thumb|250px|In finite-difference time-domain method, "Yee lattice" is used to discretize [[Maxwell's equations in space. This scheme involves the placement of electric and magnetic fields on a staggered grid.]]

Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics.

History

Finite difference schemes for time-dependent partial differential equations (PDEs) have been employed for many years in computational fluid dynamics problems,

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| 1928 || Courant, Friedrichs, and Lewy (CFL) publish seminal paper with the discovery of conditional stability of explicit time-dependent finite difference schemes, as well as the classic FD scheme for solving second-order wave equation in 1-D and 2-D.

  1. FDTD is a systematic approach. With FDTD, specifying a new structure to be modeled is reduced to a problem of mesh generation rather than the potentially complex reformulation of an integral equation. For example, FDTD requires no calculation of structure-dependent Green functions.

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Further reading

The following article in Nature Milestones: Photons illustrates the historical significance of the FDTD method as related to Maxwell's equations:

Allen Taflove's interview, "Numerical Solution," in the January 2015 focus issue of Nature Photonics honoring the 150th anniversary of the publication of Maxwell's equations. This interview touches on how the development of FDTD ties into the century and one-half history of Maxwell's theory of electrodynamics:

  • Nature Photonics interview

The following university-level textbooks provide a good general introduction to the FDTD method:

Free software/Open-source software FDTD projects:

  • FDTD++: advanced, fully featured FDTD software, along with sophisticated material models and predefined fits as well as discussion/support forums and email support
  • openEMS (Fully 3D Cartesian & Cylindrical graded mesh EC-FDTD Solver, written in C++, using a Matlab/Octave-Interface)
  • pFDTD (3D C++ FDTD codes developed by Se-Heon Kim)
  • JFDTD (2D/3D C++ FDTD codes developed for nanophotonics by Jeffrey M. McMahon)
  • WOLFSIM (NCSU) (2-D)
  • Meep (MIT, 2D/3D/cylindrical parallel FDTD)
  • (Geo-) Radar FDTD
  • bigboy (unmaintained, no release files. must get source from cvs)
  • Parallel (MPI&OpenMP) FDTD codes in C++ (developed by Zs. Szabó)
  • FDTD code in Fortran 90
  • FDTD code in C for 2D EM Wave simulation
  • (3D parallel FDTD software package, maintained by Ilker R. Capoglu)
  • GSvit (3D FDTD solver with graphics card computing support, written in C, graphical user interface XSvit available)
  • gprMax (Open Source (GPLv3), 3D/2D FDTD modelling code in Python/Cython developed for GPR but can be used for general EM modelling.)

Freeware/Closed source FDTD projects (some not for commercial use):

  • EMTL (Electromagnetic Template Library) (Free С++ library for electromagnetic simulations. The current version implements mainly the FDTD).