Mixed finite-element time-domain method for transient Maxwell equations in doubly dispersive media

IEEE Transactions on Microwave Theory and Techniques

Volumn 56, Issue 1, 2008, Pages 113-120

  Donderici, Burkay ^b   Teixeira, Fernando L ^a,b  

^a IEEE

^b The Ohio State University   (United States)

Author keywords

Dispersive media; Finite element time domain

Indexed keywords

ALGORITHMS; MAXWELL EQUATIONS; PERMITTIVITY; TIME DOMAIN ANALYSIS;

DISPERSIVE MEDIA; FINITE ELEMENT TIME DOMAIN;

FINITE ELEMENT METHOD;

EID: 38149054966     PISSN: 00189480     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMTT.2007.912217     Document Type: Article

References (42)

1. J. F. Lee, R. Lee, and A. Cangellaris, "Time-domain finite-element methods," IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 430-442, Mar. 1997.
2. A. Bossavit, Computational Electromagnetics: Variational Formulations, Complementarity, Edge Curr-ents. San Diego, CA: Academic, 1998.
3. J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. New York: Wiley, 2002.
4. P. Monk, Finite Element Methods for Maxwell's Equations. Oxford, U.K.: Oxford Univ. Press, 2003.
5. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain. Boston, MA: Artech House, 2000.
6. A. Bossavit, "Whitney forms: A class of finite elements for three-dimensional computations in electromagnetism," Proc. Inst. Elect. Eng., vol. 135, no. 8, pt. A, pp. 493-500, Nov. 1988.
7. A. Bossavit, "Mixed finite elements and die complex of Whitney forms," in The Mathematics of Finite Elements and Applications VI, J. R. Whiteman, Ed. London, U.K.: Academic, 1988, pp. 137-144.
8. P. R. Kotiuga, "Helicity functionals and metric invariance in three dimensions," IEEE Trans. Magn., vol. 25, no. 4, pp. 2813-2186, Jul. 1989.
9. F. L. Teixeira and W. C. Chew, "Lattice electromagnetic theory from a topological viewpoint," J. Math. Phys., vol. 40, no. 1, pp. 169-187, Jan. 1999.
10. Z. Ren and N. Ida, "High order differential form-based elements for die computation of electromagnetic fields," IEEE Trans. Magn., vol. 36, no. 4, pp. 1472-1478, Jul. 2000.
11. T. Tarhasaari and L. Kettunen, "Wave propagation and cochain formulations," IEEE Trans. Magn., vol. 39, no. 3, pp. 1195-1998, May 2003.
12. P. Castillo, J. Koning, R. Rieben, and D. White, "A discrete differential forms framework for computational electromagnetics," Comput. Model. Eng. Sci., vol. 5, no. 4, pp. 331-346, 2004.
13. G. A. Deschamps, "Electromagnetics and differential forms," Proc. IEEE, vol. 69, no. 6, pp. 676-696, Jun. 1981.
14. 3," Proc. Inst. Elect. Eng., vol. 133, pt. A, pp. 139-143, 1986.
15. K. F. Warnick and D. V. Arnold, "Green forms for anisotropic, inhomogeneous media," J. Electromagn. Waves Applicat., vol. 11, pp. 1145-1164, 1997.
16. F. L. Teixeira and W. C. Chew, "Differential forms, metrics, and the reflectionless absorption of electromagnetic waves," J. Electromagn. Waves Applicat., vol. 13, no. 5, pp. 665-686, 1999.
17. B. He and F. L. Teixeira, "Differential forms, Galerkin duality and sparse inverse approximations in finite element solutions of Maxwell equations," IEEE Trans. Antennas Propag., vol. 55, no. 5, pp. .1359-1368, May 2007.
18. B. He and F. L. Teixeira, "On the degrees of freedom of lattice electrodynamics," Phys. Lett. A, vol. 336, no. 1, pp. 1-7, Jan. 2005.
19. 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. Modeling, vol. 13, pp. 245-260, 2000.
20. R. Albanese and G. Rubinacci, "Integral formulation for 3-D eddy current computation using edge elements," Proc. Inst. Elect. Eng., vol. 135, pt. A, pp. 457-462, 1988.
21. J. B. Manges and Z. J. Cendes, "A generalized tree-cotree gauge for magnetic field computations," IEEE Trans. Magn., vol. 31, no. 3, pp. 1342-1347, May 1995.
