Multigrid Finite Element Methods for Electromagnetic Field Modeling

Multigrid Finite Element Methods for Electromagnetic Field Modeling

Volumn , Issue , 2006, Pages 1-408

  Zhu, Yu ^a   Cangellaris, Andreas C ^b  

^a CADENCE DESIGN SYSTEMS   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84891324278     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/0471786381     Document Type: Book

References (310)

1. H. C. Martin and G. F. Carey, Introduction to Finite Element Analysis: Theory and Application, New York: McGraw-Hill, 1973.
2. R. K. Livesley, Finite Elements: An Introduction for Engineers, Cambridge: Cambridge University Press, 1983.
3. J. M. Jin, The Finite Element Method in Electromagnetics, New York: John Wiley & Sons, Inc., 1993.
4. P. P. Silvester and R.L. Ferrari., Finite Elements for Electrical Engineering, Cambridge: Cambridge University Press, 1983.
5. J. L. Volakis, A. Chatterjee, L. C. Kempel, Finite Element Method for Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications, Piscataway, NJ: Wiley-IEEE Press Series on Electromagnetic Wave Theory, 1998.
6. M. S. Palma, T. K. Sarksar, L.E. Garcfa-Castillo, T. Roy, and A. Djordjevic. Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling, Norwood, MA: Artech House, 1998.
7. C. A. Balanis, Advanced Engineering Electromagnetics, New York: John Wiley & Sons, Inc., 1992.
8. R. F. Harrington, Time-Harmonic Electromagnetic Field, New York: McGraw-Hill, 1961.
9. J. Van Bladel, Electromagnetic Fields, New York: Hemisphere Publishing Corporation, 1985.
10. J. R. Wait, Geo-Electromagnetism, New York: Academic Press, 1982.
11. R. E. Collin, FieldTheory of Guided Waves, Piscataway, NJ: IEEE Press, 1991.
12. A. F. Peterson, S. L. Ray, and R. Mittra, Computational Methods for Engineering, New York: IEEE Press, 1998.
13. D. S. Jones, Methods in Electromagnetic Wave Propagation, 2nd ed., Piscataway, NJ: IEEE Press, 1994.
14. D. G. Dudley, Mathematical Foundations for Electromagnetic Theory, Piscataway, NJ: IEEE Press, 1994.
15. J. D. Jackson, Classical Electrodynamics, 3rd ed., New York: John Wiley & Sons, Inc., 1999.
16. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., Philadelphia: SIAM, 2003.
17. B.I. Wohlmuth, Discretization Methods for Iterative Solvers Based on Domain Decomposition, Berlin: Springer-Verlag, 2001.
18. M. Gander, F. Magoules, and F. Nataf, "Optimal Schwartz methods without overlap for the Helmholtz equation," SIAM J. Sci. Comput., vol. 24, no. 1, pp. 38-60, 2002.
19. S.-C. Lee, M.N. Vouvakis, and J.-F. Lee, "Domain decomposition method for large finite antenna arrays," Proc. IEEE Antennas and Propagation Society Symposium, vol. 4, pp. 3501-3504, Monterey, CA, Jun. 2004.
20. J. T. Ogden and G. F. Carey, Finite Elements: Mathematical Aspects, Englewood Cliffs, NJ: Prentice-Hall, Inc., 1983.
21. B. Szabó and I. Babuška, Finite Element Analysis, New York: John Wiley & Sons, Inc., 1991.
22. J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed., New York: John Wiley & Sons, Inc., 2002.
23. M. S. Palma, T. K. Sarkar, L.E. Garcfa-Castillo, T. Roy, and A. Djordjevid, Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling, Norwood, MA: Artech House, 1998.
24. R. Dyczij-Edlinger, G. Peng, and J. F. Lee, "A fast vector-potential method using tangentially continuous vector finite elements," IEEE Trans. Microwave Theory Tech. vol. 46, pp. 863-868, Jun. 1998.
25. R. F. Harrington, Time-Harmonic Electromagnetic Fields, Piscataway, NJ: IEEE Press Series on Electromagnetic Wave Theory, 2001.
26. J. C. Nédélec, "Mixed finite elements in R3," Numer. Math., vol. 35, pp. 315-34, 1980.
27. J. C. Néctélec, "A new family of mixed finite elements in R3," Numer. Math., vol. 50, pp. 57-81, 1986.
28. A. Bossavit, "Whitney forms: A class of finite elements for three-dimensional computation in electromagnetics," IEE Proceedings, vol. 135, pt. A, pp. 493-500, 1988.
29. A. Bossavit, "A rationale for edge elements in 3-D fields computations," IEEE Trans. Magn., vol. 24, pp. 74-79, Jan. 1988.
30. A. Bossavit and I. Mayergoyz, "Edge-elements for scattering problems," IEEE Trans. Magnetics, vol. 25, pp. 2816-2821, Jul. 1989.
31. Z. J. Cendes, "Vector finite elements for electromagnetic field computations," IEEE Trans. Magnetics, vol. 27, pp. 3958-3966, Sep. 1991.
32. J. F. Lee, 'Tangential vector finite elements and their application to solving electromagnetic scattering problems," Applied Computational Electromagnetic Society Newsletter, vol. 10, pp. 52-75, Mar. 1995.
33. J. F. Lee, D. K. Sun and Z. J. Cendes, 'Tangential vector finite elements for electromagnetic field computation," IEEE Trans. Magnetics, vol. 27, pp. 4032-4035, Sep. 1991.
34. J. P. Webb, "Edge elements and what they can do for you," IEEE Trans. Magnetics, vol. 29, pp. 1460-1465, Mar. 1993.
35. P. P. Silvester and G. Pelosi (editors), Finite Elements for Wave Electromagnetics: Methods and Techniques. Piscataway, NJ: IEEE Press, 1994.
36. J. P. Webb and B.Forghani, "Hierarchical scalar and vector tetrahedra," IEEE Trans. Magn., vol. 29, pp. 1495-1498, Mar. 1993.
37. T. V. Yioultsis and T. D. Tsiboukis, "Multiparametric vector finite elements: a systematic approach to the construction of three-dimensional, higher order, tangential vector shape functions," IEEE Trans. Magnetics, vol. 32, pp. 1389-1494, May 1996.
38. T. V. Yioultsis and T. D. Tsiboukis, "Development and implementation of second and third order vector finite elements in various 3-D electromagnetic field problems," IEEE Trans. Magnetics, vol. 33, pp. 1812-1815, Mar. 1997.
39. T. V. Yioultsis and T. D. Tsiboukis, C. S. Antonopoulos, and T. D. Tsiboukis, "A fully explicit Whitney element-time domain scheme with higher order vector finite elements for three-diemensional high frequency proble3ms" IEEE Trans. Magnetics, vol. 34, pp. 3288-3291, Sep. 1998.
40. R. D. Graglia, D. R. Wilton, and A. F. Peterson, "Higher order interpolatory vector bases for computational electromagnetics," IEEE Trans. Antenna and Propagation, vol. 45, pp. 329-342, Mar. 1997.
41. A. F. Peterson and D. R. Wilton, "Curl-conforming mixed-order edge elements for discretizing the 2D and 3D vector Helmholtz equation," Finite Element Software for Microwave Engineering, T. Itoh, G. Pelosi and P. P. Silvester, Eds., New York: Wiley, 1996, ch. 5, pp. 101-124.
42. J. S. Savage and A. F. Peterson, "Higher order vector finite elements for tetrahedral cells," IEEE Trans. Microwave Theory Tech., vol. 44, pp. 874-879, June 1996.
43. J. P. Webb, "Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements," IEEE Trans. Antennas and Propagation, vol. 47, pp. 1244-1253, Aug. 1999.
