A Summary Review on 25 Years of Progress and Future Challenges in FDTD and FETD Techniques

K. S. Yee, “Numerical solution of initial

boundary value problems involving

Maxwell ́s equations in isotropic media,”

IEEE Trans. Antennas Propag., vol. 14, pp.

-307, 1966.

A. Taflove and S. Hagness, Computational

Electrodynamics: The Finite-Difference

Time-Domain Method, 3 rd ed., Artech

House, 2005.

J. F. Lee, R. Lee, and A. C. Cangellaris,

“Time domain finite element methods,”

IEEE Trans. Antennas Propag., vol. 45, no.

, pp. 430-442, 1997.

J. M. Jin, The Finite Element Method in

Electromagnetics, 2 nd ed., John Wiley, 2003.

B. Donderici and F. L. Teixeira, “Mixed

finite-element time-domain method for

transient Maxwell equations in doubly

dispersive media,” IEEE Trans. Microwave

Theory Tech. , vol. 56, no. 1, pp. 113-120,

K. L. Shlager and J. B. Schneider, “A

selective survey of the finite-difference

time-domain literature,” IEEE Antennas

Propag. Mag., vol. 37, no. 4, pp. 39-56,

F. L. Teixeira, “Time-domain finite-

difference and finite-element methods for

Maxwell equations in complex media,”

IEEE Trans. Antennas Propag., vol. 56, no.

, pp. 2150-2166, 2008.

A. Taflove and M. E. Brodwin, “Numerical

solution of steady-state electromagnetic

scattering problems using the time-

dependent Maxwel l's equations,” IEEE

Trans. Microwave Theory Tech., vol. 23, pp.

–630, 1975.

R. Holland, “Threde: A free-field EMP

coupling and scattering code,” IEEE Trans.

Nuclear Sci., vol. 24, pp. 2416–2421, 1977.

K. S. Kunz and K. M. Lee, “A three-

dimensional finite-difference solution of the

external response of an aircraft to a complex

transient EM environment,” IEEE Trans.

Electromagn. Compat., vol. 20, pp. 328–

, 1978.

A. Taflove, “Application of the finite-

difference time-domain method to sinusoidal

steady state electromagnetic penetration

problems,” IEEE Trans. on Electromagn.

Compat., vol. 22, pp. 191–202, 1980.

T. Weiland, “A discretization method for the

solution of Maxwell’s equations for six-

component fields,” Electronics and

Communications AEU, vol. 31, no.3, pp.

–120, 1977.

G. Mur, “Absorbing boundary conditions for

the finite-difference approximation of the

time-domain electromagnetic field

equations,” IEEE Trans. Electromagn.

Compat., vol. 23, pp. 377–382., 1981.

Z. P. Liao, H. L. Wong, B. P. Yang, and Y.

F. Yuan, “A transmitting boundary for

transient wave analysis,” Scientia Sinica A

vol. 27, pp. 1063–1076, 1984.

G. A. Kriegsmann, A. Taflove, and K. R.

Umashankar, “A new formulation of

electromagnetic wave scattering using an

on-surface radiation boundary condition

approach,” IEEE Trans. Antennas Propag.,

vol. 35, pp. 153–161, 1987.

T. G. Moore, J. G. Blaschak, A. Taflove,

and G. A. Kriegsmann, “Theory and

application of radiation boundary

operators,” IEEE Trans. Antennas Propag .,

vol. 36, pp. 1797–1812, 1988.

K. R. Umashankar and A. Taflove, “A novel

method to analyze electromagnetic

scattering of complex objects,” IEEE Trans.

Electromagn. Compat., vol. 24, pp. 397–

, 1982.

ACES JOURNAL, VOL. 25, NO. 1, JANUARY 2010

A. Taflove and K. R. Umashankar, “Radar

cross section of general three-dimensional

scatterers,” IEEE Trans. Electromagn.

Compat., vol. 25, pp. 433–440, 1983.

D. H. Choi and W. J. Hoefer, “The finite-

difference time-domain method and its

application to eigenvalue problems,” IEEE

Trans. Microwave Theory Tech., vol. 34, pp.

–1470, 1986.

