Validating scattering calculations using boundary value and internal field checks

An absolute direct check on results is possible in principle by checking to see if the boundary conditions are satisfied, and for perfectly conducting solids, checking to see if the fields inside the body are zero. In practice it has been found that the boundary region is much more sensitive to numerical errors than the far field. Some results on far-field accuracy as a function of boundary match error are shown and discussed. The results are for spheres of diameters 0.1, 0.5, 1, and 10 wavelengths. The curves are fairly close together and indicate that RMS (root-mean-square) boundary value error -40 to -50 dB below the peak normal E-field results in a far-field backscatter accuracy of better than 0.1 dB. Results are also shown for a 5:1 hemisphere-capped dipole, and the far-field error is smaller than for a sphere with the same RMS boundary value error. This is almost certainly due to the fact that the boundary value error for the dipole is increased by a few points in the region near the junction between the cylinder and hemisphere end caps.<>