It is interesting to note that while FDTD is based on Maxwell’s equations which describe the behavior and effect of electromagnetism, the term “FDTD” itself was coined to describe the algorithm developed by Kane S. Yee in computational electromagnetism. Maxwell’s equations were based on the work of James Clerk Maxwell, a Scottish mathematician who published its initial form in 1861. Yee, born in China but acquired PhD Applied Mathematics from the University of California in Berkely, described his algorithm in 1966.
Prior to the Yee algorithm, FDTD had been used to solve problems in computational fluid dynamics. In Yee’s work, he suggested a novel way of applying FDTD operators on staggered grids for each of the vector field components in Maxwell’s equations. However, the term finite-difference time-domain (FDTD) itself was coined in by a professor Allen Taflove from the Northwestern University’s McCormick School of Engineering located in Illinois. He had published a paper on the August 1980 IEEE Trans. Electromagnetic Compatibility issue entitled “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic penetration problems.”
It was only in 1990 that FDTD techniques became popular in dealing with problems concerning interactions of electromagnetic waves, mostly because of the rise of wireless communication devices, but it is also used to model applications in the fields of geophysics and biomedical imaging and the convenience of computers equipped with fast processors and large memories. There are numerous developers for FDTD application software, including at least 27 which are proprietary, 8 which are open access, and two freeware.
The finite-difference time dimension (FDTD) method for simulating computational electromagnetism is considered the simplest and most efficient way to model the effects of electromagnetism on a certain material or object. The most commercial use of the FDTD model is in mobile communication systems, which makes use of radio frequencies, so engineers have to be able to project how the device will most likely operate in the real world by running simulations. Another application for FDTD is in fiber optics, which is also a technology that relates to communication, and there is an increasing interest in its use in nanotechnology. In a very real way, the FDTD method is used to design and improve the mobile and fixed communication technology we have today.
In terms of scalability, the FDTD method proves robust, merely requiring additional time to do the computation with no changes in the formula. However, while it is a relatively simple method, it requires fine grids to develop a model. FDTD does require a lot of computations which increase exponentially with the number of elements. In order to do an FDTD model, one will require a powerful computer with a lot of memory. It is recommended that a computer running a graphical processing unit (GPU) processor, which is specifically designed to handle large amounts of graphical data in parallel, which is exactly what is needed. How long it takes to complete a simulation will depend on the number of elements in an FDTD simulation and processing speed of the computer. In general, an FDTD model requires 30 bytes of memory per Yee cell and 80 operations per cell, per time step.
There are numerous ways to solve problems in computational electromagnetics. While all are feasible, one method has seen a meteoric rise in popularity since its inception in 1966: the finite-difference time-domain method (FDTD).
FDTD is a method of solving problems in computational electromagnetics that uses Maxwell’s equations and derivations of them to illustrate the behavior of electromagnetic fields around an object. In these equations, space and time are combined into spacetime, rather than examined as two separate entities. This means that in a FDTD problem, for any given moment in time, there is only one possible arrangement of the electromagnetic fields surrounding an object.
The finite-difference time-domain method compares the change in an electronic field in time against a change in a magnetic field across space. Conversely, it also examines the changes in a magnetic field along an analogous electronic field in space. By incrementally stepping through individual moments in time while measuring the strengths of electromagnetic fields along the space, the FDTD method creates a model of the electromagnetic fields acting on an object.
The FDTD method is performed on a given space and equations are elegant enough to account for the properties of the materials being examined, such as their electrical conductivity, permittivity, and permeability. When put through a computer, the method essentially runs a simulation of the electromagnetic fields of an object. This creates a lot of data that can be mined and visualized. It’s even possible to simulate the effects of the addition of an electromagnetic pulse to the model, making the method invaluable to engineers working with antennae and other electromagnetic receivers.
While FDTD has gained a lot of popularity for its intuitiveness and ability to outline huge models as they change through time, it does have its drawbacks. FDTD requires a great deal of preparatory planning on the system. It calls for every aspect of the item upon which the simulation is to be run to be modeled at a degree precise enough to account for tiny differences in electromagnetic wavelengths. FDTD may also take more computing time than other methods, especially depending on the shape of the object being examined.
The Future Data Testing Department uses this method as well as others in its data acquisition, visualization, and machine learning projects. Of course, this is nowhere near a full discussion of the complexities of the finite-difference time-domain method, but we believe it’s a reasonable overview of how and why we employ it.