X. Zhang, J. Fang, K. K. Mei, and Y. Liu,

“Calculation of the dispersive characteristics

of microstrips by the time-domain finite-

difference method,” IEEE Trans. Microwave

Theory Tech., vol. 36, pp. 263–267, 1988.

D. M. Sullivan, O. P. Gandhi, and A.

Taflove, “Use of the finite-difference time-

domain method in calculating EM

absorption in man models,” IEEE Trans.

Biomed. Eng., vol. 35, pp. 179–186, 1988.

K. R. Umashankar, A. Taflove, and B.

Beker, “Calculation and experimental

validation of induced currents on coupled

wires in an arbitrary shaped cavity,” IEEE

Trans. Antennas Propag., vol. 35, pp. 1248–

, 1987.

A. Taflove, K. R. Umashankar, B. Beker, F.

A. Harfoush, and K. S. Yee, “Detailed

FDTD analysis of electromagnetic fields

penetrating narrow slots and lapped joints in

thick conducting screens,” IEEE Trans.

Antennas Propag., vol. 36, pp. 247–257,

C. J. Railton, I. J. Craddock, and J. B.

Schneider, "An improved locally distorted

CPFDTD algorithm with provable stability,"

Electron. Lett., vol. 31, no. 18, pp. 1585-

, 1995.

S. Dey and R. Mittra, “A locally

conformal finite-difference time-domain

(FDTD) algorithm for modeling three-

dimensional perfectly conducting objects,”

IEEE Microwave Guided Wave Lett ., vol.

, pp. 273-275, 1997.

C. J. Railton and J. B. Schneider, "An

analytical and numerical analysis of several

locally-conformal FDTD Schemes," IEEE

Trans. Microwave Theory Tech., vol. 47, no.

, pp. 56-66, 1999

W. Gwarek, “Analysis of an arbitrarily

shaped planar circuit — A time-domain

approach,” IEEE Trans. Microwave Theory

Tech., vol. 33, pp. 1067–1072, 1985.

G. Maloney, G. S. Smith, and W. R. Scott,

Jr., “Accurate computation of the radiation

from simple antennas using the finite-

difference time-domain method,” IEEE

Trans. Antennas Propag., vol. 38, pp. 1059–

, 1990

D. S. Katz, A. Taflove, M. J. Piket-May, and

K. R. Umashankar, “FDTD analysis of

electromagnetic wave radiation from

systems containing horn antennas,” IEEE

Trans. Antennas Propag., vol. 39, pp. 1203–

, 1991.

K. Li, C. F. Lee, S. Y. Poh, R. T. Shin, and

J. A. Kong, “Application of FDTD method

to analysis of electromagnetic radiation from

VLSI heatsink configurations,” IEEE Trans.

Electromagn. Compat., vol. 35, no. 2, pp.

– 214, 1993.

R. Lee and T.T. Chia, “Analysis of

electromagnetic scattering from a cavity

with a complex termination by means of a

hybrid ray-FDTD method,” IEEE Trans.

Antennas Propag., vol. 41, pp. 1560-1569,

V. A. Thomas, M. E. Jones, M. J. Piket-

May, A. Taflove, and E. Harrigan, “The use

of SPICE lumped circuits as sub-grid

models for FDTD high-speed electronic

circuit design,” IEEE Microwave Guided

Wave Lett., vol. 4, pp. 141–143, 1994.

A. Bataineh, R. Lee, and F. Ozguner,

“Electrical characterization of high-speed

interconnects with a parallel three-

dimensional finite difference time-domain

algorithm,” Simulation, vol. 64, pp. 289-

, 1995.

E. Sano and T. Shibata, “Full-wave analysis

of picosecond photoconductive switches,”

IEEE J. Quantum Electron., vol. 26, pp.

–377, 1990.

P. M. Goorjian and A. Taflove, “Direct time

integration of Maxwell’s equations in

nonlinear dispersive media for propagation

and scattering of femtosecond

electromagnetic solitons,” Opt. Lett., vol.

, pp. 180–182, 1992.