44. Y. Zhu and A. C. Cangellaris, "Hierarchical finite element basis function spaces for tetrahedral elements," Proc. of Applied Computational Electromagnetics Society Meeting, Monterey, CA, Mar. 2001.
45. L. S. Andersen and J. L. Volakis, "Hierarchical tangential vector finite elements for tetrahedra," IEEE, Microwave Guided Wave Lett., vol. 8, pp. 127-129, Mar. 1998.
46. L. S. Andersen and J. L. Volakis, "Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics," IEEE Trans. Antenna Propagat., vol. 47, pp. 112-120, Jan. 1999.
47. L. S. Andersen and J. L. Volakis, "Accurate and efficient simulation of antennas using hierarchical mixed-order tangential vector finite elements for tetrahedra," IEEE Trans. Antenna Propagat., vol. 47, pp. 1240-1243, Aug. 1999.
48. J. Wang and J. P. Webb, "Hierarchical vector boundary elements and p-adaption for 3-D electromagnetic scattering," IEEE Trans. Antenna Propagat., vol. 45, pp. 1869-1879, Dec. 1997.
49. D. A. White, "Orghogonal vector basis functions for time-domain finite element solution of the vector wave equation," IEEE Trans. Magnetics, vol. 35, pp. 1458-1461, May 1999.
50. Y. Zhu and A. C. Cangellaris, "A New FEM Formulation for Reduced Order Electromagnetic Modeling," IEEE Microwave and Guided Wave Lett., May 2001.
51. K. Mahadevan, R. Mittra, and P. M. Vaidya, "Use of Whitney's edge and face elements for efficient finite element time domain solution of Maxwell's equations," J. Electromagnetic Waves and Appl., vol. 8, no. 9/10, pp. 1178-1191, 1994.
52. J. F. Lee and Z. Sacks, "Whitney elements time domain (WETD) methods," IEEE. Trans. Magnetics, vol. 31, pp. 1325-1329, May 1995.
53. J. F. Lee, R. Lee, and A. C. Cangellaris, "Time-domain finite element methods," IEEE Trans. Antennas Propagat., vol. AP-45, pp. 430-442, Mar. 1997.
54. H. Whitney, Geometric Integration Theory, Princeton NJ: Princeton University Press, 1957.
55. P.P. Silvester and R.L. Ferrari, Finite Elements for Electrical Engineering, Cambridge: Cambridge University Press, 1983.
56. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. 30, pp. 409-418, May 1982.
57. J. M. Gil and J. P. Webb, "A new edge element for the modeling of field singularities in transmission lines and waveguides," IEEE. Trans. Microwave Theory Tech., vol. 45, pp. 2125-2130, Dec. 1997.
58. J. F. Lee and R. Mittra, "A note on the application of edge-elements for modeling three-dimensional inhomogeneously-filled cavities," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 1767-1773, Sep. 1992.
59. G. Peng, R. Dyczij-Edlinger, and J. F. Lee, "Hierarchical methods for solving matrix equations from TVFEMs for microwave components," IEEE Trans. Magnetics, vol. 35, pp. 1474-1477, May 1999.
60. G. Strang and G. J. Fix, An Analysis of the Finite Element Method, Englewood Cliffs, NJ: Prentice-Hall, Inc., 1973.
61. J.T. Oden and G.F. Carey, Finite Elements: Mathematical Aspects, Vol. TV, Englewood Cliffs, NJ: Prentice-Hall, Inc., 1983.
62. O.C. Zienkiewicz and A. Graig, "Adaptive refinement, error estimates, multigrid solution, and hierarchic finite element method concept," in Accuracy Estimates and Adaptive Refinements in Finite Element Computations, I. Babuska, O.C. Zienkiewich, J. Gago and E.R. de A. Oliveira, (Eds.), London: John Wiley & Sons, 1986.
63. M. Salazar-Palma, T.K. Sarkar, L.-E. Garcia-Castillo, T. Roy, and A. Djordjevic, Iterative and Self-Adaptive Finite Elements in Electromagnetic Modeling, Norwood, MA: Artech House, Inc., 1989.
64. R. D. Graglia and G. Lombardi, "New higher order two-dimensional singular elements for FEM and MOM applications," Proc. of the ICEAA 03, pp. 87-89, Torino, Italy, Sep. 2003.
65. Babuska, "The p- and h-p versions of the finite element method: The state of the art," in Finite Elements Theory and Applications, D. L. Dwoyer, M.Y. Hussain and R.G. Voigt (Eds.), New York: Springer-Verlag, 1988.
66. Babuska and B.Q. Guo, "The h-p version of the finite element method for domains with curved boundaries," SIAM J. Numer. Anal, vol. 25, pp. 837-861, 1988.
67. J. Jin, The Finite Element Method in Electromagnetics, 2nd. ed., New York: John Wiley & Sons, Inc., 2002.
68. P. Bettess and J. A. Bettess, "Infinite elements for static problems," Eng. Comp., vol. 1, pp. 4-15, 1984.
69. W. Pinello, M. Gribbons, and A. C. Cangellaris, "A new numerical grid truncation scheme for the Finite Difference/Finite Element solution of Laplace's equation," IEEE Trans. Magnetics, vol. 32, no. 3, pp. 1397-1400, May 1996.
70. W. C. Chew and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microwave and Optical Tech. Lett., vol. 7, pp. 599-604, Sep. 1994.
71. P. M. Morse and H. Feshbach, Methods of Theoretical Physics: Parti, New York: McGraw-Hill Book Company, Inc., 1978.
72. J-L. Coulomb, "Finite element three diemnsional magnetic field computation," IEEE Trans. Magn., vol. 17, pp. 3241-3246, Nov. 1981.
73. M. L. Barton and Z. J. Cendes, "New vector finite elements for three-dimensional magnetic field computation," J. Phys., vol 61, pp. 3919-3921, 1987.
74. K. Preis, I. Bardi, O. Biro, C. Magele, W. Renhart, K. R. Richter, and G. Vrisk, 'Numerical analysis of 3D magnetostatic fields," IEEE Trans. Magn., vol. 27, pp. 3798-3803, Sep. 1991.
75. K. Preis, I. Bardi, O. Biro, C. Magele, G. Vrisk, and K. R. Richter, "Different finite element formulations of 3D magnetostatic fields," IEEE Trans. Magn., vol. 28, pp. 1056-1059, Mar. 1992.
76. O. Biro, K. Pries, and K. R. Richter, "On the use of the magnetic vector potential in the nodal and edge finite element analysis of 3D magnetostatic problems," IEEE Trans. Magn., vol. 32, no. 3, pp. 651-654, May 1996.
77. J. R. Brauer, S. M. Schaefer, J. F. Lee, and R. Mittra, "Asympotic boundary condition for three dimensional magnetostatic finite elements," IEEE. Trans. Magn., vol. 27, no. 6, pp. 5013-5017, Nov. 1991.
78. J. B. Manges and Z. Cendes, "A generalized tree-cotree gauge for magnetic field computation," IEEE Trans. Magn., vol. 31, no. 3, pp. 1342-1347, May 1995.
79. O. Biro and K. Preis, "On the use of magnetic vector potential in the finit element analysis of 3-D eddy currents", IEEE Trans. Magn., vol. 25, pp. 3145-359, Jul. 1989.
80. A. Kameari, "Study on 3D eddy current analysis using FEM," 4th International IGTE Symposium and European TEAM Workshop, Graz, Austria, 10-12, Oct. 1990, pp. 91-99.
81. R. Albanese and G. Rubinacci, "Solution of three dimensional eddy current problems by integral and differential methods", IEEE Trans. Magn., vol. 26, pp. 702-705, Mar. 1990.
82. O. Biro, "Edge edge formulations of eddy current problems," Computer Methods in Applied Machanics and Engineering, vol. 169, no. 3-4, pp. 391-405, 1999.
