Finite-difference time-___domain method: Difference between revisions

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{{Short description|Numerical analysis technique}}

[[File:Yee cell.png|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 field|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 equation]]s (PDEs) have been employed for many years in [[computational fluid dynamics]] problems,<ref name="vonneumann49" /> including the idea of using centered finite difference operators on staggered grids in space and time to achieve second-order accuracy.<ref name="vonneumann49" />

The novelty of Kane Yee's FDTD scheme, presented in his seminal 1966 paper,<ref name="yee66" /> was to apply centered finite difference operators on staggered grids in space and time for each electric and magnetic vector field component in Maxwell's curl equations.

The descriptor "Finite-difference time-___domain" and its corresponding "FDTD" acronym were originated by [[Allen Taflove]] in 1980.<ref name="taflove80" />

Since about 1990, FDTD techniques have emerged as primary means to computationally model many scientific and engineering problems dealing with [[electromagnetic wave]] interactions with material structures. Current FDTD modeling applications range from near-[[Direct current|DC]] (ultralow-frequency [[geophysics]] involving the entire Earth-[[ionosphere]] waveguide) through [[microwaves]] (radar signature technology, [[Antenna (radio)|antennas]], wireless communications devices, digital interconnects, biomedical imaging/treatment) to [[visible light]] ([[photonic crystal]]s, nano[[plasmon]]ics, [[soliton]]s, and [[biophotonics]]).<ref name="taflove05" /> In 2006, an estimated 2,000 FDTD-related publications appeared in the science and engineering literature (see [[#Popularity|Popularity]]). As of 2013, there are at least 25 commercial/proprietary FDTD software vendors; 13 free-software/[[Open source|open-source]]-software FDTD projects; and 2 freeware/closed-source FDTD projects, some not for commercial use (see [[#External links|External links]]).