R. W. Ziolkowski and J. B. Judkins, “Full-

wave vector Maxwell’s equations modeling

TEIXERIA: SUMMARY REVIEW ON 25 YEARS IN FDTD AND FETD

of self-focusing of ultra-short optical pulses

in a nonlinear Kerr medium exhibiting a

finite response time,” J. Opt. Soc. Am. B,

vol. 10, pp. 186–198, 1983.

R. Luebbers, F. Hunsberger, K. Kunz, R.

Standler, and M. Schneider, “A frequency-

dependent finite-difference time-domain

formulation for dispersive materials,” IEEE

Trans. Electromagn. Compat., vol. 32, pp.

–227, 1990.

R. M. Joseph, S. C. Hagness, and A.

Taflove, “Direct time integration of

Maxwell’s equations in linear dispersive

media with absorption for scattering and

propagation of femtosecond electromagnetic

pulses,” Opt. Lett., vol. 16, pp. 1412–1414,

A. C. Cangellaris, M. Gribbons, and G.

Sohos, “A hybrid spectral/FDTD method for

the electromagnetic analysis of guided

waves in periodic structures,” IEEE

Microwave Guided Wave Lett., vol. 3, no.

, pp. 375–377, 1993.

P. Harms, R. Mittra, and W. Ko,

“Implementation of the periodic boundary

condition in the finite-difference time-

domain algorithm for FSS structures,” IEEE

Trans. Antennas Propag. , vol. 42, no. 9,

pp.1317–1324, 1994.

A. Taflove and S. Hagness, “Analysis of

Periodic Structures,” in Computational

Electrodynamics: The Finite Difference

Time Domain Method. Boston, MA: Artech

House, 1995, ch. 13.

M. Celuch-Marcysiak and W. K. Gwarek,

“Spatially looped algorithms for time-

domain analysis of periodic structures,”

IEEE Trans. Microwave Theory Tech. , vol.

, no. 4, pp. 860–865, 1995.

S. Wang and F. L. Teixeira, “Dispersion-

relation-preserving FDTD schemes of large-

scale three-dimensional problems,” IEEE

Trans. Antennas Propag., vol. 51, no. 8, pp.

-1828, 2003.

B. Finkelstein and R. Kastner, “A

comprehensive new methodology for

formulating FDTD schemes with controlled

order of accuracy and dispersion,” IEEE

Trans. Antennas Propag., vol. 56, no.

, pp. 3516-3525, 2008.

Q.H. Liu, “The PSTD algorithm: A time-

domain method requiring only two cells per

wavelength,” Microwave Opt. Technol.

Lett., vol. 15, no. 3, pp. 357-361, 1997.

J. Berenger, “A perfectly matched layer for

the absorption of electromagnetic waves,” J.

Comput. Phys., vol. 114, pp. 185–200, 1994.

D. S. Katz, E. T. Thiele, and A. Taflove,

“Validation and extension to three

dimensions of the Berenger PML absorbing

boundary condition for FDTD meshes,”

IEEE Microwave Guided Wave Lett., vol. 4,

pp. 268–270, 1994.

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 . Antennas Propag .,

vol. 43, pp. 1460–1463, 1995.

F. L. Teixeira and W. C. Chew, “Complex

space approach to perfectly matched layers:

A review and some new developments,” Int.

J. Num. Model., vol. 13, no. 5, pp. 441-455,

F. L. Teixeira, K. P. Hwang, W. C. Chew,

and J. M. Jin, “Conformal PML-FDTD

schemes for electromagnetic field

simulations: A dynamic stability study,”

IEEE Trans. Antennas Propag., vol. 49, no.

, pp. 902-907, 2001.

C. D. Moss, F. L. Teixeira, Y.E. Yang, and

J. A. Kong, “Finite-difference time-domain

simulation of scattering from objects in

continuous random media,” IEEE Trans.

Geosci. Remote Sens. , vol. 40, no. 1, pp.

-186, 2002.

T. Namiki, “A new FDTD algorithm based

on alternating-direction implicit method,”

IEEE Trans. Microwave Theory Tech. , vol.

, no. 10, pp. 2003–2007, Oct. 1999.

F. Zheng, Z. Chen, and J. Zhang, “Toward

the development of a three-dimensional

unconditionally stable finite-difference time-

domain method,” IEEE Trans. Microw.

