Finite Difference Time Domain

Finite Difference Time Domain ( FDTD, English for finite difference method in the time domain ) or Yee method or method is a mathematical method for the direct integration of time-dependent differential equations . This method is usedparticularly successfully for calculating the solutions to Maxwell's equations .

history

The method was first proposed in 1966 by the Chinese-American applied mathematician Kane S. Yee (* 1934).

FDTD models using the Maxwell equation as an example

Standard arrangement of the electrical and magnetic vector components in the unit cell of a Cartesian Yee grid.
a) for a transverse electric wave (in 2D)
b) for a transverse magnetic wave (in 2D)
c) in three dimensions

The Maxwell equations describe the time evolution of electric and magnetic fields . The temporal change of the electric field is determined by the spatial change of the magnetic field, and the temporal change of the magnetic field by the spatial change of the electric field.

In the Yee method, the room is discretized with the help of a special grid ( Yee grid ). The value of the electric field strength E or the magnetic field strength H is stored at the grid points at one point in time . The new E field and the new H field for the next point in time are determined alternately at each grid point . The change in the E field is calculated from the numerical rotation of the adjacent H field. The change in the H field, in turn, is calculated from the rotation of the adjacent E field.

literature

Allen Taflove, Susan C. Hagness: Computational electrodynamics: the finite-difference time-domain method. 3rd ed. Artech House, Boston 2005, ISBN 1-58053-832-0 .

Web links

Software:

openEMS - open source 3D FDTD simulation software for Cartesian and cylindrical grids, developed at the University of Duisburg-Essen
Meep - FDTD simulation software developed at MIT
Secondspace - simulation of waves (space and time discrete), calculation by graphics card
Solitons - as particles in space, continuation of computing space

Individual evidence

^ Gilbert Strang: Scientific computing . Springer-Verlag, Heidelberg / Dordrecht / London / New York 2010, ISBN 978-3-540-78494-4 , pp. 571 ff . ( limited preview in Google Book search).
↑ ^a ^b Kane S. Yee: Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media . In: IEEE Transactions on Antennas and Propagation. 14, 1966, pp. 302-307, doi: 10.1109 / TAP.1966.1138693 .

[1] Gilbert Strang: Scientific computing . Springer-Verlag, Heidelberg / Dordrecht / London / New York 2010, ISBN 978-3-540-78494-4 , pp. 571 ff . ( limited preview in Google Book search).

[yee66-2] Kane S. Yee: Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media . In: IEEE Transactions on Antennas and Propagation. 14, 1966, pp. 302-307, doi: 10.1109 / TAP.1966.1138693 .