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=== An Overview of FDTD Modeling ===

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.

The FDTD computational domain must be discretized using an appropriate meshing scheme. EM.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.Tempo'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. EM.Tempo'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 on the right illustrates a metal ellipsoid and a 3D view of its Yee mesh.

The FDTD method provides a wideband simulation of your physical structure. 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 all affect the convergence behavior of the FDTD time marching loop. By default, EM.Tempo uses a modulated Gaussian waveform with optimal [[parameters]]. Another issue of concern is the numerical stability of the time marching scheme. You might expect to get better and more accurate results if you keep increasing the FDTD mesh resolution. However, in order to satisfy the Courant-Friedrichs-Levy (CFL) stability condition, the time step must be inversely proportional to the maximum grid cell size . A high resolution mesh requires a smaller time step. To let the fields in the computational domain fully evolve over time, a smaller time step will require a larger number of time steps to converge. EM.Tempo automatically chooses a time step that satisfies the CFL condition.