Theory Tech., vol. 48, no. 9, pp. 1550–1558,

Sep. 2000.

V. E. do Nascimento, B.-H. V. Borges, and

F. L. Teixeira, “Split-field PML

implementations for the unconditionally

stable LOD-FDTD method,” IEEE

ACES JOURNAL, VOL. 25, NO. 1, JANUARY 2010

Microwave Wireless Components Lett. , vol.

, no. 7, pp. 398-400, 2006.

K.-Y. Jung and F. L. Teixeira, “An iterative

unconditionally stable LOD-FDTD

method,” IEEE Microwave Wireless

Components Lett., vol. 18, no. 2, pp. 76-78,

S. S. Zivanovic, K. S.Yee, and K. K. Mei,

“A subgridding method for the time-domain

finite-difference method to solve Maxwell’s

equations,” IEEE Trans. Microwave Theory

Tech., vol. 39, no. 3, pp. 471–479, 1991.

S. Kapoor, “Sub-cellular technique for

finite-difference time-domain method,”

IEEE Trans. Microwave Theory Tech. , vol.

, no. 5, pp. 673–677, 1997.

M. Okoniewski, E. Okoniewska, and M. A.

Stuchly, “Three-dimensional subgridding

algorithm for FDTD,” IEEE Trans.

Antennas Propag., vol. 45, no. 3, pp. 422–

, 1997.

K. M. Krishnaiah and C. J. Railton,

‘‘Passive equivalent circuit of FDTD: an

application to subgridding,’’ Electron. Lett.,

vol. 33, 1277–1278, 1997.

P. Thoma and T. Weiland, ‘‘A consistent

subgridding scheme for the finite difference

time domain method,’’ Int. J. Num. Model.

, 359–374, 1996.

K. M. Krishnaiah and C. J. Railton, "A

stable subgridding algorithm and its

application to eigenvalue problems," IEEE

Trans. Microwave Theory Tech., vol. 47, pp.

-628, 1999.

S. Wang, F. L. Teixeira, R. Lee, and J.-F.

Lee, `Optimization of subgridding schemes

for FDTD,' IEEE Microwave Wireless

Components Lett. , vol. 12, no. 6, pp. 223-

, 2002.

B. Donderici and F. L. Teixeira, “Improved

FDTD subgridding algorithms via digital

filtering and domain overriding,” IEEE

Trans. Antennas Propag., vol. 53, no. 9, pp.

-2951, 2005.

J. P. Berenger, “A Huygens subgridding for

the FDTD method,” IEEE Trans. Antennas

Propag., vol. 54, no. 12, pp. 3797 – 3804,

R. Schuhmann and T. Weiland, “A stable

interpolation technique for FDTD on non-

orthogonal grids,” Int. J. Num. Model., vol.

, no. 6, pp. 299 – 306, 1999.

S. D. Gedney and J. A. Roden, “Numerical

stability of nonorthogonal FDTD methods,”

IEEE Trans. Antennas Propag., vol. 48,

issue 2, pp. 231-239, 2000.

A. Bossavit, “Whitney forms: A new class

of finite elements for three-dimensional

computations in electromagnetics,” IEE

Proc. A , vol. 135, pp. 493–500, 1988.

F. L. Teixeira and W. C. Chew, “Analytical

derivation of a conformal perfectly matched

absorber for electromagnetic waves,”

Microwave and Optical Technology Letters,

vol. 17, no. 4, pp. 231-236, 1998.

T. Rylander and J.-M. Jin, “Conformal

perfectly matched layers for the time domain

finite element method,” in IEEE AP-S Int.

Symp. Digest, vol. 1, pp. 698–701, 2003.

B. Donderici and F. L. Teixeira, “Conformal

perfectly matched layer for the mixed finite-

element time-domain method,” IEEE Trans.

Antennas Propag., vol. 56, no. 4, pp. 1017-

, 2008.

M. M. Ilic and B. M. Notaros, “Higher

order hierarchical curved hexahedral vector

finite elements for electromagnetic

modeling,” IEEE Trans. Microwave Theory

Tech., vol. 51, no. 3, pp. 1026-103, 2003.

