Review of PSTD methods for transient electromagnetics

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

Volumn 17, Issue 3, 2004, Pages 299-323

  Liu, Qing Huo ^a   Zhao, Gang ^a  

^a Duke University   (United States)

Author keywords

2.5 dimensional problems; Finite difference time domain (FDTD); Multidomain computation; Perfectly matched layers (PML); Pseudospectral time domain (PSTD) method; Scattering problems

Indexed keywords

ALGORITHMS; BROADBAND NETWORKS; CHEBYSHEV APPROXIMATION; ELECTRICAL ENGINEERING; ELECTROMAGNETIC WAVE SCATTERING; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; MAXWELL EQUATIONS; POLYNOMIALS; TIME DOMAIN ANALYSIS;

2,5-DIMENSIONAL PROBLEMS; FINITE-DIFFERENCE TIME-DOMAIN (FDTD); MULTIDOMAIN COMPUTATION; PERFECTLY MATCHED LAYERS (PML); PSEUDOSPECTRAL TIME-DOMAIN (PSTD) METHOD; SCATTERING PROBLEMS;

ELECTROMAGNETIC FIELD THEORY;

EID: 2442598259     PISSN: 08943370     EISSN: None     Source Type: Journal    
DOI: 10.1002/jnm.544     Document Type: Conference Paper

References (50)

1. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antennas and Propagation 1966; 14(5):302-307.
2. Liu QH. The PSTD algorithm: A time-domain method requiring only two cells per wavelength. Microwave and Optical Technology Letters 1997; 15(3):158-165.
3. Liu QH. Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm. IEEE Transactions on Ceoscience and Remote Sensing 1999; 37(2):917-926.
4. Liu QH. PML and PSTD algorithm for arbitrary lossy anisotropic media. IEEE Microwave and Guided Wave Letters 1999; 9(2):48-50.
5. Leung WK, Chen Y. Transformed-space nonuniform pseudospectral time-domain algorithm. Microwave and Optical Technology Letters 2001; 28(6):391-396.
6. Li Q, Chen Y. Applications of the PSTD for scattering analysis. IEEE Transactions on Antennas and Propagation 2002; 50(9):1317-1319.
7. Lee TW, Hagness SC. A PSTD method with fourth-order time-stepping for the analysis of nonlinear optical structures. IEEE Antennas and Propagation Society International Symposium Digest 2002; 3:232-235.
8. Li Q, Chen Y, Li CK.. Hybrid PSTD-FDTD technique for scattering analysis. Microwave and Optical Technology Letters 2002;34(1):19-24.
9. Leung WK, Chan CH. Combining the FDTD and PSTD methods. Microwave and Optical Technology Letters 1999; 23(4):249-254.
10. Yang B, Gottlieb D, Hesthaven JS. Spectral simulation of electromagnetic wave scattering. Journal of Computational Physics 1997; 134(2):216-230.
11. Hesthaven JS. Spectral collocation time-domain modeling of diffractive optical elements. Journal of Computational Physics 1999; 155(2):287-306.
12. Yang B. Hesthaven JS. A pseudospectral method for time-domain computation of electromagnetic scattering by bodies of revolution. IEEE Transactions on Antennas and Propagation 1999; 47(1):132-141.
13. Yang B, Hesthaven JS. Multidomain pseudospectral computation of Maxwell's equations in 3-D general curvilinear coordinates. Applied Numerical Mathematics 2000; 33(1-4):281-289.
14. Fan GX, Liu QH, Hesthaven JS. Multidomain pseudospectral time-domain method for simulation of scattering from buried objects. IEEE Transactions on Geoscience and Remote Sensing 2002; 40(6):1366-1373.
15. Zeng Y, Liu QH, Zhao G. Multidomain pseudospectral time-domain method for acoustic waves in Lossy media. Journal of Computational Acoustics 2003; accepted.
16. Zhao G. Liu QH. The 2.5-D multidomain pseudospectral time-domain algorithm. IEEE Transactions on Antennas and Propagation 2003; 51(3):619-627.
17. Zhao G, Zeng YQ, Liu QH. The 3-D multidomain pseudospectral time-domain method for wideband simulation. IEEE Microwave and Wireless Component Letters 2003; 13(5):184-186.
18. Liu QH, Millard XM, Tian B, Zhang ZQ. Applications of nonuniform fast transform algorithms in numerical solutions of differential and integral equations. IEEE Transactions on Geoscience and Remote Sensing 2000; 38(4):1551-1560.
19. Tian B, Liu QH. Nonuniform fast cosine transform and Chebyshev PSTD algorithm. Progress in Electromagnetics Research 2000: 28:259-279.
20. Cooley JW, Tukey JW. Algorithm for the machine computation of complex Fourier series. Mathematics and Computers 1965; 19(90):297-301.
21. Canuto C, Hussani MY, Quarteroni A, Zang T. Spectral Methods in Fluid Dynamics. Springer: New York.
22. Zhao G, Liu QH. The 3-D multidomain pseudospectral time-domain method for inhomogeneous conductive media. IEEE Transactions on Antennas and Propagation, April 2004, to appear.
23. Liu QH. An FDTD algorithm with perfectly matched layers for conductive media. Microwave and Optical Technology Letters 1997; 14(2):134-137.
24. He J, Liu QH. A nonuniform cylindrical FDTD algorithm with improved PML and quasi-PML absorbing boundary conditions. IEEE Transactions on Geoscience and Remote Sensing 1999; 37(2): 1066-1072.
25. Fan GX, Liu QH. A PML-FDTD algorithm for simulating plasma-covered cavity-backed slot antennas. Microwave and Optical Technology Letters 1998; 19(4):258-262.
26. Fan GX, Liu QH. An FDTD algorithm with PML for dispersive, conductive media. IEEE Transactions on Antennas and Propagation 2000; 48(5):637-646.
27. Abarbanel S, Gottlieb D. A mathematical analysis of the PML method. Journal of Computational Physics 1997; 134(2):357-363.
28. Fan GX, Liu QH. A well-posed PML absorbing boundary condition for lossy media. 2001 International IEEE/AP-S Symposium, vol. 3, 1999: 2-5.
29. Liu QH, He JQ. An efficient PSTD algorithm for cylindrical coordinates. IEEE Transactions on Antennas and Propagation 2001; 49(9):1349-1351.
30. Liu QH, Nguyen N. An accurate algorithm for nonuniform fast Fourier transforms (NUFFT). IEEE Microwave and Guided Wave Letters 1998; 8(1):18-20.
31. Nguyen N, Liu QH. The regular Fourier matrices and nonuniform fast Fourier transforms. SIAM Journal on Scientific Computing 1999; 21(1):283-293.
32. Carpenter MH, Kennedy CA, Fourth Order 2N-Storage Runge-Kutta Scheme 1994; Technical Report: NASA-TM-109112, 1994.
33. Funaro D, Gottlieb D. A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations. Mathematics of Computation 1988: 51(184):599-613.
34. Hesthaven JS, Warbutron T. Nodal high-order methods on unstructured grids. Journal of Computational Physics 2002; 181(1):186-221.
35. Mohammadian A, Shankar V, Hall W. Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure. Computer Physics Communications 1991: 68:175-196.
36. Zheng F, Chen Z, Zhang J. Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method. IEEE Transactions on Microwave Theory and Techniques 2000; 48(9): 1550-1558.
37. Lee J, Fornberg B. A split step approach for the 3-D Maxwell's equations. Journal of Computational and Applied Mathematics 2003; 158(2):485-505.
38. Zhao G, Liu QH. The unconditionally stable multidomain pseudospectral time-domain method. IEEE Microwave and Wireless Components Letters 2003; 13(11):475-477.
39. Lee J, Fornberg B. Some unconditionally stable time stepping methods for the 3-D Maxwell's equations. Journal of Computational and Applied Mathematics 2002; accepted.
40. Fan GX, Liu QH. Pseudospectral time-domain algorithm applied to electromagnetic scattering from electrically large objects. Microwave and Optical Technology Letters 2001; 29(2): 123-125.
41. Liu QH, Fan GX. A frequency-dependent PSTD algorithm for general dispersive media. IEEE Microwave and Guided Wave Letters 1999: 9(2):51-53.
42. Liu QH, Fan GX. Simulations of GPR in dispersive media using the PSTD algorithm. IEEE Transactions on Geoscience and Remote Sensing 1999; 37(5):2317-2324.
43. Fan GX, Liu QH, Hutchinson SA. FDTD and PSTD Simulations for plasma applications. IEEE Transactions on Plasma Science 2001; 29(2):341-348.
44. Hesthaven JS. Spectral penalty methods. Applied Numerical Mathematics 2000; 33(1-4):23-41.
45. Liu QH. A spectral-domain method with perfectly matched layers for time-domain solutions of Maxwell's equations. 1996 URSI Meeting, Baltimore, MD, July 1996.
46. Kreiss HO, Öliger J. Comparison of accurate methods for the integration of hyperbolic equations. Tellus 1972; 24:199-215.
47. Orszag SA. Comparison of pseudospectral and spectral approximation, Studies in Applied Mathematics 1972; 51:253-259.
48. Gottlieb D, Orszag SA. Numerical Analysis of Spectral Methods. SIAM: Philadelphia, 1977.
49. Fornberg B. On a Fourier method for the integration of hyperbolic equations. SIAM Journal of Numerical Analysis 1975; 12:509-528.
50. Fornberg B. A Practical Guide to Pseudospectral Methods, Cambridge University Press: New York, 1996.