83. O. Biro, P. Bohm, K. Preis, and G. Wachutka, "Edge finite element analysis of transient skin effect problems," IEEE Trans. Magn., vol. 36, no. 4, pp. 835-839, July. 2000.
84. D. Mayergoyz, "A new approach to the calculation of three-dimensional skin effect problems," IEEE Trans. Magn., vol. 19, pp. 2198-2200, Sep. 1993.
85. K. Fujiwara, T. Nakata, and H. Ohashi, "Improvement of convergence characteristics of ICCG method for the A-4> method using edge elements," IEEE Trans. Magn., vol. 32, pp. 804-807, 1996.
86. R. Dyczij-Edlinger and O. Biro, "A joint vector and scalar potential formulation for driven highfrequency problems using hybrid edge and nodal finite elements," IEEE Trans. Microwave Theory Tech., vol. 44, pp. 15-23, Jan. 1995.
87. P. P. Silvester and G. Pelosi, (Editors), Finite Elements for Electromagnetics: Methods and Techniques, Piscataway, NJ: IEEE Press, 1994.
88. J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., vol. 114, no. 2, pp. 185-200, 1994.
89. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propagat., vol. AP-43, pp. 1460-1463, Dec. 1995.
90. L. Zhao and A. C. Cangellaris, "GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids," IEEE Trans. Microwave Theory Tech., vol. 44, no. 12, pp. 2555-2563, Dec. 1996.
91. S. D. Gedney, "An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat., vol. AP-44, pp. 1630-1639, Dec. 1996.
92. R. Dyczij-Edlinger, G. Peng, and J. F. Lee "A fast vector-potential method using tangentially continuous vector finite elements," IEEE Trans. Microwave Theory Tech. vol. 46, pp. 863-868, Jun. 1998.
93. Y. Zhu and A. C. Cangellaris, "A new FEM formulation for reduced order electromagnetic modeling," IEEE Microw. Guid. Wave Lett., May 2001.
94. A. Cangellaris, M. Celik, S. Pasha, and L. Zhao, "Electromagnetic model order reduction for system-level modeling," IEEE Trans. Microw. Theory Tech., vol. 47, no. 6, pp. 840-849, June 1999.
95. A. Ruehli, "Equivalent circuit models for three-dimensional multiconductor system," IEEE Trans. Microwave Theory Tech., vol. MTT-22, pp. 216-221, Mar. 1974
96. H. Heeb and A. E. Ruehli, "Three-dimensional interconnect analysis using partial element equivalent circuits," IEEE Trans. Circuits and Systems, vol. 39, no. 11, pp. 974-982, Nov. 1992.
97. W. Pinello, A. C. Cangellaris, and A. Ruehli, "Hybrid electromagnetic modeling of noise interactions in packaged electronics based on the Partial-Element Equivalent-Circuit formulation," IEEE Trans. Microwave Theory Tech., vol. 45, no. 10, pp. 1889-1896, Oct. 1997.
98. A. E. Ruehli and A. C. Cangellaris, "Progress in the methodologies for the electrical modeling of interconnects and electronic packages," Proc. of the IEEE, vol. 89, no. 5, pp. 740-771, May 2001.
99. A. Rong, A. C. Cangellaris, and L. Dong, "Comprehensive broadband electromagnetic modeling of on-chip interconnects with a surface discretization-based generalized PEEC model," IEEE Trans. Advanced Packaging, vol. 28, no. 3, pp. 434-444, Aug. 2005.
100. R. F. Harrington, Time-Harmonic Electromagnetic Fields, Piscataway, NJ: IEEE Press Series on Electromagnetic Wave Theory, 2001.
101. S. M. Rao, D. R. Wilton, and A. W Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., vol. 30, pp. 409-418, May 1982.
102. J. Van Bladel, Electromagnetic Fields, New York: Hemisphere Publishing Corporation, 1985.
103. W. Wu, A. W. Glisson, and D. Kajfez, "A study of two numerical solution procedures for the electric field integral equation at low frequency.' Appl. Computat. Electromag. Soc. J., vol. 10, no. 3, pp. 69-80, Nov. 1995.
104. J.-S. Zhao and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," IEEE Trans. Antennas Propagat., vol. 48, no. 10, pp. 1635-1645, Oct. 2000.
105. M. Kammon, N. A. Marques, L. M. Silveira, and J. White, "Automatic generation of accurate circuit models of 3-D interconnect," IEEE Trans. Comp. Pack. & Manufacturing Tech. Part B, vol. 21, no. 3, pp. 225-234, Aug. 1998.
106. A. Rong and A. C. Cangellaris, "Electromagnetic modeling of interconnects for mixed-signal integrated circuits from DC to multi-GHz frequencies," Proc. IEEE Intl. Microwave Symposium, vol.3, pp. 1893-1896, 2002.
107. Y. Saad, Iterative Methods for Sparse Linear Systems, New York: SIAM, 2003.
108. R. Barrett, et al., Templates for Iterative Solution of Linear Systems, New York: SIAM, 1992.
109. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Baltimore: Johns Hopkins University Press, 1996.
110. R. Lee and A. Cangellaris, "A study of the discretization error in the finite element approximation of wave solutions," IEEE Trans. Antennas Propagat., vol. AP-40, pp. 542-548, May 1992.
111. W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial, 2nd ed., New York: SIAM, 2000.
112. S. McCormick, Multigrid Methods, vol 3 of SIAM Frontiers Series, Philadelphia:SIAM, 1987.
113. U. Trottenberg, C. O. Osterlee, and A. Schuller, Multigrid, London: Academic Press, 2001.
114. R. Lee and A. C. Cangellaris "A study of discretization error in the finite element approximation of wave solutions," IEEE Trans. Antennas Pmpagat., vol. 40, pp. 542-549, May 1992.
115. A. C. Cangellaris and R. Lee, "On the accuracy of numerical wave simulations based on finite methods," Journal of Electromagnetic Waves and Applications, vol. 6, pp. 1635-1653, Dec. 1992.
116. G. S. Warren and W. R. Scott, "Numerical Dispersion of Higher Order Nodal Elements in the Finite-Element Method," IEEE Trans. Antenna Prop., vol. 44, no. 3, pp. 317-327, Mar. 1996.
117. R. Mullen and T. Belytschko, "Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation," Int. J. Num. Methods Eng., vol. 18, pp. 11-29, 1982.
118. W. R. Scott, "Errors due to spatial discretization and numerical precision in the finite-element methods," IEEE Trans. Antennas, Prop., vol. 42, pp. 1565-1570, Nov. 1994.
119. M. L. Barton and Z. J. Cendes, "New vector finite elements for three-dimensional magnetic field computation," J. Appl. Phys., vol. 61, pp. 3919-3921, 1987.
120. R. Dyczij-Edlinger and O. Biro, "A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements," IEEE Trans. Micro-wave Theory Tech., vol. 44, pp. 15-23, Jan. 1996.
121. R. Dyczij-Edlinger, G. Peng, and J. F. Lee "A fast vector-potential method using tangentially continuous vector finite elements," IEEE Trans. Microwave Theory Tech. vol. 46, pp. 863-868, Jun. 1998.
122. R. Dyczij-Edlinger, G. Peng, and J. F. Lee, "Stability conditions for using TVFEMs to solve Maxwell equations in the frequency domain," Int. J. Numer. Model.: Electron. Netw. Devices Fields, vol. 13, pp. 245-260, 2000.
123. R. Beck and R. Hiptmair, "Multilevel solution of the time-harmonic Maxwell's equations based on edge elements," Int. J. Numer. Methods Eng., vol. 45, pp. 901-920, 1999.
