Multidomain pseudospectral time domain algorithm using a symplectic integrator

IEEE Transactions on Antennas and Propagation

Volumn 55, Issue 2, 2007, Pages 433-439

  Shi, Yan ^a   Liang, Chang Hong ^a  

^a XIDIAN UNIVERSITY   (China)

Author keywords

Multidomain pseudospectral time domain (PSTD); Symplectic integrator

Indexed keywords

DATA STORAGE EQUIPMENT; ELECTROMAGNETIC WAVE PROPAGATION; SPECTRUM ANALYSIS; TIME DOMAIN ANALYSIS;

MULTIDOMAIN PSEUDOSPECTRAL TIME DOMAIN; SYMPLECTIC INTEGRATOR;

ELECTROMAGNETIC FIELD THEORY;

EID: 33947394462     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2006.889906     Document Type: Article

References (36)

1. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag., vol. AP-14, pp. 302-307, May 1966.
2. A. Talfove, Computational Electrodynamics. Norwood, MA: Artech House, 1995.
3. C. Canuto, M. Y. Hussani, A. Quarteroni, and T. Zang, Spectral Methods in Fluid Dynamics. New York: Springer-Verlag, 1988.
4. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods. Philadelphia, PA: SIAM, 1977.
5. Q. H. Liu, "The PSTD algorithm: A time-domain method requiring only two cells per wavelength," Microw. Opt. Technol. Lett., vol. 15, pp. 158-165, 1997.
6. B. Yang, D. Gottlieb, and J. S. Hesthaven, "Spectral simulation of electromagnetic wave scattering," J. Comput. Phys., vol. 134, pp. 216-230, 1997.
7. B. Yang and J. S. Hesthaven, "A pseudospectral method for time-domain computation of electromagnetic scattering by bodies of revolution," IEEE Trans. Antennas Propag., vol. AP-47, pp. 132-141, Jan. 1999.
8. B. Yang and J. S. Hesthaven, "Multidomain pseudospectral computation of Maxwell's equations in 3-D general curvilinear coordinates," Appl. Numer. Math., vol. 33, pp. 281-289, 2000.
9. G.-X. Fan, Q. H. Liu, and J. S. Hesthaven, "Multidomain pseudospectral time-domain method for simulation of scattering from objects buried in lossy media," IEEE Trans. Geosci. Remote Sens., vol. GRS-40, pp. 1366-1373, June 2002.
10. G. Zhao and Q. H. Liu, "The 3-D multidomain pseudospectral time-domain algorithm for inhomogeneous conductive media," IEEE Trans. Antennas Propag., vol. AP-52, pp. 742-749, Mar. 2004.
11. J. S. Hesthaven, P. G. Dinesen, and J. P. Lynov, "spectral collocation time-domain modeling of diffractive optical elements," J. Comput. Phys., vol. 155, pp. 287-306, 1999.
12. Y. Shi, T. Su, and C. H. Liang, "Multidomain pseudospectral time-domain method for computation of electromagnetic scattering by bodies of revolution," Microw. Opt. Technol. Lett., vol. 47, pp. 92-96, 2005.
13. Y. Shi, L. Li, and C. H. Liang, "Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method," IEEE Trans. Antennas Propag., vol. AP-54, pp. 1207-1214, Apr. 2006.
14. Y. Shi, L. Li, and C. H. Liang, "Multidomain pseudospectral timedomain algorithm based on super-time-stepping method," Proc. Inst. Elect. Eng. Microw. Antennas Propag., vol. 153, pp. 55-60, 2006.
15. J. L. Young, D. Gaitonde, and J. J. S. Shang, "Toward the cfonstruction of a fourth-order difference scheme for transient EM wave simulation: Staggered grid approach," IEEE Trans. Antennas Propag., vol. AP-45, pp. 1573-1580, 1997.
