Numerical electromagnetics: The FDTD method

Numerical Electromagnetics: The FDTD Method

Volumn 9780521190695, Issue , 2011, Pages 1-390

  Inan, Umran S ^a,b   Marshall, Robert A ^c  

^a Stanford University   (United States)

^b KOÇ UNIVERSITY   (Turkey)

^c BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; FINITE DIFFERENCE TIME DOMAIN METHOD; MAXWELL EQUATIONS;

ANISOTROPIC MATERIAL; ELECTROMAGNETICS; FDTD ALGORITHM; FDTD SIMULATIONS; FIRST PRINCIPLES; MATHEMATICAL DERIVATION; NUMERICAL DISPERSIONS; PROFESSIONAL ENGINEER;

NUMERICAL METHODS;

EID: 84924003416     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511921353     Document Type: Book

References (144)

1. V Shankar and W. F. Hall, “A time domain differential solver for electromagnetic scattering,” in URSI National Meeting, Boulder, CO, 1988.
2. N. K. Madsen and R. W. Ziolkowski, “Numerical solutions of Maxwell’s equations in the time domain using irregular nonorthogonal grids,” Waves Motion, vol. 10, pp. 538–596, 1988.
3. S. M. Rao, ed., Time Domain Electromagnetics. Academic Press, 1999.
4. G. Pelosi, “The finite-element method, part i: R. I. Courant,” IEEE Antennas and Propagation Magazine, vol. 49, pp. 180–182, 2007.
5. Q. H. Liu, “The PSTD algorithm: A time-domain method requiring only two cells per wavelength,” Microwave Opt. Technol. Lett., vol. 15, pp. 158–165, 1997.
6. O. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Micro. Guided Wave Lett., vol. 37, pp. 917–926, 1999.
7. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
8. J. S. Hesthaven, S. Gottlieb, and D. Gottlieb, Spectral Methods for Time-Dependent Problems. Cambridge University Press, 2007.
9. R. S. Elliott, Electromagnetics. IEEE Press, 1993.
10. J. C. Maxwell, “A dynamical theory of the electromagnetic field,” Phil. Trans. Royal Soc., vol. 155, p. 450, 1865.
11. U. S. Inan and A. S. Inan, Engineering Electromagnetics. Addison-Wesley, 1999.
12. H. Hertz, “On the finite velocity of propagation of electromagnetic actions,” Sitzb. d. Berl. Akad. d. Wiss, February 1888.
13. H. Hertz, Electric Waves. London: MacMillan, 1893.
14. A. Einstein, “Uber die von der molekularkinetischen theorie der wrme geforderte bewegung von in ruhenden flussigkeiten suspendierten teilchen,” Annalen der Physik, vol. 322, pp. 549–650, 1905.
15. A. Einstein, H. A. Lorentz, H. Minkowski, and H. Weyl, The Principle of Relativity, Collected Papers. New York: Dover, 1952.
16. D. M. Cook, The Theory of the Electromagnetic Field. Prentice-Hall, 1975.
17. D. J. Griffiths, Introduction to Electrodynamics, 2nd edn. Prentice-Hall, 1989.
18. J. D. Jackson, Classical Electrodynamics, 2nd edn. Wiley, 1975.
19. J. C. Maxwell, A Treatise in Electricity and Magnetism. Clarendon Press, 1862, vol. 2.
20. C. A. de Coulomb, Première Memoire sur l’Électricité et Magnetismé (First Memoir on Électricity and Magnetism). Historie de l’Academie Royale des Sciences, 1785.
21. A. M. Ampère, Recueil d’Observation Electrodynamiques. Crochard, 1822.
22. M. Faraday, Experimental Researches in Electricity. Taylor, 1839, vol. 1.
23. J. Thuery, Microwaves: Industrial, Scientific and Medical Applications. Artech House, 1992.
24. U. S. Inan and A. S. Inan, Electromagnetic Waves. Prentice-Hall, 2000.
25. M. A. Plonus, Applied Electromagnetism. McGraw-Hill, 1978.
26. P. S. Neelakanta, Handbook of Electromagnetic Materials. CRC Press, 1995.
27. C. Kittel, Introduction to Solid State Physics, 5th edn. Wiley, 1976.
28. M. A. Brown and R. C. Semelka, MRI Basic Principles and Applications. Wiley-Liss, 1995.
29. J. A. Stratton, Electromagnetic Theory. McGraw-Hill, 1941.
30. H. H. Skilling, Fundamentals of Electric Waves. R. E. Krieger Publishing Co., 1974.
31. M. S. Bigelow, N. N. Lepeshkin, H. Shin, and R. W. Boyd, “Propagation of a smooth and discontinuous pulses through materials with very large or very small group velocities,” J. Phys: Cond. Matt., vol. 18, pp. 3117–3126, 2006.
