Test3d07, 7th 'benchmark test' data file for CPO3D

Capacitance of a sphere

The total charge on a sphere is reproduced in a few seconds in this benchmark test, with an error of 0.04%. By extrapolating to an infinite number of segments it is obtained essentially exactly.

(This simulation has cylindrical symmetry and so can be solved even more quickly and accurately with CPO2D).

The number of segments used in the present example is small enough for the example to be run with the ‘demo’ version of CPO3D. Higher accuracy could of course be obtained with more segments, using the standard or full versions of CPO3D.

The following data were obtained when the memory and speed of PC's was much more limited than at present, so the available number of segments was small and the requested inaccuracies were fairly high to give a quick demonstration.

An isolated sphere of radius 1 mm is at 1 V. The printing level is put at 'a', for 'all', so that the charges are put in the output file tmp7a.dat, from which it can be seen that the total charge is 6.95245E-15, which has to be multiplied by 16, for 4 reflection planes, giving 1.1124E-13 Coulomb. The correct result for a sphere of radius 1mm is 1.1127E-13 ( = 4*pi*epsilon0*.001) -an error of 0.03% This is with 100 segments. The error is 0.005% for 200 segments and extrapolates to essentially zero.

The computing time is a few seconds.