TABLE OF CONTENTS In this section the numerical results are given. As an example we calculated the capacitances of various ellipsoids, because for ellipsoids one knows the analytical formula for the capacitance, which makes it possible to evaluate the accuracy of the numerical results. Consider the ellipsoid:
It is known [43] that the exact value of the capacitance of ellipsoid with a = b is:
Let a = b = 1, and ? 0 = 1. We have calculate the capacitance C for different values of the semiaxis c. The results of the calculations are given in Table A.10.
It is known (see Chapter 3), that the capacitance of a metallic disc of radius a is C = 8a ? 0, and one can see from Table 1, that asymptotically, as c ? 0, this formula can be used practically for the ellipsoids with c ? 0.001 with the error approximately equal to 0.005.
| C | n | m | N | Exact value | Error | Relative error | Calculation time |
|---|---|---|---|---|---|---|---|
| 0.9 | 40 | 30 | 2320 | 12.144630 | -0.221200 | 0.018212 | 25 sec |
| 0.5 | 40 | 30 | 2320 | 10.392304 | -0.222042 | 0.021366 | 25 sec |
| 0.1 | 40 | 30 | 2320 | 8.5020638 | -0.301189 | 0.035425 | 25 sec |
| 0.01 | 40 | 30 | 2320 | 8.050854 | 0.072132 | 0.008959 | 25 sec |
| 0.001 | 40 | 30 | 2320 | 8.005092 | -0.821528 | 0.106374 | 25 sec |
| 0.0001 | 40 | 30 | 2320 | 8.000509 | -1.068178 | 0.133513 | 25 sec |
| 0.9 | 50 | 40 | 3900 | 12.144630 | -0.180510 | 0.014801 | 1 min 15 sec |
| 0.5 | 50 | 40 | 3900 | 10,392304 | -0.185642 | 0.017860 | 1 min 15... |