32. G. J. Fishman and D. H. Hartmann, “Gamma-ray bursts,” Scientific American, vol. July, pp. 46–51, 1997.
33. U. S. Inan and A. S. Inan, Engineering Electromagnetics. Addison-Wesley, 1999.
34. R. N. Bracewell, The Fourier Transform and its Applications, 3rd edn. McGraw-Hill, 2000.
35. L. F. Richardson, “The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam,” Phil. Trans. Roy. Soc. London, vol. 210, Series A, pp. 305–357, 1910.
36. P. Moin, Fundamentals of Engineering Numerical Analysis. Cambridge University Press, 2001.
37. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
38. P D. Lax and B. Wendroff, “Systems of conservation laws,” Comm. PureAppl. Math., vol. 13, pp. 217–237, 1960.
39. R. D. Richtmeyer, “A survey of difference methods for nonsteady fluid dynamics; NCAR Technical Note 63–2,” National Center for Atmospheric Research, Tech. Rep., 1963.
40. S. Z. Burstein, “Finite difference calculations for hydrodynamic flows containing discontinuities,” J. Comput. Phys., vol. 2, pp. 198–222, 1967.
41. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. on Ant. and Prop., vol. 14, no. 3, pp. 302–307, 1966.
42. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
43. U. S. Inan and A. S. Inan, Electromagnetic Waves. Prentice-Hall, 2000.
44. Y. Chen, R. Mittra, and P Harms, “Finite-difference time-domain algorithm for solving Maxwell’s equations in rotationally symmetric geometries,” IEEE Trans. Microwave Theory and Tech., vol. 44, pp. 832–839, 1996.
45. H. Dib, T. Weller, M. Scardelletti, and M. Imparato, “Analysis of cylindrical transmission lines with the finite difference time domain method,” IEEE Trans. Microwave Theory and Tech., vol. 47, pp. 509–512, 1999.
46. W L. Stutzman and G. A. Thiele, Antenna Theory and Design. Wiley, 1998.
47. H. Dib, T. Weller, and M. Scardelletti, “Analysis of 3-D cylindrical structures using the finite difference time domain method,” IEEE MTT-S International, vol. 2, pp. 925–928, 1998.
48. R. Holland, “THREDS: A finite-difference time-domain EMP code in 3D spherical coordinates,” IEEE Trans. Nuc. Sci., vol. 30, pp. 4592–4595, 1983.
49. G. Liu, C. A. Grimes, and K. G. Ong, “A method for FDTD computation of field values at spherical coordinate singularity points applied to antennas,” IEEE Microwave and Opt. Tech. Lett., vol. 20, pp. 367–369, 1999.
50. J. von Neumann, “Proposal and analysis of a numerical method for the treatment ofhydrody-namical shock problems,” National Defense Research Committee, Tech. Rep. Report AM-551, 1944.
51. J. von Neumann and R. D. Richtmeyer, “A method for numerical calculation of hydrodynamic shocks,” J. Appl. Phys., vol. 21, p. 232, 1950.
52. P D. Lax, “Weak solutions on non-linear hyperbolic equations and their numerical computation,” Comm. on Pure and Appl. Math., vol. 7, p. 135, 1954.
53. R. Courant, K. O. Friedrichs, and H. Lewy, “Uber die partiellen differenzengleichungen der mathematischen physik (translated as: On the partial differential equations of mathematical physics),” Mathematische Annalen, vol. 100, pp. 32–74, 1967.
54. J. von Neumann, “Proposal and analysis of a numerical method for the treatment of hydrodynamical shock problems,” National Defense Research Committee, Tech. Rep. Report AM-551, 1944.
55. J. von Neumann and R. D. Richtmeyer, “A method for numerical calculation of hydrodynamic shocks,” J. Appl. Phys., vol. 21, p. 232, 1950.
56. R. Holland, “Threde: a free-field EMP coupling and scattering code,” IEEE Trans. Nuclear Science, vol. 24, pp. 2416–2421, 1977.
57. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
58. U. S. Inan and A. S. Inan, Electromagnetic Waves. Prentice-Hall, 2000.
59. K. R. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromag. Compat., vol. 24, pp. 397–405, 1982.
60. B. Enquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comp., vol. 31, pp. 629–651, 1977.
61. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the timedomain electromagnetic field equations,” IEEE Trans. Elec. Compat., vol. EMC-23, pp. 377–382, 1981.
62. N. Trefethen and L. Halpern, “Well-posedness of one-way wave equations and absorbing boundary conditions,” Math. Comp., vol. 47, pp. 421–435, 1986.
63. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
64. T. G. Moore, J. G. Blaschak, A. Taflove, and G. A. Kriegsmann, “Theory and application of radiation boundary operators,” IEEE Trans. Ant. and Prop., vol. 36, pp. 1797–1812, 1988.
65. A. Bayliss and E. Türkei, “Radiation boundary conditions for wave-like equations,” Comm. PureAppl. Math., vol. 23, pp. 707–725, 1980.
66. A. Sommerfeld, Partial Differential Equations in Physics. New York: Academic Press, 1949.
67. A. Bayliss, M. Gunzburger, and E. Turkel, “Boundary conditions for the numerical solution of elliptic equation in exterior regions,” SIAMJ. Appl. Math, vol. 42, pp. 430–451, 1982.
68. R. L. Higdon, “Numerical absorbing boundary conditions for the wave equation,” Math. Comp., vol. 49, pp. 65–90, 1987.
69. J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, pp. 185–200, 1994.
70. U. S. Inan and A. S. Inan, Electromagnetic Waves. Prentice-Hall, 2000.
71. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
72. M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microwave and Guided Wave Lett., vol. 6, pp. 447–449, 1996.
73. J. Roden and S. D. Gedney, “Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave and Opt. Tech. Lett., vol. 27, pp. 334–339, 2000.
74. W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Opt. Technol. Lett., vol. 7, pp. 599–604, 1994.
75. A. Balanis, Advanced Engineering Electromagnetics. New York: Wiley, 1989.
76. J. A. Stratton, Electromagnetic Theory. McGraw-Hill, 1941.
77. R. Luebbers, F. P. Hunsberger, K. S. Kunz, R. B. Ständler, and M. Schneider, “A frequency-dependent finite-difference time-domain formulation formulation dispersive materials,” IEEE Trans. on Electr. Comp., vol. 32, no. 3, pp. 222–227, 1990.
78. R. P Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics. Addison Wesley, 1964.
79. P Debye, Polar Molecules, Chapter V. New York: Chemical Catalog Co., 1929.
80. A. Beneduci, “Which is the effective time scale of the fast Debye relaxation process in water?” J. Molec. Liquids, vol. 138, pp. 55–60, 2007.
81. W. H. P Pernice, F. P Payne, and D. F. G. Gallagher, “An FDTD method for the simulation of dispersive and metallic structures,” Opt. and Quant. Elec., vol. 38, pp. 843–856, 2007.
82. W. A. Beck and M. S. Mirotznik, “Generalized analysis of stability and numerical dispersion in the discrete-convolution FDTD method,” IEEE Trans. Ant. Prop., vol. 48, pp. 887–894, 2000.
83. R. Lide, CRC Handbook of Chemistry and Physics; Internet Version 2010. CRC Press, 2010.
84. U. S. Inan and A. S. Inan, Engineering Electromagnetics. Addison-Wesley, 1999.
85. U. S. Inan and A. S. Inan, Electromagnetic Waves. Prentice-Hall, 2000.
86. R. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference timedomain formulation for transient propagation in plasma,” IEEE Trans. Ant. Prop., vol. 39, p. 29, 1991.
87. D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Ant. Prop., vol. 44, pp. 792–797, 1996.
88. T. Kashiwa and I. Fukai, “A treatment of the dispersive characteristics associated with electronic polarization,” Microwave Opt. Technol. Lett., vol. 3, p. 203, 1990.
89. R. Joseph, S. Hagness, and A. Taflove, “Direct time integration of Maxwell’s equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses,” Optics Lett., vol. 16, p. 1412, 1991.
90. M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave and Guided Wave Lett., vol. 7, pp. 121–123, 1997.
91. L. Dou and A. R. Sebak, “3D FDTD method for arbitrary anisotropic materials,” IEEE Microwave Opt. Technol. Lett., vol. 48, pp. 2083–2090, 2006.
