Figure 1
Plane S with its sub-planes.
Figure 2
The domain of subdivision along axis X and axis Y.
Figure 3
The variations of magnetic flux caused by the errors.
Figure 4
The distribution of magnetic flux lines from dipole field on the magnetic equatorial plane.
Figure 5
The distribution of seed points from the equivalent magnetic flux algorithm.
Table 1
The accuracies of the traditional and improved algorithms with the same number of grids using different subdivisions.
| 4/9x4/9 subdomain A | 5/9x5/9 subdomain B | 7/9x7/9 subdomain C | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 18x18 | 27x27 | 36x36 | 18x18 | 27x27 | 36x36 | 18x18 | 27x27 | 36x36 | |||||
| N | 30.1211 | 30.1197 | 30.1192 | N | 43.6988 | 43.6973 | 43.6967 | N | 74.2201 | 74.2189 | 74.2185 | ||
| ε (%) | 7.5754 | 7.5705 | 7.5688 | ε (%) | 1.6251 | 1.6216 | 1.6204 | ε (%) | 0.2975 | 0.2959 | 0.2953 | ||
| 9x36 | 9x81 | 18x72 | 9x36 | 9x81 | 18x72 | 9x36 | 9x81 | 18x72 | |||||
| N' | 30.1136 | 30.1128 | 30.1174 | N' | 43.6903 | 43.6895 | 43.6946 | N' | 74.2134 | 74.2127 | 74.2168 | ||
| ε' (%) | 7.5486 | 7.5458 | 7.5621 | ε' (%) | 1.6053 | 1.6034 | 1.6155 | ε' (%) | 0.2884 | 0.2874 | 0.2931 | ||
Table 2
The accuracies of the traditional and improved algorithms with a different numbers of grids using different subdivisions.
| 4/9x4/9 subdomain A | 5/9x5/9 subdomain B | 7/9x7/9 subdomain C | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 18x18 | 27x27 | 36x36 | 18x18 | 27x27 | 36x36 | 18x18 | 27x27 | 36x36 | |||||
| N | 30.1211 | 30.1197 | 30.1192 | N | 43.6988 | 43.6973 | 43.6967 | N | 74.2201 | 74.2189 | 74.2185 | ||
| ε (%) | 7.5754 | 7.5705 | 7.5688 | ε (%) | 1.6251 | 1.6216 | 1.6204 | ε (%) | 0.2975 | 0.2959 | 0.2953 | ||
| 9x18 | 18x27 | 27x36 | 9x18 | 18x27 | 27x36 | 9x18 | 18x27 | 27x36 | |||||
| N' | 30.1165 | 30.1189 | 30.1189 | N' | 43.6937 | 43.6963 | 43.6964 | N' | 74.2160 | 74.2182 | 74.2183 | ||
| ε' (%) | 7.5592 | 7.5675 | 7.5677 | ε' (%) | 1.6132 | 1.6194 | 1.6196 | ε' (%) | 0.2919 | 0.2949 | 0.2950 | ||