This package – called sompy is a re-implementation of the
Sommerfeld integral [Som09] computation and the approximation by
Norton [Nor37] found in the public domain Numerical Electromagnetics
Code (NEC) in version 2 [BP81]. In particular this computes an
interpolation grid, in the original Fortran implementation this was in a
separate program named SOMNEC. The interpolation code that uses the grid
computed by somnec is found in the nec2 source code. Nowadays the
re-implementation of NEC2, in C called nec2c [Kyr] or Tim Moltenos C++
implementation [Mol.a] and Python wrapper [Mol.b] are more useful than
the original Fortran code.
The current code uses an infinitesimal dipole for generating the field.
The observation points are also thought as infinitesimal, so we can get
away with skipping a lot of integrations along antenna segments. The
interpolation grid used by NEC is re-implemented but for the (cubic)
interpolation a ready-made implementation from scipy.interpolate is
used. The grid can be exported – and read – from the original
fortran format (when compiled with the GNU Fortran compiler, the file
format seems to be compiler specific).
The code is mainly useful in antenna simulation. When used in that way
in a Method of Moments code, the field contributions need to be
integrated over the antenna segments.
In the current version the code can be used to display the waves created
by an infinitesimal dipole. In the example the lower edge is the ground,
what is seen as the Y-axis in the plot is in fact the Z-axis (height
above ground). The plot shows the field around the infinitesimal dipole
located at X=0, Z=1, lengths are in wavelength, i.e. the dipole is
located 1 wavelengths above ground. The program which has been used
for the plot is in the file display_sommerfeld.py.
The code currently doesn't have a python installer and is not on Pypi,
this may change if I make use of the code myself or you drop me a note
that you do something with it and need an installer.
The code is licensed under the MIT license, see LICENSE file.
Some notes about timing: The SOMNEC code originally took a long time to
compute a grid with some 200 points. One of the reasons is that numeric
integration is performed with an increasing number of points. Even back
in the 1990's the computation took 257 seconds on a DEC VAX 8600 and 100
seconds on a Silicon Graphics 4D/440 workstation (this is from an old
SOMNEC readme file). The implementation in Python takes about a
second. But the Fortran code today – we have floating point units in
every CPU – takes only about 20ms. So the Python code is a lot
slower even though using full vectorization in numpy. But now that
there is a Python implementation, experiments with different integration
methods might prove faster than the current variant of Romberg
integrals [Mil70].
K. A. Norton. The propagation of radio waves over the surface
of the earth and in the upper atmosphere, part II: The propagation
from vertical, horizontal, and loop antennas over a plane earth of
finite conductivity. Proceedings of the Institute of Radio
Engineers, 25(9):1203–1236, September 1937.
G. J. Burke and A. J. Poggio. Numerical electromagnetics code
(NEC) – method of moments, part I-III, January 1981. All three parts
available as ADA956129
Edmund K. Miller. A variable interval width quadrature
technique based on Romberg’s method. Journal of Computational
Physics, 5(2):265–279, April 1970.