124. R. Hiptmair, "Multigrid method for Maxwell's equations," SIAM J. Numer. Anal, vol. 36, no. 1, pp. 204-225, 1999.
125. R. Lee and A. C. Cangellaris, "A study of discretization error in the finite element approximation of wave solutions," IEEE Trans. Antennas Propagat., vol. 40, pp. 542-549, May 1992.
126. A. F. Peterson and D. R. Wilton, "Curl-conforming mixed-order edge elements for discretizing the 2D and 3D vector Helmholtz equation," in Finite Element Software for Microwave Engineering, T. Itoh, G. Pelosi and P.P. Silvester, Eds. New York: John Wiley & Sons, 1996, pp. 101-125.
127. J. P. Webb and S. McFee, "Nested tetrahedra finite elements for h-adaption," IEEE Trans. Magnetics, vol. 35, pp. 1338-1341, May 1999.
128. Y. Zhu and A. C. Cangellaris "Nested multigrid vector and scalar potential finite element method for fast computation of two-dimensional electromagnetic scattering," IEEE Trans. Antennas Propagat., Dec 2002. Vol. 50, 1850-1858.
129. J. P. Webb and S. McFee, "Nested tetrahedral finite elements for /i-adaption," IEEE Trans. Magnetics, vol. 15, pp. 1338-1341, May 1999.
130. S. P. Marin, "Computing scattering amplitudes for arbitrary cylinders under incident plane waves," IEEE Trans. Antennas Propagat., vol. AP-30, pp. 1045-1049, Nov. 1982.
131. K. D. Paulsen, D. R. Lynch and J. W. Strohbehn, "Three-dimensional finite, boundary, and hybrid element solutions of the Maxwell equations for lossy dilectric media," IEEE Trans. Microwave Theory Tech., vol. 36, pp. 682-693, Apr. 1988.
132. J. M. Jin and V. V. Liepa, "A note on hybrid finite element method for solving scattering problems," IEEE Trans. Antennas Propagat., vol. 36, pp. 1486-1490, Oct. 1988.
133. Z. Gong and A. W. Glisson, "A hybrid equation approach for the solution of electromagnetic scattering problems involving two-dimensional inhomogeneous dielectric cylinders," IEEE Trans. Antennas Propagat., vol. 38, pp. 60-68, Jan. 1990.
134. X. Yuan, "Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 1053-1058, Aug. 1990.
135. J. M. Jin and J. L. Volakis, "A hybrid finite element method for scattering and radiation by two-and three-dimensional structures," IEEE Trans. Antennas Propagat., vol. 39, pp. 1598-1604. Nov. 1991.
136. S. S. Bindiganavale and J. L. Volakis, "A hybrid FE-FMM technique for electromagnetic scattering," IEEE Trans. Antennas Propagat., vol. 45, pp. 180-183, Jan. 1997.
137. J. L. Volakis, A. Chatterjee, and J. Gong, "A class of hybrid finite element methods for electromagnetics: A review," J. Electromagn. Waves Applications, vol. 8, no. 9/10, pp. 1095-1124, 1994.
138. X. Q. Sheng, J. M. Jin, J. Song. C. C. Liu, and W. C. Chew, "On the formulation of hybrid finite-element and boundary integral methods for 3-D scattering," IEEE Trans. Antennas Propagat., vol. 46, no. 3, pp. 303-313, Mar. 1998.
139. N. Lu and J. M. Jin, "Application of fast multipole method to finite-element boundary integral solution of scattering problems," IEEE Trans. Antennas Propagat., vol. 44, no. 6, pp. 781-791, Jun. 1996.
140. J. Liu and J. M. Jin, "A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering," IEEE Trans. Antennas Propaga., vol. 50, no. 9, Sep. 2002.
141. M. C. Cote, M. B. Woodworth, and A. D. Yaghjian, "Scattering from the perfectly conducting cube," IEEE Trans. Antennas Propagat., vol. 36, pp. 1321-1329, Sep. 1988.
142. Y. Zhu and A. C. Cangellaris, "Nested multigrid vector and scalar potential finite element method for three-dimensional time-harmonic electromagnetic analysis," Radio Science, vol. 37, May 2002.
143. Y. Zhu and A. C. Cangellaris, "Robust multigrid preconditioner for fast finite element modeling of microwave devices," IEEE Microw. Wireless Compon. Letters, vol. 11, pp. 416-418, Oct. 2001.
144. D. M. Pozar, Microwave Engineering, 2nd ed., New York: John Wiley & Sons Inc., 1998.
145. R. F. Harrington, Time-Harmonic Electromagnetic Fields, IEEE Press Series on Electromagnetic Wave Theory, New York: Wiley Interscience, John Wiley & Sons Inc., 2001.
146. R. E. Collin, Field Theory of Guided Waves, 2nd ed., IEEE Press Series on Electromagnetic Wave Theory, New York: Wiley Interscience, John Wiley & Sons Inc., 1990.
147. Z. J. Cendes and J. F. Lee, "The transfinite element method for modeling MMIC devices," IEEE Trans. Microwave Theory Tech., vol 36, no. 12, pp. 1639-1649, Dec. 1988.
148. D-K. Sun, J. F. Lee, and Z. Cendes, "The transfinite element time-domain method," IEEE Antennas and Propagation Society Symposium, 2003 IEEE, vol. 1, p.693, 22-27 Jun. 2003.
149. D. Crawford and Z. Cendes, "Domain decomposition via the transfinite element method," IEEE Antennas and Propagation Society Symposium, 2004 IEEE, vol. 1, pp. 347-350, 20-25 Jun. 2004.
150. A. Morini and T. Rozzi, "On the definition of the generalized scattering matrix of a lossless multiport," IEEE Trans. Microwave Theory Tech., vol. 49, no. 1, pp. 160-165, Jan. 2001.
151. A. C. Polycarpou, P. A. Tirkas, and C. A. Balanis, "The finite-element method for modeling circuits and interconnects for electromagnetic packaging," IEEE Trans. Microwave Theory Tech., vol. 45, pp. 1868-1874, Oct. 1997.
152. G. Dfnzeo, F. Giannini, and R. Sorrentino, "Wide-band equivalent circuits of microwave planar networks," IEEE Trans. Microwave Theory Tech., vol. 10, pp. 1107-1113, Oct. 1980.
153. J. P. Webb and B. Forghani, "Hierarchical scalar and vector tetrahedra," IEEE Trans. Magnetics, vol. 29, pp. 1495-1498, May 1993.
154. G. Peng, "Multigrid preconditioning in solving time-harmonic wave propagation problems using tangential vector finite elements," Ph.D. dissertation, Worcester Polytechnic Institute, Worcester, MA, 1997.
155. G. Peng, R. Dyczij-Edlinger, and J. F. Lee, "Hierarchical methods for solving matrix equations from TVFEM for microwave components," IEEE Trans. Magnetics, vol. 35, pp. 1474-1477, May 1999.
156. Tsukerman and A. Plaks, "Hierarchical basis multilevel preconditioners for 3D magnetostatic problems," IEEE Trans. Magnetics, vol. 35, pp. 1143-1147, May 1999.
157. C. Geuzaine, B. Meys, P. Dular and W. Legros, "Convergence of high order curl-conforming finite elements," IEEE Trans. Magnetics, vol. 35, pp. 1442-1445, May 1999.
158. Y. Zhu and A. Cangellaris, "Hierarchical multilevel potential preconditioner for fast finite element modeling of microwave devices," IEEE Trans. Microwave Theory Tech., vol. 50, pp. 1984-1989, Aug. 2002.
159. Y. Zhu and A. C. Cangellaris, "Hybrid multilevel/multigrid potential preconditioner for fast finite element modeling", IEEE Microwave Wireless Compon. Lett., Volume: 12, Issue: 8, pp. 290-292, Aug. 2002.
