History of FDTD Techniques and Applications For Maxwell's Equations
An appreciation of the basis, technical development, and possible future of FDTD numerical techniques for Maxwell’s equations can be developed by first considering their history. The following lists some of the key publications in this area, starting with Yee's seminal Paper #1 (1966), which has over 4,000 citations according to the ISI Web of Science.
| Partial chronology of FDTD techniques and applications for Maxwell's equations. | |
|---|---|
| year | event |
| 1966 | Yee described the basis of the FDTD numerical technique for solving Maxwell’s curl equations directly in the time domain on a space grid. |
| 1975 | Taflove and Brodwin reported the correct numerical stability criterion for Yee’s algorithm; the first sinusoidal steady-state FDTD solutions of two- and three-dimensional electromagnetic wave interactions with material structures; and the first bioelectromagnetics models. |
| 1977 | Holland and Kunz & Lee applied Yee’s algorithm to EMP problems. |
| 1980 | Taflove coined the FDTD acronym and published the first validated FDTD models of sinusoidal steady-state electromagnetic wave penetration into a three-dimensional metal cavity. |
| 1981 | Mur published the first numerically stable, second-order accurate, absorbing boundary condition (ABC) for Yee’s grid. |
| 1982–83 | Taflove and Umashankar developed the first FDTD electromagnetic wave scattering models computing sinusoidal steady-state near-fields, far-fields, and radar cross-section for two- and three-dimensional structures. |
| 1984 | Liao et al reported an improved ABC based upon space-time extrapolation of the field adjacent to the outer grid boundary. |
| 1985 | Gwarek introduced the lumped equivalent circuit formulation of FDTD. |
| 1986 | Choi and Hoefer published the first FDTD simulation of waveguide structures. |
| 1987–88 | Kriegsmann et al and Moore et al published the first articles on ABC theory in IEEE Transactions on Antennas and Propagation. |
| 1987–88, 1992 | Contour-path subcell techniques were introduced by Umashankar et al to permit FDTD modeling of thin wires and wire bundles, by Taflove et al to model penetration through cracks in conducting screens, and by Jurgens et al to conformally model the surface of a smoothly curved scatterer. |
| 1988 | Sullivan et al published the first 3-D FDTD model of sinusoidal steady-state electromagnetic wave absorption by a complete human body. |
| 1988 | FDTD modeling of microstrips was introduced by Zhang et al. |
| 1990–91 | FDTD modeling of frequency-dependent dielectric permittivity was introduced by Kashiwa and Fukai, Luebbers et al, and Joseph et al. |
| 1990–91 | FDTD modeling of antennas was introduced by Maloney et al, Katz et al, and Tirkas and Balanis. |
| 1990 | FDTD modeling of picosecond optoelectronic switches was introduced by Sano and Shibata, and El-Ghazaly et al. |
| 1992–94 | FDTD modeling of the propagation of optical pulses in nonlinear dispersive media was introduced, including the first temporal solitons in one dimension by Goorjian and Taflove; beam self-focusing by Ziolkowski and Judkins; the first temporal solitons in two dimensions by Joseph et al; and the first spatial solitons in two dimensions by Joseph and Taflove. |
| 1992 | FDTD modeling of lumped electronic circuit elements was introduced by Sui et al. |
| 1993 | Toland et al published the first FDTD models of gain devices (tunnel diodes and Gunn diodes) exciting cavities and antennas. |
| 1994 | Thomas et al introduced a Norton’s equivalent circuit for the FDTD space lattice, which permits the SPICE circuit analysis tool to implement accurate subgrid models of nonlinear electronic components or complete circuits embedded within the lattice. |
| 1994 | Berenger introduced the highly effective, perfectly matched layer (PML) ABC for two-dimensional FDTD grids, which was extended to three dimensions by Katz et al, and to dispersive waveguide terminations by Reuter et al. |
| 1995–96 | Sacks et al and Gedney introduced a physically realizable, uniaxial perfectly matched layer (UPML) ABC. |
| 1997 | Liu introduced the pseudospectral time-domain (PSTD) method, which permits extremely coarse spatial sampling of the electromagnetic field at the Nyquist limit. |
| 1997 | Ramahi introduced the complementary operators method (COM) to implement highly effective analytical ABCs. |
| 1998 | Maloney and Kesler introduced several novel means to analyze periodic structures in the FDTD space lattice. |
| 1998 | Nagra and York introduced a hybrid FDTD-quantum mechanics model of electromagnetic wave interactions with materials having electrons transitioning between multiple energy levels. |
| 1998 | Hagness et al introduced FDTD modeling of the detection of breast cancer using ultrawideband radar techniques. |
| 1999 | Schneider and Wagner introduced a comprehensive analysis of FDTD grid dispersion based upon complex wavenumbers. |
| 2000–01 | Zheng, Chen, and Zhang introduced the first three-dimensional alternating-direction implicit (ADI) FDTD algorithm with provable unconditional numerical stability. |
| 2000 | Roden and Gedney introduced the advanced convolutional PML (CPML) ABC. |
| 2000 | Rylander and Bondeson introduced a provably stable FDTD - finite-element time-domain hybrid technique. |
| 2002 | Hayakawa et al and Simpson and Taflove independently introduced FDTD modeling of the global Earth-ionosphere waveguide for extremely low-frequency geophysical phenomena. |
| 2003 | DeRaedt introduced the unconditionally stable, “one-step” FDTD technique. |
| 2008 | Ahmed, Chua, Li and Chen introduced the three-dimensional locally one dimensional (LOD)FDTD method and proved unconditional numerical stability. |
| 2010 | Chaudhury and Boeuf demonstrated the numerical procedure to couple FDTD and Plasma fluid model for studying Microwave Plasma Interaction. |
Read more about this topic: Finite-difference Time-domain Method
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