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Finite element methods in the frequency domain are useful for a limited class of modelling. However, the matrix of finite element equations becomes very large and difficult to solve in many microwave and RF structures. Equally, to obtain a frequency response, the analysis must be performed at many frequencies over the range – especially for devices containing multiple resonances.
In the time domain, finite element methods in unstructured meshes, usually lead to a set of equations that can only be solved using an implicit method, which is not sufficiently fast for design purposes.
One of the reasons that finite element problems become very large for microwave and RF models is the need to model the wave structure in free space. Integral methods overcome this by only discretizing the surface of the geometry. For applications such as radar cross section this is a very suitable approach. However, as the structure becomes more complex, the simulation times increase rapidly – usually as the cube of the number of surface elements.
FDTD using the Yee algorithm is a well established and proven method for simulating RF and microwave problems. Although the number of equations is large, the explicit formulation is very fast.
The limitation of FDTD is that the time step is dependent on the size of the smallest finite difference cell in the grid for stability. When approximating a curved or sloping structure, a conventional FDTD method may use many small cells.
Every modeling technique has some strengths and some weaknesses. Some types of models were a given technique will excel and some types of models were the same technique will have difficulty (if it is even possible to use) performing rapidly and accurately.
FDTD is a very versatile modeling technique. It is a very intuitive technique, 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 time-domain pulse (such as a Gaussian pulse) is used as the source pulse, then a wide frequency range is solved with only one simulation. This is extremely useful in applications where resonant frequencies are not known exactly, 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 animation displays (movies) of the E/H field movement throughout the model. This type of display is extremely useful to understanding exactly what is going on in the model, and to help insure that the model is working correctly.
FDTD 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.
Since the computational domain must end at some point (or we would be modeling the entire universe!!), a boundary must be established. FDTD has a number of very good absorbing boundary conditions to chose from (and some that are not quite so good). The absorbing boundary condition (ABC) simulates the effect of free space beyond the boundary forever.
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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.
There are very good packages for those who want to start with FDTD simulation (MEEP) and photonic band gaps calculation (MPB): http://ab-initio.mit.edu/wiki/index.php/Main_Page
These packages are written for Unix but they are also very easy to use, can be installed and run on Cygwin