160. T. Sieverding and F. Arndt, "Field theoretic CAD of open or aperture matched T-junction coupled rectangular waveguide structures," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 353-363, Feb. 1992.
161. J. E. Bracken, D. K. Sun, and Z. J. Cendes, "S-domain methods for simultaneous time and frequency characterization of electromagnetic devices," IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1277-1290, Sep. 1998.
162. Y. Saad, Numerical Methods for Large Eigenvalue Problems, New York: Halsted Press, 1992.
163. J. Cullum and R. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Basel: Birkhause, 1985.
164. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Baltimores: Johns Hopkins University Press, 1996.
165. B. N. Parlett, The Symmetric Eigenvalue Problem, Englewood Cliffs, NJ: Prentice-Hall, 1980.
166. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst (eds.), Templates for the Solution of Algebraic Eigenvalue Problems-A Practical Guide, Philadelphia: SIAM, 2000.
167. E. Anderson, Z. Bai, C. Bischof, S. Blackford, D. Demmel, J. Dongarra, J. Du Croz, A. Green-baum, S. Hammarling, A. McKenney, D. Sorensen, LAPACK Users' Guide, Third edition, Philadelphia: SIAM, 1999.
168. R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, Philadelphia: SIAM, 1998.
169. S. Ahmed and P. Daly, "Finite element method for inhomogeneous waveguide," IEE Proc. vol. 116, pp. 1661-1664, Oct. 1969.
170. P. Daly, "Hybrid-mode analysis of microstrip by finite-element methods," IEEE Trans. Microwave Theory Tech., vol. MTT-19, pp. 19-25, Jan. 1971.
171. Z. J. Cendes and P. Silvester, "Numerical solution of dielectric loaded waveguides: I. Finite element analysis," IEEE Trans. Microwave Theory Tech., vol. 18, pp. 1124-1131, Dec. 1970.
172. C. Yel. K. Ha, S. B. Dong, and W. P. Brown, "Single-mode optical waveguides," Appl. Opt., vol. 18, pp. 1490-1504, May 1979.
173. K. Oyamada and T. O. Okoshi, 'Two-dimensional finite-element method calculation of propagation characteristics of axially nonsymmetrical optical fibers," Radio Science, vol 17, pp. 109-116, Jan.-Feb. 1982.
174. P. Savi, I. L. Gheorma, and R.D. Graglia, "Full-wave high-order FEM model for lossy anisotropic waveguides," IEEE Trans. Microwave Theory Tech., vol. 50, pp. 495-500, Feb. 2002.
175. W. C. Chew and M. A. Nasi "A variational analysis of anisotropic, inhomogeneous dielectric waveguides," IEEE Trans. Microwave Theory and Tech., vol. 37, pp. 661-668, Apr. 1989.
176. K. Radhakrishnan and W. C. Chew, "Full-wave analysis of multiconductor transmission lines on anisotropic inhomogeneous substrates," IEEE Trans. Microwave Theory Tech., vol. 47, no. 9, Sep. 1999.
177. A. J. Kobelansky and J. P. Webb, "Eliminating spurious modes in finite-element waveguides problems by using divergence-free fields," Electron. Lett., vol. 22, pp. 569-570, 1986.
178. J. P. Webb, "Finite element analysis of dispersion in waveguides with sharp metal edges," IEEE Trans. Microwave Theory Tech., vol. 36, pp. 1719-1824, Dec. 1988
179. J. F. Lee, D. K. Sun, and Z. J. Cendes, "Full-wave analysis of dielectric waveguides using tangential vector finite elements," IEEE Trans. Microwave Theory Tech., vol. 37, pp. 1262-1271, Aug. 1991.
180. J. F. Lee, "Finite element analysis of lossy dielectric waveguides," IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1025-1031, Jun. 1994.
181. S. V. Polstyanko and J. F. Lee, "Hi (curl) tangential vector finite element method for modeling anisotropic optical fibers," J. Lightwave Technol, vol. 13, pp. 2290-2295, Nov. 1995.
182. S. Lee, J. Lee, and R. Lee, "Hierarchical vector finite elements for analyzing waveguiding structures," IEEE Trans. Microwave Theory Tech., vol. 51, pp. 1897-1905, Aug. 2003.
183. T. Angkaes, M. Matsuhara, and N. Kumagai, "Finite-element analysis of waveguide modes: A novel approach that eliminates spurious modes," IEEE Trans. Microwave Theory Tech., vol. 35, no. 2, pp. 117-125, Feb. 1987.
184. K. Hayata, K. Miura, and M. Koshiba, "Full vectorial finite element foralism for lossy anisotropic waveguides," IEEE Trans. Microwave Theory Tech., vol. 37, pp. 875-883, May 1989.
185. I. Bardi and O. Biro, "An efficient finite-element forulation without spurious modes for anisotropic waveguides," IEEE Trans. Microwave Theory Tech., vol. 37, pp. 1131-1139, Jul. 1991.
186. Y. Lu and F. A. Fernandez, "An efficient finite element solution of inhomogeneous anisotropic and lossy dielectric waveguides," IEEE Trans. Microwave Theory Tech., vol. 41, pp. 1215-1223, Jun.-Jul. 1993.
187. M. S. Alam, K. Hirayama, Y. Hayashi, and M. Koshiba, "A vector finite elemene tanalyhsis of complex modes in shielded microstrip lines," Microwave and Optical Tech. Lett., vol. 6, no. 16, pp. 873-875, Dec. 1993.
188. B. M. Dillon and J. P. Webb, "A comparison of formulations for the vector finite element analysis of waveguides," IEEE Trans. Microwave Theory Tech., vol. 41, pp. 308-316. Feb. 1994.
189. L. Valor and J. Zapata, "Efficient finite element analysis of waveguides with lossy inhomogeneous anisotropic materials characterized by arbitrary permittivity and permeability tensors," IEEE Trans. Microwave Theory Tech., vol. 43, no. 10, pp. 2452-2552, Oct. 1995.
190. B. M. Dillon and J. P. Webb, "A comparison of formulations for the vector finite element analysis of waveguides," IEEE Trans. Microwave Theory Tech., vol. 42, no. 2, pp. 308-316, Feb. 1994.
191. R. E. Collin, Field Theory of Guided Waves, 2nd. ed., Piscataway, NJ: IEEE Press, 1991.
192. A. D. Bresler, "Vector formulations for the field equations in anisotropic waveguides," IRE Trans. Microwave Theory Tech., vol. 7, 1959.
193. A. C. Cangellaris, "Numerical error in finite element solution of electromagnetic boundary value problems," in Finite Element Software for Microwave Engineering, T. Itoh, G. Pelosi and P.P. Silvester, Eds., pp. 347-382, New York: John Wiley & Sons, 1996.
194. R. H. Jansen, "High-speed computation of single and coupled microstrip parameters including dispersion, high-order modes, loss, and finite strip thickness," IEEE Trans. Microwave Theory Tech., vol. 26, pp. 75-82, Feb. 1978.
195. C. H. Chan, K. T. Ng, and A. B. Kouki, "A mixed spectral-domain approach for dispersion analysis of suspended planar transmission lines with pedestals," IEEE Trans. Microwave Theory Tech., vol 37, pp. 1716-1723, Nov. 1989.
196. K. Ogusu, "Numerical analysis of the rectangular dielectric waveguide and its modifications," IEEE Trans. Magnetics, vol. MAG-19, pp. 2551-2554, 1983.
197. M. S. Alam, M. Koshiba, K. Hirayama, and Y. Hayashi, "Hybrid-mode analysis of multilayered and multiconductor transmission lines," IEEE Trans. Microwave Theory Tech., vol. 44, pp. 205-211, Feb. 1997.
