Test2d06, 6th 'benchmark test' data file for CPO2D
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.
The number of segments used in the present example is small enough for the example to be run with the ‘demo’ version of CPO2D. Higher accuracy could of course be obtained with more segments, using the standard or full versions of CPO2D.
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.
A sphere is set up with a radius of 1 mm, using the z = 0 plane as a plane of positive reflection symmetry.
The printing level is put at 'a', for 'all', so that the charges are put in the output file tmp6a.dat. (These charges are entered only when they have newly calculated, and not when previously calculated charges are re-used.)
It can be seen that the total charge on the segments is 5.56314E-14 Coulombs, which when multiplied by 2, for the reflection, gives 1.112628E-13 Coulomb. The correct result for a sphere of radius 1 mm is 1.112650E-13 ( = 4*pi*epsilon0*0.001). The error is therefore approximately 0.002%, but the total number of segments is only 50. The total computing time is very short.