35th benchmark test for CPO3D
Field near the tip of a cone.
Obtained from test2d19.dat, using the conversion program conv2to3.exe and setting the number of radial subdivisions to 4 and 'saving' in CPO3D.
Then the test for 'aspect ratios' has to be effectively disabled by entering -1000 in \databuilder\ printing level...\allowed reading error...\Maximum aspect ratio
The lines asking for output data on the fields are added separately.
It can be seen that the program has automatically concentrated the segments at the tip. Using the right-click zoom option we can zoom into the tip and see that the length of the last segments is only 2.6E-8.
Results obtained:
r z potential ex ez
prog exact prog exact prog exact
0.000 0.000 1.00000 1.00000 0.000 0.000 3.4E5 inf
0.000 0.002 0.88319 0.88368 0.000 0.000 20.09 20.13
0.000 0.004 0.85166 0.85213 0.000 0.000 12.80 12.80
0.002 0.000 0.91805 0.91854 14.00 14.10 23.45 23.39
0.004 0.000 0.89602 0.89645 8.960 8.962 14.91 14.87
The accuracy is similar to that obtained in test2d19.
If we disable the 'uneven distribution' option on the editing sheet for the cone then the segments are evenly spaced axially and the results are much less accurate. For example the 3rd line of the above table becomes
r z potential ex ez
prog exact prog exact prog exact
0.000 0.004 0.89920 0.85213 0.000 0.000 8.91 12.80
This can of course easily be improved by using a succession of conical surfaces with the smallest at the tip.
It is usually possible to achieve an automatic concentration of segments where the charge densities are highest by using the iterative subdivision (adaptive segmentation) option. In the present case however the segments near the tip have such a small area that the charges on them are not significantly higher than the charges on other segments (and iterative subdivision uses the charges, not the charge densities).
But the iterative subdivision option would be expected to be suitable for realistic rounded tips.