A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell's Equations with High-Order Staggered Finite Difference Schemes

Journal of Computational Physics

Volumn 139, Issue 1, 1998, Pages 184-208

  Petropoulos, Peter G ^a   Zhao, Li ^b   Cangellaris, Andreas C ^c  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

^b University of Arizona   (United States)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD;

ABSORBING BOUNDARY CONDITION; CLASSICAL TECHNIQUES; COMPUTATIONAL DOMAINS; FINITE DIFFERENCE SCHEME; HIGH-ORDER; HIGHER-ORDER; NON-DISSIPATIVE FINITE DIFFERENCE; REFLECTIONLESS; SPONGE LAYERS; TIME-DEPENDENT MAXWELL'S EQUATIONS;

MAXWELL EQUATIONS;

EID: 0002210417     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5855     Document Type: Article

References (30)

1. S. Abarbanel and D. Gottlieb, A mathematical analysis of the PML method, J. Comput. Phys. 134, 357 (1997).
2. J.-P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114, 185 (1994).
3. W. C. Chew and W. H. Weedon, A 3-D perfectly matched medium from modified Maxwell's equations with stretched coordinates, Micro. Opt. Tech. Lett. 7(13), 599 (1994).
4. T. Deveze, L. Beaulieu, and W. Tabbara, An absorbing boundary condition for the fourth-order FDTD scheme, in IEEE-APS International Symposium Proceedings, Chicago, IL, 1992, p. 342.
5. T. H. Duong and P. Joly, A principle of images for absorbing boundary conditions, Num. Meth. Part. Diff. Equations 10, 411 (1994).
6. J. Fang, Time Domain Finite Difference Computations for Maxwell's Equations, Ph.D. dissertation, Dept. of Elec. Eng., University of California, Berkeley, CA, 1989 .
7. D. Givoli, Non-reflecting boundary conditions, J. Comput. Phys. 94, 1 (1991).
8. D. Givoli and D. Cohen, Nonreflecting boundary conditions based on Kirchhoff-type Formulae, J. Comput. Phys. 117(1), 102 (1995).
9. M. J. Grote and J. B. Keller, Nonreflecting boundary conditions for time-dependent scattering, J. Comput. Phys. 127(1), 52 (1996).
10. D. Gottlieb and B. Yang, Comparisons of staggered and non-staggered schemes for Maxwell's equations, in Proceedings, 12th Annual Review of Progress in Applied Computational Electromagnetics, 1996.
11. B. Gustafson, H. O. Kreiss, and J. Oliger, Time Dependent Problems and Difference Methods (Wiley, New York, 1995).
12. B. Gustafsson, Far-field boundary conditions for time-dependent hyperbolic systems, SIAM J. on Scientific and Statistical Computing 9(5), 812 (1988).
13. R. L. Higdon, Radiation boundary conditions for elastic wave propagation, SIAM J. Numer. Anal. 27(4), 831 (1990).
14. M. Israeli and S. A. Orszag, Approximation of radiation boundary conditions, J. Comput. Phys. 41, 115 (1981).
15. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
16. S. Karni, Far-field filtering operators for suppression of reflections from artificial boundaries, SIAM J. Numer. Anal. 33(3), 1014 (1996).
17. A. R. Levander, Use of the telegraphy equation to improve absorbing boundary efficiency for fourth-order acoustic wave finite differences schemes, Bull. Seism. Soc. Am. 75(6), 1847 (1985).
18. Y Liu, Fourier analysis of numerical algorithms for the Maxwell equations, J. Comput. Phys. 124,396(1996).
19. A. Nachman, A brief perspective on computational electromagnetics, J. Comput. Phys. 126, 237 (1996).
20. A. C. Newel and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, MA, 1992).
21. P. G. Petropoulos, Phase error control for FD-TD methods of second and fourth order accuracy, IEEE Trans. on Antennas and Propagation 42, 859 (1994).
22. P. G. Petropoulos, The wave hierarchy for propagation in relaxing dielectrics, Wave Motion 21, 253 (1995). [The computation of linear dispersive electromagnetic waves, ACES J. 11, 8(1996)]
23. P. G. Petropoulos, The wave hierarchy for propagation in relaxing dielectrics, Wave Motion 21, 253 (1995). [The computation of linear dispersive electromagnetic waves, ACES J. 11, 8(1996)]
24. P. G. Petropoulos, Analysis of exponential time-differencing for FD-TD in lossy dielectrics, IEEE Trans. Antennas Propag. 45(6), 1054 (1997).
25. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, A perfectly matched anisotropic absorber for use as an absorbing boundary condition, IEEE Trans. on Antennas and Propagation 43(12), 1460 (1995).
26. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 1995).
27. J. W. Thomas, Numerical Partial Differential Equations-Finite Difference Methods (New York: Springer-Verlag, 1995).
28. S. V. Tsynkov, An application of nonlocal external conditions to viscous flow computations, J. Comput. Phys. 116(2), 212 (1995).
29. K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in Isotropic media, IEEE Trans. Antennas Propagat. 14, 302 (1966).
30. L. Zhao and A. C. Cangellaris, GT-PML: Generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids, IEEE Trans. Microwave Theory Tech. 44(12), 2555 (1996).