE Trans. Microwave Theory Tech., vol. 42, pp. 441-449, Mar. 1994.
136. M. De Pourc, "Field and power-density calculations in closed microwave systems by three-dimensional finite differences," Proc. IEE, Pt. H, vol. 132, no. 6, pp. 360-368, Oct. 1985.
137. R. Luebbers, J. Beggs, and K. Chamberiin, "Finite difference time-domain calculation of transients in antennas with nonlinear loads," IEEE Trans. Antennas Propagat., vol. 41, pp. 566-573, May 1993.
138. A. Taflove and M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," IEEE Trans. Microwave Theory Tech., vol. 23, pp. 623-630, Aug. 1975.
139. A. Konrad and J. O. Y. Lo, "Time domain solution of planar circuits," J. Electronmagn. Waves Appl., vol. 7, pp. 77-92, 1993.
140. J. O. Y. Lo and A. Konrad, "Time domain simulation of lossy planar networks," IEEE Trans. Magn., vol. 29, pp. 1717-1721, Mar. 1993.
141. C. J. Railton and E. M. Daniel, "A comparison of the properties of radiating boundary conditions in the FDTD method for finite discretisation and non-planar waves," IEEE Trans. Antennas Propagat., vol. 42, pp. 276-281, Feb. 1994.
142. K. K. Mei and J. Fang, "Superabsorption-A method to improve absorbing boundary conditions," IEEE Trans. Amennas Propagat., vol. 40, pp. 1001-1010, Sept. 1992.
143. J. R. Brauer, S. M. Schaefer, and R. Mittra, "Simulation of static open boundary problems in MSC/EMAS," presented at the MSC 1991 World Users' Conf., E/EAD Paper 69, Mar. 1991.
144. J. F. Lee and R. Mittra, "Mesh truncation in the finite element analysis for static and magnetic fields," presented at the MSC 1991 World Users' Conf., E/EAD Paper 66, Mar. 1991.
145. J. R. Brauer, S. M. Schaefer, J. F. Lee, and R. Mittra, "Asymptotic boundary condition for three-dimensional magnetostatic finite elements," IEEE Trans. Magn., vol. 27, pp. 5013-5015, Nov. 1991.
146. J. R. Brauer and F. Hirtenfelder, "Surface integrals on 3D and 2D finite element models for skin effect excitations and open boundaries," IEEE Trans. Magn., vol. 28, pp. 1659-1662, Mar. 1992.
147. A. Khebir, A. B. Kouki, and R. Mittra, "Asymptotic boundary conditions for finite element analysis of three-dimensional transmission line discontinuities," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1427-1432, Oct. 1990.
148. _, "Higher order asymptotic boundary condition for the finite element modeling of two-dimensional transmission line structures," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1433-1438, Oct. 1990.
149. S. Subramaniam, M. Feliziani, and S. R. H. Hoole, "Open boundary eddy-current problems using edge elements," IEEE Trans. Magn., vol. 29, pp. 1499-1503, Mar. 1993.
150. Q. Chen, A. Konrad, and S. Baronijan, "Asymptotic boundary conditions for axisymmetric finite element electrostatic analysis," IEEE Trans. Magn., vol. 30, pp. 4335-4337, Nov. 1994.
151. Q. Chen, A. Konrad, and P. P. Biringer, "Computation of three dimensional unbounded eddy current problems using asymptotic boundary conditions," IEEE Trans. Magn., vol. 31, pp. 1348-1351, May 1995.
152. K. K. Mei, R. Pous, Z. Chen, and Y. W. Liu, "Measured equation of invariance: A new concept in field computation," in Proc. IEEE ALS Int. Symp., Chicago, July 1992, pp. 2047-2050.
153. A. C. Cangellaris and D. B. Wright, "Application of the measured equation of invariance to electromagnetic scattering by penetrable bodies," IEEE Trans. Magn., vol. 29, pp. 1628-1631, Mar. 1993.
154. D. B. Wright and A. C. Cangellaris, "Performance evaluation of MEI-based mesh truncation conditions for finite element modeling of electromagnetic scattering by penetrable bodies," in Proc. 9th Annu. Rev. Progressa Appl. Computat. Electromagn., Monterey, CA, Mar. 1993, pp. 863-870.
155. M. D. Prouty, K. K. Mei, S. E. Schwarz, and R. Pous, "A new approach to quasi-static analysis with application to microstrip," IEEE Microwave Guided Wave Lett., vol. 3, pp. 302-304, Sept. 1993.
156. J. O. Jevtic and R. Lee, "A theoretical and numerical analysis of the measured equation of invariance," IEEE Trans. Antennas Propagat., vol, 42, pp. 1097-1105, Aug. 1994.
157. K. K. Mei, R. Pous, Z. Chen, Y. Liu, and M. Prouty, "Measured equation of invariance: A new concept in field computations," IEEE Trans. Antennas Propagat., vol. 42, pp. 320-328, Mar. 1994.
158. B. Stupfel and R. Mittra, "A theoretical study of numerical absorbing boundary conditions," IEEE Trans. Antennas Propagat., vol. 43, pp. 478-487, May 1995.
159. J. C. Sabonnadiere and A. Konrad, "Computing EM fields," IEEE Spectrum (Focus Report: Engineering Software), vol. 29, pp. 52-56, Nov. 1992.