Technical Notes

For any classical electromagnetic problem, electric and magnetic fields of varying amplitudes exist at all points in some region of space and may change as a function of time. There are a variety of methods, both analytical and numerical, that can be applied to such problems.

Analytical methods are superior when achievable, but have limited scope due to the complexities of real geometries and materials.

Some numerical techniques calculate the electric and magnetic fields at particular points by summing over all electric and magnetic current elements on the surfaces of scatterers. This may require extensive computations for each point at which field values are desired. Many of these techniques require matrix inversions and are therefore limited to the capabilities of the inversion technique.

Although the electric and magnetic fields at any point in space were created by some source, these fields are not directly dependent upon the source. For instance, the electric fields associated with an electromagnetic wave generated at some point, and now at a great distance from this point, change as a function of the surrounding magnetic fields and no longer depend upon the source that created the wave, which may no longer exist. Thus, electric and magnetic fields can be easily computed by utilizing appropriate neighboring fields. This fact can greatly reduce complexities and numerical tedium.

In any volume of space, there is an infinite number of points. In classical electromagnetic problems, the electric and magnetic field vectors at each of these points may possess unique directions and magnitudes that may change with time. Whatever numerical method is employed, to compute all field values at all points in such a volume is consistently beyond computer capabilities. However, if space is discretized in such a fashion that the spatial resolution of the discretization can adequately resolve all necessary field gradients, then the associated results closely approximate those of actual space. This is the basis of the three-dimensional finite difference technique.

EMA3D employs the finite difference time domain technique (FDTD) in a numerical solution of Maxwell’s equations. As the name implies, the FDTD technique results in a solution of Maxwell’s equations in the time domain.