92. A. Yariv and P. Yeh, Optical Waves in Crystals. Wiley, 1984.
93. E. Kriezis and S. J. Elston, “Light wave propagation in liquid crystal displays by the 2-D finite-difference time domain method,” Optics Comm., vol. 177, pp. 69–77, 2000.
94. M. G. Kivelson and C. T. Russell, Introduction to Space Physics. Cambridge University Press, 1995.
95. D. A. Gurnett and A. Bhattacharjee, Introduction to Plasma Physics: With Space and Laboratory Applications. Cambridge University Press, 2005.
96. J. A. Bittencourt, Fundamentals of Plasma Physics. Springer-Verlag, 2004.
97. U. S. Inan and A. S. Inan, Electromagnetic Waves. Prentice-Hall, 2000.
98. J. H. Lee and D. Kalluri, “Three-dimensional FDTD simulation of electromagnetic wave transformation in a dynamic inhomogeneous magnetized plasma,” IEEE Trans. Ant. Prop., vol. 47, no. 7, pp. 1146–1151, 1999.
99. T. W. Chevalier, U. S. Inan, and T. F. Bell, “Terminal impedance and antenna current distribution of a VLF electric dipole in the inner magnetosphere,” IEEE Trans. Ant. Prop., vol. 56, no. 8, pp. 2454–2468, 2008.
100. M. A. Alsunaidi, “FDTD analysis of microstrip patch antenna on ferrite substrate,” IEEE Microwave Opt. Technol. Lett., vol. 50, pp. 1848–1851, 2008.
101. R. W. Ziolkowski and J. B. Judkins, “Applications of the nonlinear finite difference time domain (NL-FDTD) method to pulse propagation in nonlinear media: Self-focusing and linear-nonlinear interfaces,” Radio Science, vol. 28, pp. 901–911, 1993.
102. R. W. Ziolkowski and J. B. Judkins, “Nonlinear finite-difference time-domain modeling of linear and nonlinear corrugated waveguides,” J. Opt. Soc. Am., vol. 11, pp. 1565–1575, 1994.
103. L. Teixeira, “Time-domain finite-difference and finite-element methods for Maxwell equations in complex media,” IEEE Trans. Ant. Prop., vol. 56, pp. 2150–2166, 2008.
104. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
105. M. E. Veysoglu, R. T. Shin, and J. A. Kong, “A finite-difference time-domain analysis of wave scattering from periodic surfaces: oblique incidence case,” J. Electro. Waves andAppl., vol. 7, pp. 1595–1607, 1993.
106. J. A. Roden, S. D. Gedney, M. P. Kesler, J. G. Maloney, and P H. Harms, “Time-domain analysis of periodic structures at oblique incidence: Orthogonal and nonorthogonal FDTD implementations,” IEEE Trans. Microwave Theory Techqs., vol. 46, pp. 420–427, 1998.
107. P. H. Harms, J. A. Roden, J. G. Maloney, M. P. Kesler, E. J. Kuster, and S. D. Gedney, “Numerical analysis of periodic structures using the split-field algorithm,” in Proc. 13th Annual Review of Progress in Applied Computational Electromagnetics, March 1997.
108. S. Dey and R. Mittra, “A locally conformal finite-difference time-domain algorithm for modeling three-dimensional perfectly conducting objects,” IEEE Microwave Guided Wave Lett., vol. 7, pp. 273–275, 1997.
109. S. Dey and R. Mittra, “A modified locally conformal finite-difference time-domain algorithm for modeling three-dimensional perfectly conducting objects,” IEEE Microwave Opt. Techqs. Lett., vol. 17, pp. 349–352, 1998.
110. C. J. Railton and J. B. Schneider, “An analytical and numerical analysis of several locally conformal FDTD schemes,” IEEE Trans. Microwave Theory Techqs., vol. 47, pp. 56–66, 1999.
111. J. G. Maloney and G. S. Smith, “The efficient modeling of thin material sheets in the finite-difference time-domain FDTD method,” IEEE Trans. Ant. Prop., vol. 40, pp. 323–330, 1992.
112. U. S. Inan and A. S. Inan, Electromagnetic Waves. Prentice-Hall, 2000.
113. C. A. Balanis, Advanced Engineering Electromagnetics. Wiley, 1989.
114. J. D. Jackson, Classical Electrodynamics, 2nd edn. Wiley, 1975.
115. R. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference timedomain formulation for transient propagation in plasma,” IEEE Trans. Ant. Prop., vol. 39, p. 29, 1991.
116. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Ant. Prop., vol. 14, no. 3, pp. 302–307, 1966.
117. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
118. F. Zheng, Z. Chen, and J. Zhang, “A finite-difference time-domain method without the courant stability conditions,” IEEE Microwave Guided Wave Lett., vol. 9, pp. 441–443, 1999.
119. F. Zheng, Z. Chen, and J. Zhang, “Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method,” IEEE Trans. on Microwave Theory Tech., vol. 48, pp. 1550–1558, 2000.
120. F. Zheng and Z. Chen, “Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method,” IEEE Trans. Microwave Theory and Techqs., vol. 49, pp. 1006–1009, 2000.
121. J. D. Hoffman, Numerical Methods for Engineers and Scientists. McGraw-Hill, 1992.
122. J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type,” Proc. Camb. Phil. Soc., vol. 43, pp. 50–67, 1947.
123. Y. Yang, R. S. Chen, and E. K. N. Yung, “The unconditionally stable Crank Nicolson FDTD method for three-dimensional Maxwell’s equations,” IEEE Microwave Opt. Technol. Lett., vol. 48, pp. 1619–1622, 2006.
124. J. Van Bladel, Electromagnetic Fields, 2nd edn. Wiley Interscience, 2007.
125. C. M. Rappaport, M. Kilmer, and E. Miller, “Accuracy considerations in using the PML ABC with FDFD Helmholtz equation computation,” Int. J. Numer. Model., vol. 13, pp. 471–482, 2000.
126. P. Monk and E. Suli, “A convergence analysis of Yee’s scheme on non-uniform grids,” SIAM J. Num. Analysis, vol. 31, pp. 393–412, 1994.
127. P Monk, “Error estimates for Yee’s method on non-uniform grids,” IEEE Trans. Magnetics, vol. 30, pp. 3200–3203, 1994.
128. A. R. Zakharian, M. Brio, and J. V Moloney, “FDTD based second-order accurate local mesh refinement for Maxwell’s equations in two space dimensions,” Comm. Math. Sci., vol. 2, pp. 497–513, 2004.
129. M. J. Berger and J. Oliger, “Adaptive mesh refinement for hyperbolic partial differential equations,” J. Comp. Phys., vol. 53, pp. 484–512, 1984.
130. C. D. Sams, Adaptive Mesh Refinement for Time-Domain Numerical Electromagnetics. Morgan & Claypool, 2007.
131. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference TimeDomain Method, 3rd edn. Artech House, 2005.
132. J. F. Thompson, B. K. Soni, andN. P Weatherill, Handbook of Grid Generation. CRC Press, 1999.
133. Shankar, A., H. Mohammadian, and W. F. Hall, “A time-domain, finite-volume treatment for the Maxwell equations,” Electromagnetics, vol. 10, pp. 127–145, 1990.
134. M. Remaki, “A new finite volume scheme for solving Maxwell’s system,” COMPEL, vol. 19, pp. 913–931, 2000.
135. F. G. Harmon, “Application of a finite-volume time-domain Maxwell equation solver to three-dimensional objects,” Master’s thesis, Air Force Institute of Technology, 1996.
136. N. K. Madsen and R. W. Ziolkowski, “A three-dimensional modified finite volume technique for Maxwell’s equations,” Electromagnetics, vol. 10, pp. 147–161, 1990.
137. K. S. Yee and J. S. Chen, “Conformal hybrid finite difference time domain and finite volume time domain,” IEEE Trans. Ant. Prop., vol. 42, pp. 1450–1455, 1994.
138. K. S. Yee and J. S. Chen, “The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell’s equations,” IEEE Trans. Ant. Prop., vol. 45, pp. 354–363, 1997.
139. S. M. Rao, Time Domain Electromagnetics. Academic Press, 1999.
140. J. Jin, The Finite Element Method in Electromagnetics, 2nd edn. Wiley, 2002.
141. J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer, 2008.
142. F. Q. Hu, M. Y. Hussaini, and P Rasetarinera, “An analysis of the discontinuous Galerkin method for wave propagation problems,” J. Comp. Phys., vol. 151, pp. 921–946, 1999.
143. J. S. Hesthaven and T. Warburton, “Nodal high-order methods on unstructured grids: I. time-domain solution of Maxwell’s equations,” J. Comp. Phys., vol. 181, pp. 186–221, 2002.
144. T. Lu, P Zhang, and W. Cai, “Discontinuous Galerkin methods for dispersive and lossy Maxwell’s equations and PML boundary conditions,” J. Comp. Phys., vol. 200, pp. 549–580, 2004.