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/* An EM.Tempo Primer */
In the Finite Difference Time Domain (FDTD) method, a discretized form of Maxwell’s equations is solved numerically and simultaneously in both the 3D space and time. During this process, the electric and magnetic fields are computed everywhere in the computational domain and as a function of time starting at t = 0. From knowledge of the primary fields in space and time, one can compute other secondary quantities including frequency domain characteristics like scattering [[parameters]], input impedance, far field radiation patterns, radar cross section, etc.
Since FDTD is a finite domain numerical technique, the computational domain of the problem must be truncated. At the boundaries of the computational domain, proper boundary conditions must be enforced. In a shielded structure, all objects are enclosed within a perfect electric (or magnetic) conductor box. In an open boundary problem like an antenna, some kind of absorbing boundary conditions such as a perfectly matched layer (PML) must be used to emulate the free space.
The computational domain is discretized using an appropriate meshing scheme. [[EM.Cube]] Tempo uses a non-uniform, variable, staircase (pixelated) Yee mesh with a mesh density that you can customize. A fixed-cell mesh generator is also available, where you can set constant cell dimensions along the three principal axes for the entire computational domain. The variable mesh density is specified in terms of the effective wavelength inside material media. As a result, the mesh resolution and average mesh cell size differ in regions that are filled with different types of material. [[EM.Cube]]'s non-uniform mesher generates more cells in the areas that are occupied by dielectric materials, fewer cells in the free space regions and no cells inside (impenetrable) PEC regions. [[FDTD Module]]'s default "adaptive" mesh generator also refines the mesh around curved segments of lines, surface or solids to produce a far more accurate representation of your geometry. The example below illustrates a dielectric ellipsoid and a 3D view of its Yee mesh:
{{Twoimg|FDTD93.png|A Dielectric Object...|FDTD94.png|...and its Yee mesh.}}
===Waveform, Bandwidth & Stability===
The FDTD method provides a wideband simulation of your physical structure. Frequency domain techniques often require a tedious frequency sweep to calculate the port characteristics (S/Y/Z [[parameters]]). By contrast, [[EM.Cube]]'s [[FDTD Module]] performs a discrete Fourier transform (DFT) of the time domain data to calculate these characteristics at the end of a single FDTD simulation run. In order to produce sufficient spectral information, an appropriate wideband temporal waveform is needed to excite the physical structure.
The choice of the waveform, its bandwidth and time delay are important for the convergence behavior of the FDTD time marching loop. By default, [[EM.Cube]] uses a modulated Gaussian waveform with optimal [[parameters]]: t = 0.966/Δf and t<sub>0</sub> = 4.5t, where Δf is the specified bandwidth of the simulation. The time delay t<sub>0</sub> is chosen so that the temporal waveform has an almost zero value at t = 0.
