|
'''Finite-Difference Time-Domain (FDTD)''' is a popular electromagnetic modeling techniquestechnique. 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 difference equation|partial differential]] form) are modified to central-difference equations, discretized, and implemented in software. The equations are solved in a leap-frogleapfrog manner: the electric field is solved at a given instant in time, then the magnetic field areis solved at the next instant in time, and the process is repeated over and over again.
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 Curlcurl). This results in the basic FDTD time-stepping 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-dD, 2-dD, and 3-dD FDTD techniques. When multiple dimensions are considered, calculating the spatial differential becomes more complicated.
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 beare determined at every point in space within that computational ___domain. The material of each cell within the computational ___domain must be specified. Typically, the material will beis 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 materialmaterials isare 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 pointpoints within the computational ___domain. The simulation evolves the E and H fields forward in time.
Processing may be done on the E and H fields returned by the simulation. Data processing may also occur while the simulation is ongoing.
FDTD is a versatile modeling technique used to solve Maxwell's equations. 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 calculates the E and H fields everywhere in the computational ___domain as they evolve in time, 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. AllA materialswide arevariety possibleof linear and dielectrics,nonlinear dielectric and magnetic materials, etc. can be simplynaturally modeledand withouteasily the need to resort to work arounds or tricks to model these materialsmodeled.
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.
== What are the weaknesses of the FDTD Technique?==
Since FDTD requires that the entire computational ___domain be gridded, and thesethe grid spatial gridsdiscretization must be smallsufficiently comparedfine to resolve both the smallest electromagnetic wavelength and smaller than the smallest geometrical feature in the model, very large computational domains can be developed, which resultresults 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 processingpostprocessing.
Since theFDTD simulationsimulations calculatescalculate the E and H fields at all points within the computational ___domain, itthe iscomputational best___domain ifmust thebe computationalfinite ___domainto ispermit finiteits residence in the computer memory. In many cases this is achieved by creatinginserting artificial boundaries into the simulation space. Care must be taken to minimize errors introduced by such boundaries. There are a number of available highly effective absorbing boundary conditions to chose from(ABCs) to simulate thean effectinfinite of surrounding theunbounded computational ___domain with infinite free space.
Because FDTD is solved by propagating the fields forward in the time ___domain, the electromagnetic time response of the medium through which they travel needs tomust be modelledmodeled explicitly. For an arbitrary response, this will involveinvolves a computationally expensive time convolution, although in most cases the time response of the medium (or [[Dispersion_(optics)]]) can be modelledadequately moreand simply modeled using either the recursive convolution (RC) technique or the auxiliary differential equation (ADE) technique. 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.▼
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 ==
| 