Finite-Difference Time-Domain (FDTD) is a popular electromagnetic modeling techniques. It is considered easy to understand and easy to implement in software. Since it is a time-___domain technique solutions can cover a wide frequency range with a single simulation run.
The FDTD method belongs in the general class of differential time ___domain numerical modeling methods. Maxwell's equations (in partial differential form) are modified to central-difference equations, discretized, and implemented in software. The equations are solved in a leap-frog manner: the electric field is solved at a given instant in time, then the magnetic field are solved at the next instant in time, and the process is repeated over and over again.
Workings of the FDTD method
When Maxwell's differential form equations are examined, it can be seen that the change in the E field in time (the time derivative) is dependent on the change in the H field across space (the Curl). This results in the basic FDTD equation that the next value of the E field in time is dependent on the old value of the E field and the local distribuition of the H field in space.
The H field is found in a similar manner. The rate of change of the H field is proportional to the spatial distribution of the E field.
This description holds true for 1-d, 2-d, and 3-d FDTD techniques. When multiple dimensions are considered, calculating the spatial differential becomes more complicated.
Using the FDTD method
In order to use FDTD a computational ___domain must be established. The computational ___domain is simply the physical region over which the simulation will be performed. The E and H fields will be determined at every point within the computational ___domain. The material of each cell within the computational ___domain must be specified. Typically, the material will be either free-space (air), metal, or dielectric. Any material can be used as long as the permeability, permittivity, and conductivity are specified.
Once the computational ___domain and the grid material is established, a source is specified. The source can be an impinging plane wave, a current on a wire, or an applied electric field, depending on the application.
Since the E and H fields are determined directly, the output of the simulation is usually the E or H field at a point or a series of point within the computational ___domain.
Processing may be done on the E and H fields returned by the simulation. Data processing may also occur while the simulation is ongoing.
Strengths of the FDTD technique
Every modeling technique has strengths and weaknesses, and the FDTD method is no different.
FDTD is a versatile modeling technique. It is intuitive, so users can easily understand how to use it and know what to expect from a given model.
FDTD is a time ___domain technique, and when a broad-band pulse (such as a Gaussian pulse) is used as the source, then the response of the system over a wide range of frequencies can be obtained with a single simulation. This is useful in applications where resonant frequencies are not exactly known, or anytime that a broadband result is desired.
Since FDTD is a time-___domain technique which finds the E/H fields everywhere in the computational ___domain, it lends itself to providing animated displays of the electromagnetic field movement through the model. This type of display is useful in understanding what is going on in the model, and to help ensure that the model is working correctly.
The FDTD technique allows the user to specify the material at all points within the computational ___domain. All materials are possible and dielectrics, magnetic materials, etc. can be simply modeled without the need to resort to work arounds or tricks to model these materials.
FDTD allows the effects of apertures to be determined directly. Shielding effects can be found, and the fields both inside and outside a structure can be found directly.
FDTD provides the E and H fields directly. Since most EMI/EMC modeling applications are interested in the E/H fields, it is best that no conversions must be made after the simulation has run to get these values.
What are the weaknesses of the FDTD Technique?
Since FDTD requires that the entire computational ___domain be gridded, and these grids must be small compared to the smallest wavelength and smaller than the smallest feature in the model, very large computational domains can be developed, which result in very long solution times. Models with long, thin features, (like wires) are difficult to model in FDTD because of the excessively large computational ___domain required.
FDTD finds the E/H fields directly everywhere in the computational ___domain. If the field values at some distance (like 10 meters away) are desired, it is likely that this distance will force the computational ___domain to be excessively large. Far field extensions are available for FDTD, but require some amount of post processing.
Since the simulation calulates the E and H fields at all points within the computational ___domain, it is best if the computational ___domain is finite. In many cases this is achieved by creating artificial boundaries into the simulation. Care must be taken to minimize errors introduced by such boundaries. There are a number of boundary conditions to chose from to simulate the effect of surrounding the computational ___domain with infinite free space.
Because FDTD is solved by propagating the fields forward in the time ___domain, the time response of the medium through which they travel needs to be modelled explicitly. For arbitrary response, this will involve a computationally expensive convolution, although in most cases the time response (or Dispersion_(optics)) can be modelled more simply. An alternative way of solving Maxwell's_equations that can treat arbitrary dispersion easily is the Pseudospectral Spatial-Domain method (PSSD), which instead propagates the fields forward in space.
References
Journal Articles
University level textbooks
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