Abstract
We present a family of unconditionally stable algorithms, based on the Suzuki product-formula approach, that solve the time-dependent Maxwell equations in systems with spatially varying permittivity and permeability. Salient features of these algorithms are illustrated by computing the density of states and by simulating the propagation of light in a two-dimensional photonic material.
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References
M. Born and E. Wolf, Principles of Optics, (Pergamon, Oxford, 1964).
K.S. Yee, IEEE Transactions on Antennas and Propagation 14, 302 (1966).
A. Taflove and S.C. Hagness, Computational Electrodynamics-The Finite-Difference Time-Domain Method, (Artech House, Boston, 2000).
J.S. Kole, M.T. Figge, and H. De Raedt, Phys. Rev. E 64, 066705 (2001).
M. Suzuki, J. Math. Phys. 26, 601 (1985); ibid 32 400 (1991).
G.D. Smith, Numerical solution of partial differential equations, (Clarendon, Oxford, 1985).
H.F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959).
M. Suzuki, S. Miyashita, and A. Kuroda, Prog. Theor. Phys. 58, 1377 (1977).
H. De Raedt and B. De Raedt, Phys. Rev. A 28, 3575 (1983).
H. De Raedt, Comp. Phys. Rep. 7, 1 (1987).
H. Kobayashi, N. Hatano, and M. Suzuki, Physica A 211, 234 (1994).
H. De Raedt, K. Michielsen, Comp. in Phys. 8, 600 (1994).
A. Rouhi, J. Wright, Comp. in Phys. 9, 554 (1995).
B.A. Shadwick and W.F. Buell, Phys. Rev. Lett. 79, 5189 (1997).
M. Krech, A. Bunker, and D.P. Landau, Comp. Phys. Comm. 111, 1 (1998).
P. Tran, Phys. Rev. E 58, 8049 (1998).
K. Michielsen, H. De Raedt, J. Przeslawski, and N. Garcia, Phys. Rep. 304, 89 (1998).
H. De Raedt, A.H. Hams, K. Michielsen, and K. De Raedt, Comp. Phys. Comm. 132, 1 (2000).
E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
K.M. Ho, C.T. Chan and C.M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
C.M. Anderson and K.P. Giapis, Phys. Rev. Lett. 77, 2949 (1996).
R. Alben, M. Blume, H. Krakauer, and L. Schwartz, Phys. Rev. B 12, 4090 (1975).
V.G. Veselago, Sov. Phys. USPEKHI 10, 509 (1968).
R.A. Shelby, D.R. Smith, and S. Schultz, Science 292 77 (2001).
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© 2002 Springer-Verlag Berlin Heidelberg
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Kole, J.S., Figge, M.T., De Raedt, H. (2002). New Unconditionally Stable Algorithms to Solve the Time-Dependent Maxwell Equations. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46043-8_81
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DOI: https://doi.org/10.1007/3-540-46043-8_81
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