Quote from: lmbfan on 07/03/2015 08:04 pm Considering that Dr. Rodal's analysis shows only 3 slices of the frustum, what are the odds that there are some vectors in the field that are not show actually point the other way? Is there some way to sum the entire Poynting field, including those not shown in the cross sectional views? I notice that in Meep there is the option to output the Poynting vectors here:



http://ab-initio.mit.edu/wiki/index.php/Meep_Reference#Output_functions



Notably this section:



Quote output-Xfield-x, output-Xfield-y, output-Xfield-z, output-Xfield-r, output-Xfield-p Output the x, y, z, r, or φ component respectively, of the field X, where X is either h, b, e, d, or s for the magnetic, electric, displacement, or Poynting field, respectively. If the field is complex, outputs two datasets, e.g. ex.r and ex.i, within the same HDF5 file for the real and imaginary parts, respectively. Note that for outputting the Poynting field, you might want to wrap the step function in synchronized-magnetic to compute it more accurately; see Synchronizing the magnetic and electric fields.



I wonder if there is a HDF5 reduction tool that can sum up fields in the file and reduce the entire field to one vector, or how complicated it would be to write such a tool. Seems to me to be just adding up a bunch of numbers... which computers are rumored to be good at.

Nothing left to chance here. In Cartesian coordinates three views should suffice, plus common knowledge of transverse electromagnetic variation with the azimuthal angle. There are only two planes shown at azimuthal angles of 0 and 90 degrees, but the variation with azimuthal angle is shown in the base view and it is a conventional harmonic m=1, n=1 variation.



It is for higher modes, m>1 that what you are discussing would apply, not for m=1, n=1.



We know what the antenna looks like: it is a dipole antenna, the plane views are consistent with it.



To double check this all that is needed is to provide other circular cross-sections: I would favor one at the antenna location, another one close to it, within the same longitudinal wave-pattern, and another one in the next longitudinal wave pattern away from it towards the big base.



Concerning <<seems to me to be just adding up a bunch of numbers... which computers are rumored to be good at.>>, the csv files are available to the public, so anybody can perform their own postprocessing calculations based on the csv, all you have to do is to calculate this can be done by anybody without using HDF5



Somebody sent me a Personal Message asking "How can you be sure that nothing is left to chance ?"ANSWER: Because this is not a Monte Carlo analysis where statistical uncertainty is inherent in the model. This is a Finite Difference analysis where Maxwell's equations are solved with a Finite Difference discretization scheme both in time and space. As such we are solving Maxwell's equations. The complication comes in through the RF antenna feed, but it is a dipole antenna with a simple geometry: we know what is the field variation produced by such an antenna. We also know what the standing waves look like, because I have run the exact solution for this model (so the truncated cone geometry does not introduce uncertainty). We know that the mode is m=1, n=1 and therefore we know the variation in the azimuthal direction.These are the errors that can be present:1) Human error. Human errors in @aero's modeling or human error in my postprocessing to compute the Poynting vector. I have double-checked my solution. The best way to further address this is through indepedent post-processing by others of the same csv files.2) Finite Difference discretization errors: time space FD discretization was recently addressed by aero by doubling the number of FD gridpoints. This serves to analyze the FD discretization in space. FD discretization in time can be addressed by halving the FD time step and marching to twice the number of time steps to arrive at the same time: compare the results3) Not having reached steady state: we could examine further marching for another 100 time steps for example.4) As previously discussed to double check the results I advise to output other circular cross-sections closer to the antenna, to see whether the mode shape deviates from m=1, n=1 closer to the antenna.