The complementary operators method in FDTD simulations

IEEE Antennas and Propagation Magazine

Volumn 39, Issue 6, 1997, Pages 33-45

  Ramahi, Omar M ^a  

^a HEWLETT PACKARD COMPANY   (United States)

Author keywords

Boundary conditions; Computational electromagnetics; FDTD methods

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; MATHEMATICAL OPERATORS; TIME DOMAIN ANALYSIS;

ELECTROMAGNETICS;

ELECTROMAGNETIC WAVE REFLECTION;

EID: 0031332539     PISSN: 10459243     EISSN: None     Source Type: Journal    
DOI: 10.1109/74.646801     Document Type: Article

References (34)

1. A. Bayliss, M. Gunzburger and T. Turkel, "Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions," SIAM Journal of Applied Mathematics, 42, pp. 430-451.
2. B. Engquist and A. Majda, "Radiation Boundary Conditions for the Numerical Simulation of Waves," Mathematics of Computation, 31, 1977, pp. 629-651.
3. R. Mittra and O. M. Ramahi, "Absorbing Boundary Conditions for the Direct Solution of Partial Differential Equations Arising in Electromagnetic Scattering Problems," in M. Morgan (ed.), Finite Element and Finite Difference Methods in Electromagnetic Scattering, Volume II, New York, Elsevier Science, Inc., 1989, pp. 133-173.
4. G. Mur, "Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Transactions on Electromagnetic Compatibility, EMC-23, 4, November 1981, pp. 377-382.
5. R. L. Higdon, "Absorbing Boundary Conditions for Difference Approximations to the Multi-Dimensional Wave Equation," Mathematics of Computation, 47, 176, October 1986, pp. 437-459.
6. R. L. Higdon, "Radiation Boundary Conditions for Elastic Wave Propagation," SIAM Journal of Numerical Analysis, 27, 4, August 1990, pp. 831-870.
7. Z. P. Liao, H. L. Wong, B. P. Yang and Y. F. Yuan, "A Transmitting Boundary for Transient Wave Analyses," Scientia Sinica (Series A), 27, 10, October 1984, pp. 1063-1076.
8. E. L. Lindman, "'Free-space' Boundary Conditions for the Time Dependent Wave Equation," Journal of Computational Physics, 18, 1975, pp. 66-78.
9. B. H. McDonald and A. Wexler, "Finite-Element Solution of Unbounded Field Problems," IEEE Transactions on Microwave Theory and Techniques, MTT-20, 12, December 1972, pp. 841-847.
10. J. De Moerloose and D. De Zutter, "Surface Integral Representation Radiation Boundary Condition for the FDTD Method," IEEE Transactions on Antennas and Propagation, AP-41, 7, July 1993, pp. 890-896.
11. O. M. Ramahi, A. Khebir and R. Mittra, "Numerically-Derived Absorbing Boundary Conditions for the Solution of Open Region Scattering Problems," IEEE Transactions on Antennas and Propagation, AP-39, 3, March 1991, pp. 350-353.
12. K. K. Mei, R. Pous, Z. Chen, Y-W Liu and M. D. Prouty, "Measured Equation of Invariance: A New Concept in Field Computations," IEEE Transactions on Antennas and Propagation, AP-42, 3, March 1994, pp. 320-328.
13. J-P. Berenger, "A Perfectly Matched Layer for the Absorption of Electromagnetic Waves," Journal of Computational Physics, 114, 1994, pp. 185-200.
14. U. Pekel and R. Mittra, "A Finite-Element-Method Frequency-Domain Application of the Perfectly Matched Layer (PML) Concept," Microwave and Optical Technology Letters, 9, 3, June 1995, pp. 117-122.
15. O. M. Ramahi, "Application of the Complementary Operator Method to the Finite-Difference-Time-Domain Solution of the Three-Dimensional Radiation Problem," Microwave and Optical Technology Letters, 9, 3, June 1995, pp. 147-149.
16. O. M. Ramahi, "Complementary Operators: A Method to Annihilate Artificial Reflections Arising from the Truncation of the Computational Domain in the Solution of Partial Differential Equations," IEEE Transactions on Antennas and Propagation, AP-43, 7, July 1995, pp. 697-704.
17. O. M. Ramahi, "Correction to 'Complementary Operators: A Method to Annihilate Artificial Reflections Arising from the Truncation of the Computational Domain in the Solution of Partial Differential Equations,'" IEEE Transactions on Antennas and Propagation, AP-44, 8, August 1996, p. 1199.
18. O. M. Ramahi, "Complementary Boundary Operators for Wave Propagation Problems," Journal of Computational Physics, in press.
19. K. K. Mei and J. Fang, "Superabsorption-A Method to Improve Absorbing Boundary Conditions," IEEE Transactions on Antennas and Propagation, AP-40, 9, September 1992.
20. W. D. Smith, "Nonreflecting Plane Boundary for Wave Propagation Problems," Journal of Computational Physics, 15, 1974, pp. 492-503.
21. R. L. Higdon, "Absorbing Boundary Conditions for Acoustic and Elastic Waves in Stratified Media," Journal of Computational Physics, 101, 1992, pp. 386-418.
22. R. L. Higdon, "Radiation Boundary Conditions for Dispersive Waves," SIAM Journal of Numerical Analysis, 31, 1, February 1994, pp. 64-100.
23. O. M. Ramahi, "On the Use of Absorbing Boundary Conditions in Finite Difference Time Domain Solutions of Unbounded Geometry Problems," IEEE International Symposium on Antennas and Propagation Digest, Seattle, Washington, June, 1994, pp. 168.
24. K. Demarest, R. Plumb and Z. Huang, "The Performance of FDTD Absorbing Boundary Conditions for Buried Scatterers," IEEE International Symposium on Antennas and Propagation Digest, Seattle, Washington, June, 1994, pp. 169.
25. W. C. Chew and R. L. Wagner, "A Modified Form of Liao's Absorbing Boundary Condition," IEEE International Symposium on Antennas and Propagation Digest, Chicago, Illinois, July 1992, pp. 536-539.
26. M. Moghaddam and W. C. Chew, "Stabilizing Liao's Absorbing Boundary Conditions using Single-Precision Arithmetic," IEEE International Symposium on Antennas and Propagation Digest, London, Ontario, Canada, June 1991, pp. 430-433.
27. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Norwood, MA, Artech House, 1995.
28. O. M. Ramahi, "Stable FDTD Solutions with Higher Order Absorbing Boundary Conditions," Microwave and Optical Technology Letters, in press.
29. A. H. Kamel, "On the Accuracy of Absorbing Boundary Conditions for Wave Propagation," Journal of Electromagnetic Waves and Applications, 8, 5, 1994, pp. 647-657.
30. C. Brench, private communications.
31. J. Schneider and O. M. Ramahi, "Complementary Boundary Operators for Acoustic Wave Propagation," submitted to Journal of the Acoustical Society of America.
32. J. Schneider and O. M. Ramahi, "A Comparison and Evaluation of the PML and COM Mesh Truncation Techniques for FDTD Simulations," IEEE International Symposium on Antennas and Propagation Digest, Montreal, Canada, July 13-18, 1997.
33. O. M. Ramahi, "Concurrent Implementation of the Complementary Operators Method," IEEE Microwave and Guided Wave Letters, 7, 6, June 1997.
34. O. M. Ramahi, "Extension of the Concurrent COM Mesh-Truncation Technique to Three-Dimensional FDTD Simulations," submitted to IEEE Microwave and Guided Wave Letters, April 1997.