198. K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd edition, Norwood, MA: Artech House, 1996.
199. F. Di Paolo, Networks and Devices Using Planar Transmissions Lines, CRC Press, 2000.
200. C.R.Paul, Analysis of MulticonductorTransmission Lines, New York: Wiley-Interscience, 1994.
201. F. Olyslager, Electromagnetic Waveguides and Transmission Lines, Oxford: Clarendon Press, 1999.
202. T. V. Yioultsis and A. C. Cangellaris, "Optimal synthesis of finite difference models for multi-conductor transmission lines via Gaussian spectral rules," Proc. 2002 Electronic Components and Technology Conference (ECTC), May 2002.
203. T. V. Yioultsis, A. Woo, and A. C. Cangellaris, "Passive synthesis of compact frequency-dependent interconnect models via quadrature spectral rules," ICCAD-2003 Digest of Technical Papers, pp. 827-834, Nov. 2003.
204. D. M. Pozar, Microwave Engineering, 2nd. ed., New York: John Wiley & Sons, Inc., 1998.
205. J. F. Lee and R. Mittra, "A note on the application of edge-elements for modeling three-dimensional inhomogeneously-filled cavities," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 1767-1773, Sep. 1992.
206. J. F. Lee, G. M. Wilkins, and R. Mittra, "Finite element analysis of axisymmetric cavity resonator using hybrid edge element technique," IEEE Trans. Microwave Theory Techn., vol. 41, no. 11, pp. 1981-1987, Nov. 1993.
207. S. Prepelitsa, R. Dyczij-Edlinger, and J. F. Lee, "Finite-element analysis of arbitrarily shaped cavity resonators using HI (curl) elements," IEEE Trans. Magnetics, vol. 33, pp. 1776-1779, Mar. 1997.
208. D. B. Davidson, "Comments on and extension of "A note on the application of edge-elements for modeling three-dimensional inhomogeneously-filled cavities," IEEE Trans. Microwave Theory Tech., vol. 46, no. 9, Sep. 1998.
209. C. Liu and J. F. Lee, "Jacobi-Davidson algorithm and its application to modeling RF/Microwave detection circuits," Comput. Methods Appl. Meek Engrg., vol. 169, pp. 359-375, 1999.
210. W. P. Carpes Jr. L. Pichon, A. Razek, "Efficient analysis of resonant cavities by finite element method in the time domain," IEE Proc. Microw. Antennas Propag., vol. 147, no. 1, pp. 53-57, Feb. 2000.
211. D. Schmitt and T. Weiland, "2D and 3D computations of eigenvalue problems," IEEE Trans. Magnetics, vol. 28, pp. 1793-1796, Mar. 1992.
212. D. Schmitt and T. Weiland, "2D and 3D computations of lossy eigenvalue problems," IEEE Trans. Magnetics, vol. 30, no. 5, pp. 3578-3581, Sep. 1994
213. Y. Lu, S. Zhu, and F. A. Fernandez, "The efficient solution of large sparse nonsymmetric and complex eigensystems by subspace iterations," IEEE Trans. Magnetics, vol. 30, no. 5, pp. 3582-3585, Sep. 1994.
214. S, Groiss, I. Bardi, O. Biro, K. Preis, and K. R. Richter, "Parameters of lossy cavity resonators calculated by the finite element method," IEEE Trans. Magnetics, vol. 32, pp. 894-897, May 1996.
215. J. Wang and N. Ida, "Eigenvalue analysis in EM cavities using divergence-free finite elements," in Proc. Fourth Biennial IEEE Conf. on Electromagnetic Field Computation, Toronto, Canada, 1990.
216. J. S. Wang and N. Ida, "Eigenvalue analysis in electromagnetic cavities using divergence free finite elements," IEEE Trans. Magnetics, vol. 27, pp. 3378-3381, Sep. 1991.
217. A. Konrad, "A direct three-dimensional finite element methods for the solution of electromagnetic fields in cavities," IEEE Trans. Magnetics, MAG-21, no. 6, pp. 2276-2279, 1985.
218. J. P. Webb, "The finite-element method for finding modes of dielectric-loaded cavities," IEEE Trans. Microwave Theory Tech., MTT-33, pp. 635-639, Jul. 1985.
219. A. J. Kobelansky and J. P. Webb, " Eliminating spurious modes in finite-element waveguides problems by using divergence-free fields," Electron. Lett., vol. 22, pp. 569-570, 1986.
220. J. P. Webb, " Efficient generation of divergence-free fields for the finite element analysis of 3D cavity resonators," IEEE Trans. Magnetics, vol. 24, no. 1, pp. 162-165, 1988.
221. K. Sakiyama, H. Kotera, and A. Ahagon, "3-D electromagnetic field mode analysis using finite-element mode by edge element," IEEE Trans. Magnetics, vol. 26, no 5, pp. 1759-1761, 1990.
222. D. Baillargeat, S. Verdeyme, M. Aubourg, and P. Guillon, "CAD applying the finite-element method for dielectric resonator filters," IEEE Trans. Microwave Theory Tech., vol. 46, no. 1. pp. 10-17, Jan. 1998.
223. Y. Zhu and A. C. Cangellaris, "A new FEM formulation for reduced order electromagnetic modeling," IEEE Microw. Guid. Wave Lett., vol. 11, pp. 211-213. May 2001.
224. Y. Zhu and A. C. Cangellaris, "Robust finite element solution of lossy and unbounded electromagnetic eigenvalue problems," IEEE Trans. Microwave Theory Tech., vol. 50, pp. 2331-2338, Oct. 2002
225. J.D. Jackson, Classical Electrodynamics, 3rd ed., New York: John Wiley & Sons, Inc., 1999.
226. R.E. Collin, Field Theory of Guided Waves, 2nd ed., Piscataway, NJ: IEEE Press, 1991.
227. R.S. Elliott, An Introduction to Guided Waves and Microwave Circuits, Englewood Cliffs, NJ: Prentice-Hall, Inc., 1993.
228. Y. Saad, Numerical Methods for Large Eigenvalue Problems, New York: John Wiley & Sons, 1992.
229. J. F. Lee, R. Lee, and A. Cangellaris, "Time-domain finite-element methods," IEEE Trans. Antennas Propagat., vol. 45, pp. 430-442, Mar. 1997.
230. Advanced Design System EDA Software, Agilent EEsof EDA, URL: http://eesof.tm.agilent.com/.
231. R. E. Collin, Foundations for Microwave Engineering, 2nd edition, New York: McGraw-Hill Inc., 1992.
232. D. M. Pozar, Microwave Engineering, 2nd edition, New York: John Wiley & Sons, 1998.
233. R. F. Harrington, Time-Harmonic Electromagnetic Fields, 2nd edition, Piscataway, NJ: Wiley-IEEE Press, 2001.
234. J.M. Jin, The Finite Element Method in Electromagnetics, 2nd edition, New York: John Wiley & Sons, 2002.
235. J.-D. Benamou and B. Després, "A domain decomposition method for the Helmholtz equation and related optimal control problems," J. Comput. Phys., vol. 136, pp. 68-82, 1997.
236. A. Piacentini and N. Rosa, "An improved domain decomposition method for the 3D Helmholtz equation," Comput. Methods Appl. Mech. Engrg., vol. 162, pp. 113-124, 1998.
237. M. Gander, F. Magoules, and F. Nataf, "Optimized Schwarz methods without overlap for the Helmholtz equation," SI AM J. Sci. Comput, vol. 24, no. 1, pp. 38-60, 2002.
238. M. N. Vouvakis and J.-F. Lee, "A fast DP-FETI like domain decomposition algorithm for the solution of large electromagnetic problems," Proc. Eighth Copper Mountain Conference on Iterative Methods Copper Mountain, Co, Mar. 2004.