16. D. W. Zingg, "High-order finite-difference methods in computational electromagnetics," in IEEE AP-S Int. Symp. Dig., Montreal, QC, Canada, 1997, pp. 110-113.
17. E. Turkel and A. Yefet, "Fourth order method for Maxwell's equations on a staggered mesh," in IEEE AP-S Int. Symp. Dig., Montreal, QC, Canada, 1997, pp. 2156-2159.
18. M. H. Carpenter and C. A. Kennedy, Fourth order 2N-stroage Runge-Kutta scheme Tech. Rep. NASA-TM-109112, 1994.
19. T. Hirono, W. Lui, S. Seki, and Y. Yoshikuni, "A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator," IEEE Trans. Microw. Theory Tech., vol. 49, pp. 1640-1648, 2001.
20. I. Saitoh, Y. Suzuki, and N. Takahashi, "The symplectic finite difference time domain method," IEEE Trans. Magn., vol. 37, pp. 3251-3254, 2001.
21. T. Hirono, W. W. Lui, and S. Seki, "Successful applications of PML-ABC to the symplectic FDTD scheme with 4th-order accuracy in time and space," in IEEE MTT-S Int. Symp. Dig., Anaheim, CA, 1999, pp. 1293-1296.
22. I. Saitoh and N. Takahashi, "Stability of symplectic finite-difference time-domain methods," IEEE Trans. Magn., vol. 38, pp. 665-668, 2002.
23. R. Rieben, D. White, and G. Rodrigue, "High-order symplectic integrator methods for finite element solutions to time dependent Maxwell equations," IEEE Trans. Antennas Propag., vol. AP-52, pp. 2190-2195, 2004.
24. R. Rieben, D. White, and G. Rodrigue, "High-order symplectic integration methods for finite element solutions to time dependent Maxwell equations," IEEE Trans. Antennas Propag., vol. AP-52, pp. 2190-2195, 2004.
25. J. Lee and B. Fornberg, "A split step approach for the 3-D Maxwell's equations," J. Comput. Appl. Math., vol. 158, pp. 485-505, 2003.
26. L. L. Jiang, J. F. Mao, and X. L. Wu, "Symplectic finite-difference time-domain method for Maxwell equations," IEEE Trans. Magn., vol. 42, pp. 1991-1995, 2006.
27. Z. Huang, W. Sha, X. Wu, and M. Chen, "A novel high-order timedomain scheme for three-dimensional Maxwell's equations," Microw. Opt. Technol. Lett., vol. 48, pp. 1123-1125, 2005.
28. M. Kusaf, A. Y. Oztoprak, and D. S. Daoud, "Optimized exponential operator coefficients for symplectic FDTD method," IEEE Microw. Wireless Compon. Lett., vol. 15, pp. 86-88, Nov. 2005.
29. J. P. Berenger, "A perfectly matched layer for the absorption EM waves," J. Comput. Phys., vol. 114, pp. 185-200, 1994.
30. W. C. Chew and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microw. Opt. Tech. Lett., vol. 7, pp. 599-604, 1994.
31. S. Abarbanel and D. Gottlieb, "A mathematical analysis of the PML method," Comput. Phys., vol. 134, pp. 357-363, 1997.
32. S. Abarbanel and D. Gottlieb, "On the construction and analysis of absorbing layers in CEM," in Proc. 13th Annu Rev. Progress in Applied Computational Electromagnetics, 1997, pp. 876-883.
33. G. X. Fan and Q. H. Liu, "A strongly well-posed PML in lossy media," IEEE Antennas Wireless Propag. Lett., vol. 2, pp. 97-100, 2003.
34. H. Yoshida, "Construction of higher order symplectic integrators," Phys. Lett. A, vol. 150, pp. 262-268, 1990.
35. M. Glasner, D. Yevick, and B. Hermansson, "Sixth-order generalized propagation technique," Electron. Lett., vol. 27, pp. 475-478, 1991.
36. E. Forest and R. D. Ruth, "Fourth-order symplectic integration," Phys. D, vol. 43, pp. 105-117, 1990.