R. N. Rieben , G. H. Rodrigue , and D. A.

White, “A high order mixed vector finite

element method for solving the time

dependent Maxwell equations on

unstructured grids,” J. Comp. Phys ., vol.

, no. 2, pp. 490-519, 2005.

G. Cohen, Higher Order Numerical

Methods for Transient Wave Equations ,

Springer-Verlag, 2001.

N. Marais and D. B. Davidson, “Numerical

evaluation of high-order finite element time

domain formulations in electromagnetics,”

IEEE Trans. Antennas Propag., vol. 56, no.

, pp. 3743-3751, 2008.

B. He and F. L. Teixeira, “A sparse and

explicit FETD via approximate inverse

Hodge (mass) matrix,” IEEE Microwave

Wireless Components Lett. , vol. 16, no. 6,

pp. 348-350, 2006.

M. Wong, O. Picon, and V. F. Hanna, “A

finite element method based on Whitney

TEIXERIA: SUMMARY REVIEW ON 25 YEARS IN FDTD AND FETD

forms to solve Maxwell equations in the

time domain,” IEEE Trans. Magn. , vol. 31,

no. 3, pp. 1618–1621, 1995.

F. L. Teixeira and W. C. Chew, “Lattice

electromagnetic theory from a topological

viewpoint,” J. Math. Phys., vol. 40, no. 1,

pp. 169–187, 1999.

G. Cohen and P. Monk, “Gauss point mass

lumping schemes for Maxwell’s equations,”

Numer. Meth. Partial Diff. Eq., vol. 14 , pp.

–88, 1998.

J. R. Munkres, Elements of Algebraic

Topology, Addison-Wesley, Reading, Mass.,

F. L. Teixeira (ed.), Geometrical Methods

for Computational Electromagnetics,

Progress In Electromagnetics Research

Series 32, EMW Publishing, Cambridge,

Mass., 2001.

B. He and F. L. Teixeira, “On the degrees of

freedom of lattice electrodynamics,” Phys.

Lett. A, vol. 336, pp. 1-7, 2005.

P. Monk, Finite Element Methods for

Maxwell's Equations, Oxford Univ. Press,

S. Adams, J. Payne, and R. Boppana, “Finite

Difference Time Domain (FDTD)

Simulations Using Graphics Processors,”

Proc. 2007 DoD High Performance

Computing Modernization Program Users

Group Conf., pp. 334-338, 2007.

Y. Liu and C.D. Sarris, “Fast Time-Domain

Simulation of Optical Waveguide Structures

with a Multilevel Dynamically Adaptive

Mesh Refinement FDTD Approach,” J.

Lightwave Technol., vol. 24, no. 8, pp. 3235-

, 2006.

R. A. Abd-Alhameed and P. S. Excell,

Complex computational electromagnetic

using hybridization techniques,” in

Advances in Information Technologies for

Electromagnetics (L. Tarricone, A. Espostio,

eds.), Springer-Verlag, pp.69-145, 2006.

B. Donderici and F. L. Teixeira, “Accurate

interfacing of heterogeneous structured

FDTD grid components,” IEEE Trans.

Antennas Propag., vol. 54, no. 6. pp. 1826-

, 2006.

A. Lew, A., J.E. Mardsen, M. Ortiz, and M.

West, “Asynchronous variational

integrators,” Arch. Rational Mech. Anal. ,

vol. 167, p. 85, 2003.

D. J. Riley and C. D. Turner, “VOLMAX: a

solid-model-based, transient volumetric

Maxwell solver using hybrid grids,” IEEE

Antennas Propag. Mag., vol. 39, no. 1, pp.

-33, 1997.

C.-T. Hwang and R.-B. Wu, “Treating late-

time instabilit y of hybrid finite-

element/finite-difference time-domain

method,” IEEE Trans. Antennas Propag. ,

vol. 47, no. 2. pp. 227-232, 1999.

T. Rylander and A. Bondeson, “Stable

FDTD-FEM hybrid method for Maxwell’s

equations,” Comp. Phys. Comm., vol. 125,

pp. 75–82, 2000.

J. Jin and D. J. Riley, Finite Element

Analysis of Antennas and Arrays , Wiley-

IEEE Press, 2009