239. L. T. Pillage and R. A. Rohrer, "Asymptotic waveform evaluation for timing analysis," IEEE Trans. Computer-Aided Design, vol. 33, no. 9, pp. 352-366, Apr. 1990.
240. E. Chiprout and M.S. Nakhla, Asymptotic Waveform Evaluation and Moment Matching for Interconnect Analysis, Norwell, MA: Kluwer Academic Publishers, 1994.
241. P. Feldmann and R. W. Freund, "Efficient linear circuit analysis by Pad6 approximation via the Lanczos process," IEEE Trans. Computer-Aided Design, vol. 34, pp. 639-649, May 1995.
242. R. Freund, "Reduced-order modeling techniques based on Krylov subspaces and their use in circuit simulation," Bell Laboratories, Murray Hill, NJ., Numerical Analysis Manuscript 98-3-02, Feb. 1998.
243. R. W. Freund, "Passive reduced-order models for interconnect simulation and their computation via Krylov-subspace algorithms," in Proc. 1999 Design Automation Conference, Jun. 1999.
244. D.L. Boley, "Krylov space methods on state-space control models," Circuits, Syst. Signal Process., vol. 18, pp. 733-758, 1994.
245. K. Gallivan, E. Grimme, and P. Van Dooren, "Padd approximation of large-scale dynamic systems with Lanczos method," in Proc. 33rd Conference on Decision and Control, Buena Vista, FL., Dec. 1994, pp. 443-448.
246. A. Odabasioglu, M. Celik, andL. T. Pileggi, "PRIMA: Passive reduced-order interconnect macro-modeling algorithm," IEEE Trans. Computer-Aided Design, pp. 645-653, Aug. 1998.
247. M. Celik, L. Pileggi, and A. Odabasioglu, IC Interconnect Analysis, Norwell, MA: Kluwer Academic Publishers, 2002.
248. M. A. Kolbehdari, et al., "Simultaneous time and frequency domain solution of EM problems using finite element and CFH techniques," IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1526-1534, Sep. 1996.
249. J. P. Zhang and J. M. Jin, "Preliminary study of AWE method for FEM analysis of scattering problems," Microwave and Optical Tech. Letters, vol. 17, no. 1, pp. 7-12, Jan. 1998.
250. J. E. Bracken, D. K. Sun, and Z. J. Cendes, "S-domain methods for simultaneous time and frequency characterization of electromagnetic devices," IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1277-1290, Sep. 1998.
251. X. M. Zhang and J. F. Lee, "Application of the AWE method with the 3-D TVFEM to model spectral responses of passive microwave components," IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1735-1741, Nov. 1998.
252. D. K. Sun, J. F. Lee, and Z. Cendes "ALPS-A new fast frequency-sweep procedure for microwave devices," IEEE Trans. Microwave Theory Tech., vol. 49, no. 2, pp. 398-401, Feb. 2001
253. M. Celik and A. C. Cangellaris, "Simulation of dispersive multiconductor transmission lines by Pade' approximation via the Lanczos process," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 2525-2535, Dec. 1996.
254. M. Zunoubi, K. C. Donepudi, J. M. Jin, and W. C. Chew, "Efficient time-domain and frequency-domain finite-element solution of Maxwell's equations using spectral Lanczos algorithms," IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1141-1149, Aug. 1998.
255. J. Rubio, J. Garcia, and J. Zapata, "SFELP: A hybrid 3-D finite elements / segmentation method with fast frequency sweep based on the SyMPVL algorithm for the analysis of passive microwave circuits," in Proc. of the 2000 IEEE APS International Symposium, Salt Lake City, UT, July 2000.
256. Y. Zhu and A. C. Cangellaris, "A new FEM formulation for reduced order electromagnetic modeling," IEEE Microw. Guid. Wave Lett., vol. 11. no. 5, May 2001, pp. 211-213. May 2001.
257. Y. Zhu and A. C. Cangellaris, "Macro-elements for efficient FEM simulation of small geometric features in waveguide components," IEEE Trans. Microwave Theory Tech., vol. 48, pp. 2254-2260, Dec. 2000.
258. Y. Zhu and A. C. Cangellaris, "Macro-modeling of microwave components using finite elements and model order reduction," in 5th Workshop on Finite Element Methods for Microwave Engineering, Boston, June 2000
259. Y. Zhu and A. C. Cangellaris, "Finite element-based model order reduction of electromagnetic devices", International Journal of Numerical Modeling: Electronic Networks, Devices and Fields, vol. 15, Issue 1, pp. 73-92, 2002.
260. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst (eds.), Templates for the Solution of Algebraic Eigenvalue Problems-A Practical Guide, Philadelpia: SIAM, 2000.
261. R. A. Rohrer and H. Nosrati, "Passivity considerations in stability studies of numerical integration algorithms," IEEE Trans. Circuits Syst., vol. 17, pp. 857-866, 1981.
262. R. Achar and M.S. Nakhla, "Simulation of high-speed interconnects," Proc. IEEE, vol. 89, no. 5, pp. 693-728, May 2001.
263. A. C. Cangellaris and L. Zhao, "Passivity of discrete electromagnetic systems," in Proc. 14th Annu. Rev. Progress Appl. Computat. Electromag., Monterey, CA., pp. 721-731, Mar. 1998.
264. Z. Bai, R. D. Slone, W. T. Smith, and Q. Ye, "Error bound for reduced system model by Pad6 approximation via the Lanczos process," IEEE Trans. Computer-Aided Design, vol. 48, pp. 133-141, Feb. 1999.
265. A. Odabasioglu, M. Celik, and L. T. Pileggi, "Practical considerations for RLC circuit reduction," in IEEE/ACM Proc. oflCCAD, San Jose, CA, Nov. 1999.
266. G. H. Golub and C. F. Van Loan, Matrix Computation, 3rd ed., Baltimore: Johns Hopkins University Press, 1996.
267. A. C. Cangellaris and L. Zhao, "Rapid FDTD simulation without time stepping," IEEE Microwave and Guided Wave Letters, vol. 9, no. 1, pp. 4-6, Jan. 1999.
268. A. C. Cangellaris, M. Celik, M. Pasha, and L. Zhao, "Electromagnetic model order reduction for system-level modeling," IEEE Trans. Microwave Theory Tech., vol. 47, no. 6, pp. 840-850, Jun. 1999.
269. R. F. Remis and P. M. van den Berg, "A modified Lanczos algorithm for the computation of transient electromagnetic wavefields," IEEE Trans. Microwave Theory Tech., vol. 45, no. 12, pp. 2139-2149, Dec. 1997.
270. R. F. Remis, "Low-frequency model-order reduction of electromagnetic fields without matrix factorization," IEEE Trans. Microwave Theory Tech., vol. 52, no. 9, pp. 2298-2304, Sep. 2004.
271. B. Denecker, F. Olyslager, L. Knockaert, and D. De Zutter, "Generation of FDTD subcell equations by means of reduced order modeling," IEEE Trans. Antennas Propagat., vol. 51, no. 8, pp. 1806-1817, Aug. 2003.
272. L. Kulas and M. Mrozowski, "Reduced order models of refined Yee's cells," IEEE Microwave and Wireless Components Letters, vol. 13, no. 4, pp. 164-166, Apr. 2003.
273. L. Kulas and M. Mrozowski, "Multilevel model order reduction," IEEE Microwave and Wireless Components Letters, vol. 14, no. 4, pp. 165-167, Apr. 2004.
274. T. Wittig, I. Munteanu, R. Schuhmann, and T. Weiland, 'Two-step Lanczos algorithm for model order reduction," IEEE Trans. Magnetics, vol. 38, no. 2, pp. 673-676, Mar. 2002.
275. R.H. Voelker and R. J. Lomax, "A finite-difference transmission line matrix method incorporating a nonlinear device model," IEEE Trans. Microwave Theory Tech., vol. 38, pp. 302-312, Mar. 1990.