22. C-T. Hwang and R.-B. Wu, "Treating late-time instability of hybrid finite-element/finite-difference time-domain method," IEEE Trans. Antennas Propag., vol. 47, no. 2, pp. 227-232, Feb. 1999.
23. M. Wong, O. Picon, and V. F. Hanna, "A finite element method based on Whitney forms to solve Maxwell equations in the time domain," IEEE Tran. Magn., vol. 31, no. 3, pp. 1618-1621, May 1995.
24. B. He and F. L. Teixeira, "Sparse and explicit FETD via approximate inverse Hodge (mass) matrix," IEEE Microw. Wireless Compon. Lett., vol. 16, no. 6, pp. 348-350, Jun. 2006.
25. B. He and F. L. Teixeira, "Mixed E-B finite elements for solving 1-D, 2-D, and 3-D time-harmonic Maxwell curl equations," IEEE Microw. Wireless Compon. Lett., vol. 17, no. 5, pp. 313-3.15, May 2007.
26. J. Koning, R. N. Rieben, and G. H. Rodrigue, "Vector finite-element modeling of the full-wave Maxwell equations to evaluate power loss in bent optical fibers," J. Lightw. Technol., vol. 23, no. 12, pp. 4147-4154, Dec. 2005.
27. R. N. Rieben, G. H. Rodrigue, and D. A. White, "A high order mixed vector finite element method for solving the time dependent Maxwell equations on unstructured grids," J. Comput. Phys., vol. 204, pp. 490-519, 2005.
28. R. N. Rieben, D. A. White, and G. H. Rodrigue, "High-order symplectic integration methods for finite element solutions to time dependent Maxwell equations," IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 2190-2195, Aug. 2004.
29. D. Jiao and J.-M. Jin, "Time-domain finite-element modeling of dispersive media," IEEE Microw. Wireless Compon. Lett., vol. 11, no. 5, pp. 220-222, May 2001.
30. N. S. Stoykov, T. A. Kuiken, M. M. Lowery, and A. Taflove, "Finite-element time-domain algorithms for modeling linear Debye and Lorentz dielectric dispersions at low frequencies," IEEE Trans. Biomed. Eng., vol. 50, no. 9, pp. 1100-1107, Sep. 2003.
31. M. S. Yeung, "Application of the hybrid FDTD-FETD method to dispersive materials," Microw. Opt. Technol. Lett., vol. 23, pp. 238-242, Nov. .1999.
32. V. F. Rodriguez-Esquerre, M. Koshiba, and H. E. Hernandez-Figueroa, "Frequency-dependent envelope finite-element time-domain analysis of dispersion materials," Microw. Opt. Technol, Lett., vol. 44, pp. 13-16, Jan. 2005.
33. F. Maradei, "A frequency-dependent WETD formulation for dispersive materials," IEEE trans. Magn., vol. 37, no. 5, pp. 3303-3306, Sep. 2001.
34. R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 70, 2004, 046608.
35. G. Lubkowski, R. Schuhmann, and T. Weiland, "Extraction of effective metamaterial parameters by parameter fitting of dispersive models," Microw. Opt. Technol. Lett., vol. 49, pp. 285-288, Feb. 2007.
36. F. L. Teixeira and W. C. Chew, "On causality and dynamic stability of perfectly matched layers for FDTD simulations," IEEE Trans. Microw. Theory Tech., vol. 47, no. 6, pp. 775-785, Jun. 1999.
37. W. C. Chew and W. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microw. Opt. Technol, Lett., vol. 7, no. 13, pp. 599-604, 1994.
38. D. Jiao, J.-M. Jin, E. Michielssen, and D. J. Riley, "Time-domain finiteelement simulation of three-dimensional scattering and radiation problems using perfectly matched layers," IEEE Trans. Antennas Propag., vol. 51, no. 2, pp. 296-305, Feb. 2003.
39. F. L. Teixeira and W. C. Chew, "General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media," IEEE Microw. Guided Wave Lett., vol. 8, no. 6, pp. 223-225, Jun. .1998.
40. J. E. Hipp, "Soil electromagnetic parameters as functions of frequency, density, and soil moisture," Proc. IEEE, vol. 62, no. 1, pp. 98-103, Jan. 1974.
41. C. A. Balanis, Advanced Engineering Electromagnetics. New York: Wiley, 1989.
42. C. M. Furse, D. H. Roper, D. N. Buechler, D. E. Christinsen, and C. H. Durney, "The problem and treatment of DC offsets in FDTD simulations," IEEE Trans. Antennas Propag., vol. 48, no. 7, pp. 1.198-1201, Jul. 2000.