High-order accurate modeling of electromagnetic wave propagation across media - Grid conforming bodies

Journal of Computational Physics

Volumn 218, Issue 2, 2006, Pages 816-835

  Kashdan, Eugene ^a   Turkel, Eli ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

CEM; Discontinuities; Discontinuous coefficients; FDTD; High order accuracy; High order methods; Time dependent Maxwell equations

Indexed keywords

ELECTROMAGNETIC WAVE PROPAGATION; FOURIER SERIES; PERMITTIVITY;

CEM; DIELECTRIC PERMITTIVITIES; DISCONTINUITY; DISCONTINUOUS COEFFICIENTS; FDTD; HIGH-ORDER METHODS; HIGHER ORDER ACCURACY; HIGHER-ORDER METHODS; ORDER OF ACCURACY; TIME-DEPENDENT MAXWELL'S EQUATIONS;

MAXWELL EQUATIONS;

EID: 33748798020     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.03.009     Document Type: Article

References (31)

1. U. Andersson, Time-Domain Methods for the Maxwell's Equations, Ph.D. Thesis, Royal Institute of Technology, Sweden, 2001.
2. U. Andersson, B. Engquist, Regularization of material interfaces for finite difference methods for the Maxwell equations, Report 2002-01, Parallel and Sci. Comp. Inst. Royal Institute of Technology and Uppsala University, 2002.
3. Cai W., and Dong S. An upwinding embedded boundary method for Maxwell's equations in media with material interfaces: 2-D case. J. Comput. Phys. 19 1 (2003) 159-183
4. Cangellaris A.C., and Wright D.B. Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena. IEEE Trans. Antenn. Propag. 39 10 (1991) 1518-1525
5. Carpenter M.H., Gottlieb D., and Abarbanel S. The stability of numerical boundary treatments for compact high-order finite difference schemes. J. Comput. Phys. 108 2 (1993) 541-559
6. Carpenter M.H., Gottlieb D., and Abarbanel S. Stable and accurate boundary treatment for compact high-order finite difference scheme. Appl. Numer. Anal. 12 (1993) 55-81
7. Dridi K.H., Hesthaven J.S., and Ditkowski A. Staircase-free finite-difference time-domain formulation for general materials in complex geometries. IEEE Trans. Antenn. Propag. 49 5 (2001) 749-756
8. Gedney S.D. An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices. IEEE Trans. Antenn. Propag. 4 12 (1996) 1630-1639
9. Gedney S.D. The perfectly matched layer absorbing medium. In: Taflove A. (Ed). Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (1998), Artech House, Boston, MA 263-344 (Chapter 5)
10. Gedney S.D., Roden J.A., Madsen N.K., Mohammadian A.H., Hall W.F., Shankar V., and Rowell C. Explicit time-domain solutions of Maxwell's equations via generalized grids. In: Taflove A. (Ed). Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (1998), Artech House, Boston, MA 163-262 (Chapter 4)
11. D. Gottlieb, B. Yang, Comparisons of staggered and non-staggered schemes for Maxwell's equations, in: 12th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, 1996, pp. 1122-1131.
12. Hesthaven J.S. High-order accurate methods in time-domain computational electromagnetics. A review. Adv. Imaging Electron Phys. 127 (2003) 59-123
13. Holland R. THREDS: A finite-difference time-domain EMP code in 3D spherical coordinates. IEEE Trans. Nucl. Sci. NS-30 (1983) 4592-4595
14. Holland R. Pitfalls of staircase meshing. IEEE Trans. Electromag. Compat. 35 (1993) 434-439
15. Hyman J.M. Accurate monotonicity preserving cubic interpolation. SIAM J. Sci. Stat. Comput. 4 (1983) 645-654
16. Jiang B., Wu J., and Povinelli L.A. The origin of spurious solutions in computational electromagnetics. J. Comput. Phys. 125 (1996) 104-123
17. Joannopoulos J.D., Meade R.D., and Winn J.N. Photonic Crystals: Molding the Flow of Light (1995), Princeton University Press, Princeton, NJ
18. E. Kashdan, High-Order Accurate Methods for Maxwell Equations, Ph.D. Thesis, Tel Aviv University, 2004.
19. E. Kashdan, B. Galanti, A new parallelization strategy for solution of the time-dependent three-dimensional Maxwell's equations using a high-order accurate compact implicit scheme, Int. J. Numer. Model. (submitted for publication).
20. E. Kashdan, E. Turkel, A high order accurate method for frequency domain Maxwell equations with discontinuous coefficients, J. Sci. Comput. (2006). doi:10.1007/s10915-005-9049-5.
21. E. Kashdan, E. Turkel, Numerical solution of Maxwell's equations in spherical coordinates, in: 19th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, March, 2003, pp. 188-192.
22. Taflove A., and Hagness S.C. Computational Electrodynamics: The Finite-Difference Time-Domain Method. third ed. (2005), Artech House, Norwood, MA
23. Teixeira F.L., and Chew W.C. Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates. IEEE Microwave Guided Wave Lett. 7 11 (1997) 371-373
24. Tornberg A.K., and Engquist B. Regularization techniques for numerical approximation of PDEs with singularities. J. Sci. Comput. 19 (2003) 527-552
25. Turkel E. High-order methods. In: Taflove A. (Ed). Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method (1998), Artech House, Boston, MA 63-110 (Chapter 2)
26. E. Turkel, A. Yefet, Fourth order method for Maxwell's equations on a staggered mesh, in: IEEE Antennas Propagation Society, International Symposium, Montréal, Canada, 1997, pp. 2156-2159.
27. Yang B., and Petropoulos P.G. Plane-wave analysis and comparision of split-field, biaxial and uniaxial PML methods as ABCs for pseudospectral electromagnetic wave simulation in curvilinear coordinates. J. Comput. Phys. 146 (1998) 747-774
28. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antenn. Propag. 1 3 (1966) 302-307
29. A. Yefet, Fourth Order Accurate Compact Implicit Method for the Maxwell Equations, Ph.D. Thesis, Tel Aviv Univ, 1998.
30. Yefet A., and Turkel E. Fourth order compact implicit method for the Maxwell equations with discontinuous coefficients. Appl. Numer. Math. 33 (2000) 125-134
31. D.W. Zingg, T.T. Chisholm, Runge-Kutta methods for linear problems, in: Proceedings of 12th AIAA Comp. Fluid Dynamics Conference, 1995.