Progress In Electromagnetics Research
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Nonuniform Fast Cosine Transform and Chebyshev PSTD Algorithms

By B. Tian and Q. H. Liu

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B. Tian and Q. H. Liu, "Nonuniform Fast Cosine Transform and Chebyshev Pstd Algorithms," Progress In Electromagnetics Research, Vol. 28, 253-273, 2000.

1. Rao, K. R. and P. Yip, Discrete Cosine TransformAlgorithms, Advantages, Applications, Academic Press, London, 1990.

2. Chen, W. A., C. Harrison, and S. C. Fralick, "A fast computational algorithm for the discrete cosine transform," IEEE Trans. Commu., Vol. 25, No. 9, 1004-1011, 1977.

3. Lee, B. G., "A new algorithm to compute the discrete cosine ransform," IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-32, No. 6, 1243-1245, 1984.

4. Dutt, A. and V. Rokhlin, "Fast Fourier transforms for nonequispaced data," SIAM J. Sci. Comput., Vol. 14, No. 6, 1368-1393, November 1993.

5. Beylkin, G., "On the fast Fourier transform of functions with singularities," Appl. Computat. Harmonic Anal., Vol. 2, 363-382, 1995.

6. Liu, Q. H. and N. Nguyen, "An accurate algorithm for nonuniform fast Fourier transforms," IEEE Microwave Guided Wave Lett., Vol. 8, No. 1, 18-20, 1998.

7. Liu, Q. H. and X. Y. Tang, "Iterative algorithm for nonuniform inverse fast Fourier transform (NU-IFFT)," Electronics Letters, Vol. 34, No. 20, 1913-1914, 1998.

8. Nguyen, N. and Q. H. Liu, "The regular Fourier matrices and nonuniform fast Fourier transforms," SIAM J. Sci. Compt., Vol. 21, No. 1, 283-293, 1999.

9. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propagat., Vol. AP-14, 302-307, 1966.

10. Kunz, K. S. and R. J. Luebbers, Finite Difference Time Domain Method for Electromagnetics, CRC Press Inc., Florida, 1993.

11. Taflove, A., Computational Electrodynamics: The Finite Difference Time Domain Method, Artech House, Inc., Norwood, MA, 1995.

12. Fang, J., "Time domain finite difference computation for Maxwell’s equations,", Ph.D. dissertation, University of California, Berkeley, CA, 1989.

13. Hadi, M. F. and M. Piket-May, "A modified FDTD (2,4) scheme for modeling electrically large structures with high phase accuracy," 12th Annu. Rev. Progress Appl. Computat. Electromagnet., Monterey, CA, March 1996.

14. Carpenter, M. H., D. Gottlieb, and S. Abarbanel, "The stability of numerical boundary treatments for compact higher-order finite difference schemes," Inst. Comput. Applicat. Sci. Eng., Rep. 91-71, 1991.

15. Young, J. L., D. Gaitonde, and J. J. S. Shang, "Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach," IEEE Trans. Antennas Propagat., Vol. 45, No. 11, 1573-1580, 1997.

16. Orszag, S. A., "Comparison of pseudospectral and spectral approximation," Stud. Appl. Math., Vol. 51, 253-259, 1972.

17. Gottlieb, D. and S. A. Orszag, Numerical Analysis of Spectral Methods, SIAM, Philadelphia, 1977.

18. Fornberg, B., A Practical Guide to Pseudospectral Methods, Cambridge University Press, New York, 1996.

19. Berenger, J.-P., "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational Physics, Vol. 114, 185-200, 1994.

20. Liu, Q. H., "The PSTD algorithm: a time-domain method requiring only two cells per wavelength," Microwave Opt. Tech. Lett., Vol. 15, No. 3, 158-165, 1997.

21. Liu, Q. H., "Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm," IEEE Trans. Geosci. Remote Sensing, Vol. 37, No. 2, 917-926, 1999.

22. Liu, Q. H., "PML and PSTD algorithm for arbitrary lossy anisotropic media," IEEE Microwave Guided Wave Lett., Vol. 9, No. 2, 48-50, 1999.

23. Liu, Q. H. and G.-X. Fan, "A frequency-dependent PSTD algorithm for general dispersive media," IEEE Microwave Guided Wave Lett., Vol. 9, No. 2, 51-53, 1999.

24. Liu, Q. H. and G.-X. Fan, "Simulations of GPR in dispersive media using the PSTD algorithm," IEEE Trans. Geosci. Remote Sensing, Vol. 37, No. 5, 2317-2324, 1999.

25. Liu, Q. H., "The PSTD algorithm for acoustic waves in inhomogeneous, absorptive media ," media,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., Vol. 45, No. 4, 1044-1055, 1998.

26. Yang, B., D. Gottlieb, and J. S. Hesthaven, "On the use of PML ABC’s in spectral time-domain simulations of electromagnetic scattering," Proc. ACES 13th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, 926-933, 1997.

27. Yang, B., D. Gottlieb, and J. S. Hesthaven, "Spectral simulations of electromagnetic waves scattering," J. Comp. Phys., Vol. 134, 216-230, 1997.

28. Sarkar, T. K., "Application of conjugate gradient method to electromagnetics and signal analysis," PIER 5, Progress in Electromagnetics Research, Elsevier, New York, 1991.

29. Catedra, M. F. and R. P. Torres, J. Basterrechea, and E. Gago, The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics, Boston: Artech House, 1995.

30. Chew, W. C. and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates," Microwave Opt. Tech. Lett., Vol. 7, 599-604, 1994.

31. Liu, Q. H., "An FDTD algorithm with perfectly matched layers for conductive media," Micro. Opt. Tech. Lett., Vol. 14, No. 2, 134-137, 1997.

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