276. W. Sui, D.A. Christensen, and C.H. Dumey, "Extending the two-dimensional FDTD method to hybrid electromagnetic systems with active and passive lumped elements", IEEE Trans. Microwave Theory Tech., vol. 40, pp. 724-730, Apr. 1992.
277. Yu-Sheng Tsuei, A.C Cangellaris, and J.L.Prince, "Rigorous electromagnetic modeling of chip-to-package (first-level) interconnections", IEEE Trans. Comp., Hybrids, Manuf. Technoi, vol. 16, pp. 876-883, Dec. 1993.
278. M. Piket-May, A. Taflove, and J. Baron, "FD-TD modeling of digital signal propagation in 3D circuits with passive and active loads," IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1514-1523, Aug. 1994.
279. K. Guillouard, Man-Fai Wong, V.F. Hanna, and J. Citerne, "A new global finite element analysis of microwave circuits including lumped elements", IEEE Trans Microwave Theory Tech., vol. 44, pp. 2587-2594, Dec. 1996.
280. M. Feliziani and F. Maradei, "Modeling of electromagnetic fields and electrical circuits with lumped and distributed elements by the WETD method," IEEE Trans. Magnetics, vol. 35, pp. 1666-1669, May 1999.
281. S.-H. Chang, R. Coccioli, Y. Qian, and T. Itoh, "A global finite-element time-domain analysis of active nonlinear microwave circuits," IEEE Trans. Microwave Theory Tech., vol. 47, no. 12, pp. 2410-2416, Dec. 1999.
282. H. Wu and A.C. Cangellaris, "Model-order reduction of finite-element approximations of passive electromagnetic devices including lumped electrical-circuit models," IEEE Trans. Microwave Theory Tech., vol. 52, no. 9, pp. 2305-2313, Sep. 2004.
283. T. Sieverding and F. Arndt, "Field theoretic CAD of open or aperture matched T-junction coupled rectangular waveguide structures," IEEE Trans. Microwave Theory Tech., vol. 28, pp. 353-362, Feb. 1992.
284. T. Ishikawa and E. Yamashita, "Experimental evaluation of basic circuit components using buried microstrip lines for constructing high-density microwave integrate circuits," IEEE Trans. Microwave Theory
285. S. D. Gedney and R. Mittra, "Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution," IEEE Trans. Antennas Propagat., vol. 39, pp. 1605-1614, Nov. 1991.
286. S. D. Gedney, J. F. Lee, and R. Mittra, "A combined FEM/MoM approach to analyze the planewave diffraction by arbitrary gratings," IEEE Trans. Microwave Theory Tech., vol. 40, pp. 363-370, Feb. 1992.
287. G. Pelosi, A. Freni, and R. Coccioli, "Hybrid technique for analyzing scattering from periodic structures," Microwaves, Antennas and Propagation, IEE Proceedings., vol. 140, pp. 65-70, Apr. 1993.
288. J. Jin and J. L. Volakis, "Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite-element method," IEEE Trans. Antennas Propagat., vol. 41, no. 11, pp. 1580-1585, Nov. 1993.
289. D. T. McGrath and V. R Pyati, "Phased array antenna analysis with the hybrid finite element method," IEEE Trans. Antennas Propagat, vol. 42, pp. 1625-1630, Dec. 1994.
290. E. W. Lucas and T. P. Fontana, "A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite period arrays," IEEE Trans. Antennas Propagat., vol. 43, pp. 145-153, Feb. 1995.
291. J. D. Angelo and I. Mayergoyz, "Phased array antenna analysis," in Finite Element Software for Microwave Engineering, G. Pelosi, P. Silvester and T. Itoh, Eds., New York: John Wiley & Sons, Inc., 1996.
292. T.F. Eibert, J.L. Volakis, D.R. Wilton, and D.R. Jackson, "Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald Transformation", IEEE Trans. Antennas Propagat., vol. 42, no. 5. pp. 843-851, May 1999.
293. J. L. Volakis, T. F. Eibert, D. S. Filipovic, Y. E. Erdemli, and E. Topsakal, "Hybrid Finite Element Methods for Array and FSS Analysis Using Multiresolution Elements and Fast Integral Techniques," Electromagn., vol. 22, no. 4, pp. 297-313, 2002.
294. R.E. Collin, "Field Theory of Guided Waves," 2nd ed., Piscataway, NJ: IEEE Press, 1991.
295. D. S. Sacks, D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use asan absorbing boundary condition," IEEE Trans. Antennas Propagat., vol. 43, pp. 1460-1463, Dec. 1995.
296. Z.J. Cendes and J.-F. Lee, "The transfinite element method for modeling MMIC devices," IEEE Trans. Microwave Theory Tech., vol. 36, no. 12, pp. 1639-1649, Dec. 1988.
297. Y. Zhu and R. Lee, "TVFEM Analysis of Periodic Structures for Radiation and Scattering," Progress in Electromagnetic Research Series (PIER-25), pp. 1-22, ISSN 1070 4698, EMW, 2000.
298. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational Phys., vol. 114, no. 2, pp. 185-200, Oct. 1994.
299. D. C. Katz, E. T. Thiele, and A. Talove, "Validation and extension to three dimensions of the Berenger absorbing boundary condition forFDTD meshes," IEEE Microwave Guided Wave Lett., vol. 4, no. 3, pp. 268-270, Aug. 1994.
300. R. Mittra and U. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microwave Guided Wave Lett., vol, 5, no. 4, pp. 84-87, Mar. 1995.
301. W. C. Chew and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equation with stretched coordinates," Microwave Optical Technol. Lett., vol. 7, no. 13, pp. 599-604, Sep. 1994.
302. D. M. Kingsland, J. Gong, J. L. Volakis, and J. F.Lee, "Performance of an anisotropic artificial absorber for truncating finite-element meshes," IEEE Trans. Antennas Propagat., vol. 44, pp. 975-981, Jul. 1996.
303. J. Y. Wu, D. M. Kingsland, J. F. Lee, and R. Lee, "A comparison of anisotropic PML to Berenger's PML and its application to the finite-element method for EM scattering," IEEE Trans. Antennas Propagat., vol. 45, pp. 40-50, Jan. 1997.
304. C. P. Wu and V. Galindo, "Properties of a phased array of rectangular waveguides with thin walls," IEEE Trans. Antennas Propagat., vol. 14, pp. 163-173, Mar. 1966.
305. V. Galindo and C. P. Wu, "Numerical solutions for an infinite phased array of rectangular waveguides with thick walls," IEEE Trans. Antennas Propagat., vol. 14, pp. 149-158, Mar. 1966.
306. H. L. Bertoni, L. S. Cheo, and T. Tamir, "Frequency-selective reflection and transmission by a periodic dielectric layer," IEEE Trans. Antennas Propagat., vol. 37, pp. 78-83, Jan. 1989.
307. W. P. Pinello, R. Lee, and A. C. Cangellaris, "Finite element modeling of electromagnetic wave interactions with periodic dielectric structures," IEEE Trans. Microwave Theory Tech., vol. 33, pp. 1083-1088, Oct. 1985.
308. R. C. Compton and D. B. Rutledge, "Approximation techniques for planar periodic structures," IEEE Trans. Microwave Theory Tech., vol. 33, pp. 1083-1099, Oct. 1985.
309. M. Hofer, R. Lerch, N. Finger, G. Kovacs, J. Schoberl, S. Zaglmayr, and U. Langer, "Finite element calculation of wave propagation and excitation in periodic piezoelectric systems," Fifth World Congress on Computational Mechanics, 7-12, Jul. 2002.
310. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals-Molding the Flow of Light, Princeton, NJ: Princeton University Press, 1995.